Engstruct d-20-01718 reviewer

Engineering Structures
Effectiveness of nonlinear fluid viscous dampers in controlling the seismic response of
the base-isolated buildings
--Manuscript Draft--
Manuscript Number: ENGSTRUCT-D-20-01718
Article Type: Research Paper
Keywords: Base isolation; Damping Exponent; Fluid Viscous Damper; Isolation Period; Lead
Rubber Bearing; Nonlinear response; Steel Frame.
Manuscript Region of Origin: Middle East
Abstract: Recently, many buildings have originally designed as base-isolated to mitigate the
structural vibration. However, the buildings with the base isolation systems can be
induced excessive displacement/amplification demand due to the inherent nonlinear
behaviour of the base isolators especially for earthquake-prone regions. Hence, it is
required to control the seismic response of the base-isolated buildings using
supplemental damping device. This paper investigated the effectiveness of nonlinear
fluid viscous damper (NFVD) considering design parameters for the base-isolated
buildings with lead rubber bearing (LRB). For this, 10-storey benchmark steel moment
resisting frame isolated with LRB having a series of isolation periods (T) of 3, 3.5, 4,
and 5 s was used. Then, NFVD is alternatively placed to the mid, corners, and all bays
of the frame at the ground level with the damping exponents (α) of 0.15, 0.30, 0.50,
and 0.70. The base-isolated case study frames are modelled with a finite element
program in which LRB is assumed as bi-linear hysteretic behaviour while NFVD is
simulated by considering Maxwell model having an elastic spring and a viscous
dashpot in series, and evaluated by the nonlinear time history analyses using five
ground motion records. The analyses results were comparatively evaluated
considering certain engineering demand parameters such as storey, bearing, and
relative displacements, roof and inter-storey drift ratios, absolute acceleration, base
shear, base moment, input energy, and hysteretic curves. One of the main outcomes of
this study is that the base-isolated building with the passive damping device as control
attenuation satisfactorily responded when associated with appropriated design
parameters.
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Highlights
 Influence of nonlinear fluid viscous dampers for upgrading the
structural performance of the base-isolated buildings is investigated.
 Buildings isolated with lead rubber bearings having different isolation
periods are studied.
 Various characteristics and configurations of the dampers are
considered.
 A total of 52 base isolated building models with and without dampers
were evaluated under various ground motions.
 Statistical evaluations validate the response of dampers upgrading the
structural performance of the base-isolated building.
Highlights

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Effectiveness of nonlinear fluid viscous dampers in controlling the seismic response of the
base-isolated buildings
Ahmet Hilmi Deringöl a,
* and Esra Mete Güneyisia
a
Department of Civil Engineering, Gaziantep University, 27310, Gaziantep, Turkey
*
Corresponding author: Tel: +90-342-3172400, Fax: +90-342-3601107, E-mail: ad20401@mail2.gantep.edu.tr
Abstract
Recently, many buildings have originally designed as base-isolated to mitigate the structural
vibration. However, the buildings with the base isolation systems can be induced excessive
displacement/amplification demand due to the inherent nonlinear behaviour of the base isolators
especially for earthquake-prone regions. Hence, it is required to control the seismic response of
the base-isolated buildings using supplemental damping device. This paper investigated the
effectiveness of nonlinear fluid viscous damper (NFVD) considering design parameters for the
base-isolated buildings with lead rubber bearing (LRB). For this, 10-storey benchmark steel
moment resisting frame isolated with LRB having a series of isolation periods (T) of 3, 3.5, 4,
and 5 s was used. Then, NFVD is alternatively placed to the mid, corners, and all bays of the
frame at the ground level with the damping exponents (α) of 0.15, 0.30, 0.50, and 0.70. The
base-isolated case study frames are modelled with a finite element program in which LRB is
assumed as bi-linear hysteretic behaviour while NFVD is simulated by considering Maxwell
model having an elastic spring and a viscous dashpot in series, and evaluated by the nonlinear
time history analyses using five ground motion records. The analyses results were comparatively
evaluated considering certain engineering demand parameters such as storey, bearing, and
relative displacements, roof and inter-storey drift ratios, absolute acceleration, base shear, base
moment, input energy, and hysteretic curves. One of the main outcomes of this study is that the
base-isolated building with the passive damping device as control attenuation satisfactorily
responded when associated with appropriated design parameters.
Keywords: Base isolation; Damping Exponent; Fluid Viscous Damper; Isolation Period; Lead
Rubber Bearing; Nonlinear response; Steel Frame.
1. Introduction
Seismic isolation has gained great importance after the catastrophic earthquakes such as
Northridge (1994, USA), Hyogoken-Nanbu (1995, Japan), and Chi-Chi (1999, Taiwan) caused
high levels of mortality and damaging of buildings and transportation structures [1]. It was
accepted as an innovative earthquake protection technique in which the structural safety of the
buildings was provided by means of the utilization of the seismic control systems (SCS) [2].
Although attempting a few implementations of SCS in the developed countries before the 2000s
thereafter it has attracted much more attention from the construction industry especially for the
public and private buildings even in developing countries. As a result of the advancement on the
seismic isolation, the provisions of building codes were required to update in Italy (2008), USA
(2009), Japan (2010), China (2010), Taiwan (2011), Turkey (2018) [3]. Thus, many SCS have
Manuscript File Click here to view linked References

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recently been proposed to improve the seismic performance of the aged buildings or design
newly upgraded structures against seismic excitations. SCS can be categorized as passive, semi-
active, active, and hybrid systems [4]. As passive SCS, the base isolation systems and dampers
can be admitted as the most powerful tools because of having simple preliminary design, robust
technique and inexpensive implementation procedure [5]. The mechanical characteristics and
design methods of the base isolation systems were investigated by Kelly [6] in which three
bearings were introduced as lead rubber bearing, friction pendulum bearing, and high damping
rubber bearing. The former has been much more adopted by engineering communities and
researchers since lead rubber bearing (LRB) has fully sealed and embedded steel plates
preserved in the elastomeric material (i.e., rubber) against corrosion, anchor plated enabling easy
maintenance, the lead core resists to shear forces, plastically deforms thereby it contributes to
additional energy dissipation [7-8]. As shown in Figure 1(a), LRB is made of elastomeric
materials such as rubber and lead core. The former is vulcanized with alternating steel plates and
anchored to the top and bottom of the loading caps and resists to the immense vertical loading
while the latter is centered in the middle of the rubber to bear with the lateral forces [9]. Many
researchers have investigated some characteristics of LRB to improve the seismic response of the
base-isolated structures. For example, Kim et al. [10] experimentally tested various specimens
characterized with different strain levels to evaluate the mechanical behaviour of LRB under
unidirectional and bidirectional loadings. The smooth hysteretic curves were obtained under the
unidirectional load, however it was deteriorated when increased the strain level. Haiyang et al.
[11] set up a shake table test to evaluate the effect of the multi-layer soil foundation and isolation
layer on the seismic response of the base-isolated buildings with LRB under earthquake waves.
The earthquake characteristics significantly affected the seismic performance of LRB especially
in soft soil due to the effect of earth-filtering. Ye et al. [12] proposed a direct displacement
design method to be able to reach the predefined displacement limits of the multi-storey base-
isolated buildings with LRB. The preset limit states of the performance objectives were obtained
with errors less than 10 %. Shoaei et al. [13] studied on the seismic reliability of the steel
structures with LRB considering two main design parameters (i.e., the period and isolator
displacement) in order to predict the most optimum limits of the initial stiffness and the yielding
force of the bearing. A series of seismic performance tracking methods was proposed in the
study of Ouyang et al. [14] to overcome the structural control problems of the benchmark
building with LRB under original earthquake records. Bhandari et al. [15] examined the effect of
isolator stiffness (i.e., hard, medium, stiff) of two reinforced concrete buildings with LRB
regarding the seismic performance capacity method. It was shown that the plastic hinge
formations decreased when the isolator stiffness changed from stiff to flexible. Yaghmaei-
Sabegh et al. [16] examined the structural behaviour of the base-isolated buildings with LRB. It
was observed that the inelastic displacement demand enhanced when the isolation period
increased. Compared to the near fault earthquakes, the significant reduction on the drift was
occurred under far fault earthquakes. The seismic response of the benchmark building was
effected with the earthquake pulses (i.e., symmetric, asymmetric), however it was decreased by
means of the base-isolated building with LRB. The pounding effect of adjacent steel buildings of
3, 5, and 7-storey with and without LRB was evaluated by damage level index in the study of
Yaghmaei-Sabegh and Panjehbashi-Aghdam [17]. The average damage indexes of 3, 5, and 7-
storey fixed base buildings were as 50, 60, 67.5 % while it was as 11.5, 15, 35.5 % for isolated

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building, respectively. Ishii and Kikuchi [18] presented an improved analytical model in which
the compressive modulus distribution was adopted to describe exact buckling behaviour of LRB
as well as shear force-drift hysteresis response. The modulus distribution model accurately
predicted the inelastic behaviour of LRB especially in extreme loadings. Shin and Kim [19]
investigated the influence of the restoring force on the seismic response of the base-isolated
buildings with LRB, which were alternatively designed for high and low seismic zones and
subjected to different seismic loadings. When located at the low seismic zone and subjected to
the wind excitation the base-isolated buildings presented relatively less absolute acceleration
reduction due to the minimum restoring force demand. Kazeminezhad et al. [20] studied on the
isolator design method of LRB based on the performance point and capacity spectrum of the
isolation system was considered respond to not only predefined design forces but also all
earthquake loads. Time history analysis results showed that compared to the fixed base, the
proposed method decreased the building responses (i.e., relative displacement, base shear,
interstorey drift) ranged between 48 and 82 %. Lu et al. [21] developed simplified methods
aimed to evaluate the seismic capacity of LRB using free vibration responses acquired from snap
back test to provide quicker convergence and accurate initial displacement estimation. Deringöl
and Güneyisi [22] compared the seismic response of LRB, friction pendulum bearing, and high
damping rubber bearing were installed to ordinary steel frame. LRB was advised against the
structural vibration since the base shear was reduced as 84 %. The studies [10-22] on the LRB
testified significant advantage of mitigating the seismic response of the examined buildings.
However, the single use of the base isolation systems may induce the excessive displacement,
which increase the pounding incidence depend on the clearances of the base-isolated building
with neighboring structures [23]. Thus, the amplification of the base-isolated buildings with LRB
should be controlled with the supplemental damping device.
The dampers have been utilized as control device in many types of structures against seismic
excitations. The engineers and researchers were theoretically and experimentally pronounced
numerous dampers such as metallic, friction, fluid, viscous, fluid viscous, and tuned mass
damper (see, e.g., [24-27]). Compared to the other dampers, the representative features of the
nonlinear fluid viscous damper (NFVD) mainly includes the remarkable energy dissipation
capacity, enhancing the structural damping ratio up to 25 % without adding extra stiffness,
requiring lower damper force for equal displacements, being active not only in short time sources
of excitations (i.e., shock loads) but also in long time forces induced by the earthquake and wind
[28-30]. Thus, NFVD has come into prominence for a few decades in newly design or retrofit of
civil engineering structures as well as in automotive industry, aerospace application, and military
hardware [31, 32]. The operation principle of the fluid viscous damper based on the flowing of
the fluid through orifices as well as around the piston head subjected to external loadings to be
compressed or stretched [33]. The required damping force was generated by means of the
friction force occurred during the travelling action of the fluid as shown in Figure 2(a) [34].
There are many research efforts on the device development, empirical validities, design
improvements, and configuration of the placement of the fluid viscous damper. For example,
Guo et al. [35] presented various NFVD configurations for seismically defective Hotel building.
The interstorey drifts and shear forces were remarkably reduced especially for upper storeys with
saving the architectural appearance. Parcianello et al. [36] proposed an optimization method in

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which, genetic algorithm was used to place NFVD regarding the predefined targets and
restrictions with the aim of upgrading the seismic response of the buildings. Moradpour and
Dehestani [37] also studied on the optimum distribution of NFVD over the height of the four
different steel buildings to achieve the estimated seismic performance. When regarded the
offered method on the design of NFVD caused remarkable mitigation in the damper force and
damping coefficient. Ras and Boumechra [38] analyzed the seismic behaviour of steel buildings
with and without fluid viscous dampers (FVD) regarding the distribution of those among the
different bays. When decreased the numbers and damping coefficients of FVD, the more
efficient buildings (i.e., minimized the base shear and acceleration) were obtained. Narkhede and
Sinha [39] studied the effect of damper nonlinearity and damping ratio under sinusoidal-shock
excitations. Some design charts were provided to characterize the behaviour of NFVD after half-
sine shock loading. Uriz and Whittaker [40] retrofitted low-rise steel frame with FVD, and
analyzed using nonlinear time-history analyses. It was shown that the plastic hinges occurred in
the beam remarkably reduced, however considerable increases in the shear and axial forces of
the column were observed due to immense lateral loads of the damper. Similarly, the study of
Karavasilis [41] showed that 10 and 20-storey steel frames with viscous dampers enhanced the
likelihood of the column plastic hinges in comparison to 5-storey steel frame. Gidaris and
Taflanidis [42] provided seismic improvement of 3-storey building with NFVD considering life
cycle optimal cost design approach. The proposed method ensured the optimal NFVD design
scenarios (i.e., configuration, sizing) as well as suppressed the structural vibration. Jiao et al.
[43] investigated the nonlinear dynamic behaviours of NFVD concerned with the dimension of
the orifice, fluidity of the material, and characteristic of the excitations. When subjected to low
frequency excitation, the difference between linear and nonlinear pressure gradient was getting
smaller. Del Gobbo et al. [44] constructed a new relationship between damping ratio and the
retrofitting cost of the buildings with FVD rather than the structural drift designs. The optimum
damping ratio was asserted between 25 and 45 % corresponded the minimum earthquake repair
cost. Ras and Boumechra [45] compared the influence of linear and nonlinear FVD considering
the variations of the damper exponent and damping coefficient on the seismic performance of the
buildings under earthquake loads. On one hand the inefficient seismic response was observed in
case of the damper exponent of the nonlinear FVD greater than 1, on the other hand the lower
damping exponent described better seismic performance especially for linear FVD. Banazadeh
and Ghanbari [46] also compared the seismic response of the steel buildings with the linear and
nonlinear FVD under far-field earthquakes. It was obtained that the linear FVD represented
better collapse performance. The probabilistic drifts of three steel buildings upgraded with
NFVD having various damping coefficients and nonlinearities were evaluated by fragility curves
in the study of Yahyazadeh and Yakhchalian [47]. The lower damping exponent value provided
the lowest mean annual frequency of exceeding each predefined drift values for each building. In
the study of De Domenico and Ricciardi [48], a series of design methods have been alternatively
presented to evaluate the currency of the optimum design philosophies of NFVD complied with
the minimizing performance indices when subjected to the stochastic excitation. In the optimum
design of NFVD, the non-Gaussian stochastic method was obtained as better energy based
technique due to allowing to identification of the damper characteristics. Lin and Chopra [49]
studied the effect of using NFVD for controlling the structural deformation under earthquakes.
They compared the dynamic characteristics of the damper considering the variation in

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supplemental damping ratio and nonlinearity of the damper force. It was reported that the former
was more decisive on the earthquake response of the single degree of freedom systems. Chen et
al. [50] stated that since the high-rise buildings subjected to the excessive immense wind forces,
the probabilistic analysis of the case study 20-storey steel buildings with FVD was asserted a
solution to suppress the structural vibrations. It was revealed that the randomness of the design
parameters of the damper and wind excitations could be taken into account. Scozzese et al. [51]
proposed a comprehensive framework to investigate the seismic reliability of low rise steel
building with linear and nonlinear FVD to remove the uncertain properties of the damper. The
damper force was determined as the most decisive parameter due to the deviation of the damping
exponent value. The studies [35-51] provided that NFVD remarkably restrained the displacement
and drifts of the buildings. However, the seismic response of NFVD substantially changed with
the characteristic of the earthquakes, placement of the damper, nonlinearity of the device (i.e.,
damping exponent, damper coefficient), thus those parameters should be carefully examined to
design seismically efficient structures.
This study aimed to find out the effectiveness of NFVD for the seismic improvement of the base-
isolated buildings with LRB. For this, a series of isolation models were developed to design
more efficient seismic control systems, to govern the excessive structural response of the base-
isolated buildings with LRB when used NFVD as supplemental seismic control damper, to
understand how the damping nonlinearity and alternative placement of NFVD influenced the
structural vibration of the base-isolated buildings. Hence, 10-storey benchmark steel moment
resisting frame isolated with LRB having various isolation periods (T) of 3, 3.5, 4, and 5 s was
used. Then, NFVD was alternatively placed to the mid, corners, and all bays of the frame at the
ground level with the damping exponents (α) of 0.15, 0.30, 0.50, and 0.70. Totally, 52 different
frame models were generated. Thereafter, the nonlinear responses of the base-isolated frame with
and without NFVD are comparatively evaluated through time-history dynamic analyses using
five ground motion records. The obtained analysis results are elaborately discussed.
2. Details of the case study frames, modelling and analysis
Moment resisting frames (MRF) are one of the most favourable lateral load resisting systems due
to the having flexible structural response and providing the versatile architectural design projects
even in active seismic zone [52]. In this study, 10-storey steel moment resisting frame was
devised as a case study frame which was previously designed by Karavasilis et al. [53] according
to Eurocode 8 [54]. It was designed to withstand the maximum earthquake acceleration of 0.35
g. The soil type, building importance factor, and behaviour factor were assumed as B, II, and 6.5,
respectively. The storey height is equal to 3.2 m except the ground level is 4 m. The bay width of
the storey is 8 m. As shown in Table 1, the beams and columns are made of steel W section
whose the minimum yield strength are designed as 275 and 335 MPa, respectively. The
elevation view of the 10-storey base-isolated frame with LRB is shown in Figure 3(a). Moreover,
the fundamental period of the building is 2.42 s. According to ASCE [55] and FEMA 356 [56],
the plastic hinges are assumed to locate at the end of the beam and column, furthermore, the
panel zones and rigid diaphragms employed in the design of steel MRF. The other information
about the case study frame could be found in the study of Karavasilis et al. [53]. Since the

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benchmark office building has symmetrical plan, only two-dimensional structural model of the
horizontal axis is created in SAP 2000 [57] in which the nonlinear response of the fixed base
framed building characterized with the lumped plasticity method. In the current study, 10-storey
steel MRF was firstly equipped with the base isolators of LRB considering different the isolation
periods, and then the seismic responses of the base-isolated structures with and without NFVDs
were examined comparatively.
As previously mentioned, the lateral flexible behaviour of LRB is rooted in the mechanical
features of the alternate rubber layers. They are able to withstand the lateral force as well as
prolonged the first period of the fixed base building whose gravitational loads carried by the lead
core positioned center of the LRB as shown in Figure 1(a) [9]. The typical hysteretic behaviour
of LRB presented in Figure 1(b) [9]. The shear force-displacement behaviour of LRB modelled
with the nonlinear link element of "Rubber Isolator" to represent the elastic-plastic deformations
which was recommended by Park et al. [58] and Wen [59]. Thus, NLlink elements were
employed to model the isolators using finite element program of SAP2000 [57]. The approach of
Naeim and Kelly [6] based on the iterative computational method was adopted in the design of
the base isolators. First, the bearing displacement was assumed. The yield displacement was
omitted, and then the iteration was to be proceeded until obtain the presumed value. The post
yield stiffness ratio defined as the ratio of the post-yield stiffness (k2) to the initial stiffness (k1),
and considered as 21. Hence, a set of different base-isolated buildings has been developed to
evaluate the isolator characteristics of LRB having isolation period (T = 3, 3.5, 4, and 5 s). The
bilinear hysteresis curve of LRB (see Figure 3(b)) was constructed in the light of the following
equations [6];
The effective stiffness, keff;
keff =
W
g
x(
𝟐𝐱π
T
)2
(1)
hysteresis loop (the energy dissipated per cycle), WD;
WD = 2xπxkeffxβeff
xD2
(2)
characteristics strength, Q;
Q =
WD
4(D−Dy)
(3)
post-yield stiffness of the isolator, k2;
k2 = keff −
Q
D
(4)
yield displacement, Dy is given by;
Dy =
Q
(k1−k2)
(5)
effective period, Teff

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Teff = 2π√
W
keff.g
(6)
damping reduction factor, B;
1
B
= 0.25(1 − lnβeff) (7)
displacement of isolation, D
D =
g.Sa.Teff
2
B.4π2 (8)
and yield strength, Fy
Fy = Q + kd. Dy (9)
where T is target period, Sa is spectral acceleration, B is damping reduction factor, gravitational
acceleration is g, Q is characteristic strength, W is total weight on the isolator, g is gravitational
force, Dy is yield displacement, and βeff is effective damping ratio.
One of the most important advantageous of NFVD is the ability of restraining the forces
provided in the damper whereby the considerable amount of the seismic energy was dissipated
[60]. The mechanism of NFVD is as the following. Once the external forces were subjected to
the damper, the piston starts to pass through the orifice thereby the fluidity viscous material (e.g.,
silicone gel) is stimulated to flow from one chamber to another relative to the cylinder (see
Figure 2(a)). As the viscous materials almost are not able to be compressed, the volume of the
fluid decreased resulted in the generation of the restoring force [61]. The damper force, fd, is
computed using the equation of 10 where the damping coefficient and the relative velocity are c
and v, respectively. The damping exponent of α describes the nonlinearities of the damper
response may vary between typically 0.15 and 1.0. The idealized damper force of NFVD, fd, is
computed as [62];
fd = cd𝑣α
sign(v) (10)
where fd stands for the damper force of NFVD, cd is the damping coefficient, 𝑣 is the damper
velocity, α is the damping exponent (i.e., velocity exponent), and sign is the signum function.
The variations of the damper force with the displacement and the velocity were presented in
Figure 2(c) and 2(d), respectively. The effectiveness of NFVD was enhanced for the lower
velocities that also generated higher damping force when α is lower than 1.0 [39]. The analytical
modelling of NFVD is based on the generalized Maxwell model consisted of an elastic spring
and a viscous dashpot in series as shown in Figure 2(b) [63]. The visco-elastic hysteresis
behaviour of NFVD modelled with the nonlinear link element newly developed in SAP2000 [57]
as "Exponential Maxwell Damper Element". The variation of the damping coefficient (cd) and the
maximum damper force (fd) were determined as 210 kNs/m and 2000 kN, respectively. Hence,
the variation of those parameters was not taken into accounted. They were assumed to be fixed
as stated in the study of Yang et al. [64]. In the current investigation, the damping exponents (α)

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were only varied as 0.15, 0.30, 0.50, and 0.70. Two-dimensional models of the benchmark
building with LRB, LRB with NFVD in mid bay, LRB with NFVD in corner bays, and LRB
with NFVD in all bays were developed as shown in Figure 3. The detailed layout of the
implementation of NFVD to the base-isolated buildings with LRB was schematically illustrated
in Figure 4 where can be seen that the load conveyed to the upper part of the base column carried
by LRB anchored to the lower part of the base column while NFVD controlled the response of
the base-isolated buildings with LRB. The generated base isolation models of the isolation
systems were labeled depend on the isolation period of LRB, the placement and damping
exponent of NFVD. For example, "T = 3 s" means that 10-storey building was equipped with
LRB having the isolation period of 3 s and "0.7 VD-corner bays" stands for the placement of
NFVD only corner bays with the damping exponent of 0.7.
As finite element program, SAP 2000 [57] was used to evaluate the seismic performance of the
developed models through performing the nonlinear time-history analyses including the direct
integration method. Five ground motion records (e.g., Gazlı 1976, Tabas 1978, Cape Mendocino
1992, Chi-Chi 1999, and San Salvador 1986) were taken from Pacific Earthquake Engineering
Research Centre (PEER) [65], and scaled in convenience with ASCE 7-10 [66] standard. It was
progressed considering the scaled records would not only less than the design spectrum but also
being in the ranges between 0.2T and 1.5T. Since the ground motion records considerably
characterized with the peak ground accelerations (PGA) was used as Intensity Measure (IM).
The information about the characteristic of the earthquakes was given in Table 4. The responses
of the scaled earthquake records were also presented in Figure 5.
3. Results and discussion
The nonlinear seismic responses of the base-isolated buildings with and without passive control
dampers have been obtained by means of the time-history analyses. The results are presented in
terms of the engineering demand parameters (EDP) included: storey displacement, bearing
displacement, relative displacement, roof drift, interstorey drift ratio, absolute acceleration, base
shear, base moment, input energy, and hysteretic curves. The standard deviation (σ) is also
computed for the variation of storey and relative displacements, interstorey drift ratio, absolute
acceleration, and base shear for a better estimation of the nonlinear responses of the proposed
models. Those were elaborately discussed.
3.1 Displacements
The case study building was upgraded with the base isolator of LRB regarding the variation of
the isolation periods T (i.e., 3, 3.5, 4, 5 s), and those seismic responses were aimed to control by
the supplementary passive dampers of NFVD alternatively placed to different locations at
ground level (i.e., mid bay, corner bays, all bays) and characterized with various damping
exponents α (i.e., 0.15, 0.30, 0.50, 0.70). When performed the nonlinear time history analyses
within five different earthquakes, the maximum storey displacements and the variation of storey
displacement over the height of the building were computed and presented in Figures 6 and 7,
respectively. Since the enhancement of T gradually decreased the isolator stiffness in the light of
Eqn. 1, which caused to increase the storey displacement demand. For example, when increased

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T from 3 s to 3.5, 4, and 5 s that was characterized the isolator effective stiffness, and decreased
from 2317.2 kN/m to 1702.4, 1303.4, 834.2 kN/m (see Table 2) resulted in considerable
amplification of the average values of the maximum storey displacements from 56.92 cm to
64.67, 70.94, and 71.84 cm (see Figure 6), respectively. The effect of T on the storey
displacement distributions was also observed in Figure 7. When evaluated the standard deviation
(σ) of the isolation systems testified the most uniform storey displacement as well as the greatest
roof displacement reduction with respect to LRB without NFVD. For example, σ was as 10.4
(see Table 5) by "0.15 VD-all bays" for T of 3 s, reduced the roof storey displacement from
104.96 to 80.24 cm (see Figure 7(a)) corresponded to the greatest reduction of 23.6 % compared
to the response of LRB. "0.15 VD-all bays". It was as 10.79 for T of 3.5 s, provided the greatest
reduction as 24.5 %. In addition, σ of "0.70 VD-all bays" were 9.1 and 8.5 led to the greatest
roof displacement reductions as 25.9 and 17.0 % for T of 4 and 5 s, respectively. The inclusion
of NFVD in the isolation systems as supplementary damping device mitigated the maximum
storey displacement response of the case study buildings under all earthquakes except Cape
earthquake. For example, the greatest reductions of the maximum storey displacements were
experienced in the isolation systems of "0.30 VD-all bays", "0.15 VD-all bays", and again "0.15
VD-all bays" as 26.2, 15.5, and 23.6 % under Gazlı, Tabas, and Chi-Chi earthquakes for the
isolation period of 3 s (see Figure 6(a)) while it was as 32.1, 27.1, and 24.5 % (see Figure 6(b))
for the isolation period of 3.5 s, respectively. In addition, the implementation of "0.15 VD-all
bays" caused the greatest storey displacement reductions as 34.6 and 26.8 % under Tabas and
Chi-Chi earthquake for the isolation period of 4 s (see Figure 6(c)) while it was as 30.1 and 31.1
% under Gazlı and Tabas earthquakes, as 11.39 and 16.20 % under Cape and Chi-Chi earthquake
for the isolation period of 5 s (see Figure 6(d)), respectively. When subjected to Salvador
earthquake "0.50 VD-mid bay" succeeded the lowest value of the maximum isolator
displacements as 15.49, 14.48, and 13.93 cm for T of 3, 3.5, and 4 s as shown in Figure 6(a), (b),
and (c), respectively. The lowest value of the average maximum storey displacements were
experienced as 48.60, 51.89, and 54.19 cm in the isolation systems of "0.30 VD-all bays" for the
isolation period of 3, 3.5, and 4 s. It was proved by "0.70 VD-all bays" as 57.46 cm when LRB
designed with T of 5 s. As a summary, the utilization of the lowest and moderate α (i.e., 0.15 and
0.30) substantially reduced the storey displacements when T varied between 3 and 4 s (see
Figures 6(a-c) and 7(a-l)). In addition, it was valid for the modest and greatest α values (i.e., 0.3
and 0.7) for T of 5 s (see Figures 6(d) and 7(m-p)). Compared to the other placement locations,
the implementation of NFVD to all bays remarkably not only mitigated the storey displacements
but also provided more uniform storey displacement distributions irrespective of T, α, and
characteristic of the earthquakes.
The maximum bearing displacements of the case study base-isolated building with and without
NFVD were presented in Figure 8. The use of only LRB with T of 3, 3.5, 4, and 5 s produced the
greatest average values of the maximum bearing displacements as 32.96, 43.41, 51.81, and 58.55
cm, respectively. However, the implementation of NFVD in the base-isolated buildings with
LRB substantially mitigated the bearing displacement based on the earthquake characteristics,
placement and α of NFVD. It was worth noting that any type of placement and α of NFVD
decreased the bearing displacement. But, as the most favourable isolation system of "0.15 VD-all
bays" proved the lowest values of the maximum bearing displacements as 13.56, 40.24, 21.66,

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and 49.04 cm for T of 3 s under Gazlı, Tabas, Cape, and Chi-Chi earthquakes (see Figure 8(a))
while they were as 16.82, 49.44, 25.20, and 60.71 cm for T of 3.5 s (see Figure 8(b)),
respectively. When subjected to Gazlı, Tabas, and Chi-Chi earthquakes the bearing
displacements occurred as 19.49, 58.50, and 70.91 cm for T of 4 s (see Figure 8(c)), respectively.
On one hand LRB with T of 5 s controlled by "0.30 VD-all bays" the lowest bearing
displacements of 24.61 and 72.73 cm were obtained under Gazlı and Tabas earthquakes, on the
other hand those were as 30.75, 82.78, and 10.08 cm in the isolation systems of "0.70 VD-all
bays" under Cape, Chi-Chi, and Salvador earthquakes as shown in Figure 8(d), respectively.
Similarly, the lowest average values of the maximum bearing displacements were experienced in
the lower α (i.e., "0.15 VD-all bays") as 26.81, 32.52, and 37.70 cm for the base-isolated case
study building with LRB having T of 3, 3.5, and 4 s (see Figure 8(a), (b) and (c)), respectively. It
was as 44.92 cm for the upper-intermediate α (i.e., "0.70 VD-all bays") with T of 5 s. The
advantage of the lower α and all bays placement on the reduction of the bearing displacement
induced by LRB was proved.
The relative displacement considered as significant quantity of EDP is defined as the lateral
displacement difference of jth storey of the building and base, where j = 1, 2, 3, …N [67]. The
maximum relative displacements of the case study buildings were presented in Figure 9. The
equipment of the greater T on the base-isolated building with LRB reduced the maximum
relative displacement under each of the considered earthquakes. For example, the average values
of the maximum relative displacements were computed as 23.96, 21.25, 19.13, and 13.29 cm for
T of 3, 3.5, 4, and 5 s, respectively. The proposed supplementary damping device successfully
restrained the relative displacement of the case study building depended on the characteristic of
NFVD even if mid bay placement. When subjected to Salvador earthquake the relative
displacements induced by LRB with T of 3.5, 4, and 5 s as 5.48, 4.35, and 2.85 cm reduced up to
5.01, 4.04, and 2.73 as shown in Figure 9(b), Figure 9(c), Figure 9(d), thanks to "0.15 VD-mid
bay" under Salvador earthquake, respectively. Similarly, "0.15 VD-corner bays" satisfied the
lowest values of the maximum relative displacements as 9.5 and 6.3 cm for 3.5 and 4 s under
Gazlı earthquake as shown in Figure 9(b) and 9(c), respectively. However, the all bay placement
was much more effective in the reduction of the maximum relative displacement. For example,
"0.50 VD-all bays", "0.30 VD-all bays", and "0.15 VD-all bays" proved the lowest values of the
maximum relative displacements as 12.84, 29.74, and 31.20 cm under Gazlı, Tabas, Chi-Chi
earthquakes for T of 3 s, respectively. "0.70 VD-all bays" reduced it up to 27.45 and 6.12 cm
under Chi-Chi and Cape earthquakes for T of 4 and 5 s, respectively. The lowest average value
of the maximum relative displacements of 21.07, 18.52, 15.65, and 12.54 cm were obtained by
"0.50 VD-all bays", "0.70 VD-mid bay", "0.70 VD-all bays", and again "0.70 VD-all bays" for T
of 3, 3.5, 4, and 5 s as shown in Figure 9(a), Figure 9(b), Figure 9(c), and Figure 9(d),
respectively. The effect of the design and placement of NFVD on the relative displacement
variation of the case study building under Chi-Chi earthquake was illustrated in Figure 10. The
increase of T actually regulated the distribution of the relative displacement. The use of only
LRB designed with T of 4 s instead of 3 s reduced the maximum relative displacement of roof
storey (from 42.17 to 24.99 cm) corresponded to the greatest reduction as 40.7 %. All bays
placement of NFVD always reduced the storey relative displacement and obtained more uniform
distribution trend irrespective of T, which also valid for α of 0.15 in lower T (i.e., 3, 3.5 s) as

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shown in Figure 10(a-h) and α of 0.70 in greater T (i.e., 4, 5 s) as shown in Figure 10(ı-p). When
T was fixed as 3 and 3.5 s to find out the effectiveness of NFVD, it was shown that either use of
all bay placement or lowest α not only reduced the relative displacement but also presented much
more uniform distribution trend. It was valid for T of 4 and 5 s providing that NFVD was located
to all bay and lowest α. For example, "0.15 VD-all bays" having σ of 9.6 and 10.0 (see Table 5)
mitigated the roof storey displacement from 42.17 to 31.20 cm (see Figure 10(a)) and 40.29 to
32.17 cm (see Figure 10(e)) for T of 3 and 3.5 s, respectively, furthermore, "0.70 VD-all bays"
having the lowest σ as 8.4 (see Table 5) reduced the roof storey displacement from 38.06 to
27.45 cm (see Figure 10(l)) for T of 4 s behaved the most uniform relative displacement
compared to the response of LRB.
3.2 Roof drift
The roof drift is defined as the ratio of the maximum roof horizontal displacement to the overall
building height [68]. The case study building isolated with LRB and damped with NFVD whose
the roof displacements were obtained through the nonlinear time history analyses, and
normalized by the total building height of 32.8 m whereby the roof drifts were presented in
Figure 11. As previously stated, the increase of T led to the enhancement of the lateral
displacement demand of the buildings with LRB. Hence, the case study building with LRB
produced the highest values of the average roof drifts as 1.74, 1.97, 2.16, and 2.19 for T of 3, 3.5,
4, and 5 s, respectively. When controlled LRB by NFVD with the damping exponent of 0.15 and
placed all bays of the case study building, namely, "0.15 VD-all bays" proved the lowest values
of the maximum roof drift as 2.15 and 2.45 for T of 3 s (see Figure 11(a)), 2.32 and 2.83 for T of
3.5 s (see Figure 11(b)), 2.47 and 3.06 for T of 4 s (see Figure 11(c)) under Tabas and Chi-Chi
earthquakes, respectively. It was as 0.84, 0.86, 0.87, and 0.91 in case of "0.30 VD-all bays"
under Gazlı earthquake for T of 3, 3.5, 4, and 5 s, respectively. "0.70 VD-all bays" produced the
lowest values of the maximum roof drift as 1.12 and 3.29 under Cape and Chi-Chi earthquake
for T of 5 s (see Figure 11(d)), respectively. In addition, the lowest average values of the
maximum roof drifts were observed as 1.48, 1.58, and 1.65 in case of "0.30 VD-all bays" for 3,
3.5, and 4 s, respectively, while "0.70 VD-all bays" proved it as 1.75 when T was as 5 s. The
placement of NFVD in mid bay was also succeeded the lowest value of the maximum roof drift
ratio as 0.47 with "0.50 VD-mid bay", 0.43 with "0.70 VD-mid bay", and 0.42 with "0.70 VD-
mid bay" under Salvador earthquake 3, 35, and 4 s, respectively. When considered the overall
result of the roof drift responses it was shown that the lower damping exponents (i.e., 0.15 and
0.30) and all placement of NFVD were much more effective in the reduction of the roof drifts for
T of 3 and 3.5 s. But, α of 0.70 was favourable when T was yielded to 4 and 5 s.
3.3 Interstorey drift ratio
As a significant EDP, the interstorey drift ratio is used to evaluate the structural response of the
buildings. It was computed by subtracting the consecutive storeys displacement and divided by
the corresponded storey height [69]. Figure 12 described the maximum interstorey drift ratios of
the case study building equipped with LRB and NFVD in percentage. Herein the effectiveness of
NFVD considering the reduction percentages of interstorey drift ratios comparatively discussed.

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When the case study building isolated with LRB considering T as 3, 3.5, 4, and 5 s and subjected
to all earthquakes, the average interstorey drift ratios were gradually reduced as 1.02, 0.97, 0.89,
and 0.66 %, respectively. When controlled the base-isolated case study building by NFVD of
"0.50 VD-all bays", "0.30 VD-all bays", and "0.15 VD-all bays", provided the greatest
reductions as 13.1, 12.8, and 31.5 % under Gazlı, Tabas, and Chi-Chi earthquakes for T of 3 s as
shown in Figure 12(a), respectively. "0.30 VD-all bays", "0.15 VD-all bays", again "0.15 VD-all
bays", and "0.70 VD-mid bay" proved the greatest reductions as 18.48, 17.82, 25.31, and 2.70 %
under Gazlı, Tabas, Chi-Chi, and Salvador earthquakes (see Figure 12(b)), respectively,
compared to LRB having T of 3.5 s. Similarly, the greatest reductions of 23.7, 24.9, 15.8, and
20.2 % were occurred by means of "0.70 VD-all bays", "0.15 VD-all bays", "0.70 VD-corner
bays", and "0.70 VD-all bays" under Gazlı, Tabas, Cape, and Chi-Chi eartquakes for T of 4 s as
shown in Figure 12(c), respectively. "0.30 VD-all bays", "0.15 VD-corner bays", "0. 50 VD-all
bays", and "0.15 VD-corner bays" provided the greatest interstorey drift reductions as 45.6, 23.6,
21.4, and 1.7 % under Gazlı, Tabas, Cape, and Salvador eartquakes for T of 5 s as shown in
Figure 12(d). The greatest average maximum interstorey drift ratio reductions of 5.3, 14.2, 20.8,
and 15.0 % were experienced in "0.30 VD-all bays", "0.50 VD-corner bays", "0.30 VD-all bays",
and "0.70 VD-all bays", respectively. In addition, the variation of the interstorey drift ratio over
the case study building with LRB and NFVD under Chi-Chi earthquake was illustrated in Figure
13(a-p). The use of NFVD based on the placement of the device and damping exponent were
mitigated the maximum interstorey drift ratios. It was evident that all bays placement of NFVD
substantially decreased the interstorey drifts as well as uniformly behaved the interstorey drifts
distribution over the case study building independent of T. As for damping exponent namely α of
NFVD, compared the the isolation system of LRB (T = 3 s) with "0.15 VD-all bays", "0.30 VD-
all bays", "0.50 VD-all bays", "0.70 VD-all bays" those σ were 0.46, 0.48, 0.49, and 0.51,
respectively, as seen in Table 5. The former presented the lowest interstorey drift ratio and the
most uniform distribution over the storey height as well (see Figure 13(a-h)). In addition, the use
of LRB (T = 3 s) with "0.15 VD-all bays" produced the greatest interstorey drift ratio reduction
at the roof storey as 16.2 % (from 0.68 to 0.57 %), respectively (see Figure 13(a)). But, the
increase of T changed the response of the isolation systems. For example, when T were as 4 and
5 s, "0.70 VD-all bays" had the lowest σ as 0.38 and 0.35 (see Table 5), respectively. The former
isolation period provided the interstorey drift reduction at roof storey as 18.0 % (from 0.61 to
0.50 %) as shown in Figure 13(l).
3.4 Absolute acceleration
The effect of the isolation system characteristics such as isolation period of LRB (T), placements
of the damper (mid, corner, and all bays), and damping exponent of NFVD (α) on the variation
of the maximum absolute accelerations were computed under five earthquakes and presented in
Figure 14. On average, the maximum absolute accelerations of 3.36, 2.93, 2.47, and 1.83 m/s2
induced by LRB with T of 3, 3.5, and 4, and 5 s, respectively. The lowest absolute accelerations
were obtained as 2.80, 3.09, and 3.27 m/s2
under Gazlı, Cape, and Salvador earthquakes (see
Figure 14(a)) when LRB having T as 3 s was controlled by "0.70 VD-mid bay". It was as 2.69
and 2.74 m/s2
for T of 3.5 s under Chi-Chi and Salvador earthquakes (see Figure 14(b)),
respectively. Additionally, the lowest absolute accelerations of 2.11 and 1.81 m/s2
occurred

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under Gazlı and Cape earthquakes for T of 4 and 5 s as shown in Figure 14(c) and 14(d),
respectively. Another SCS of "0.30 VD-mid bay" was capable of reaching the lowest absolute
accelerations as 3.03 and 2.29 m/s2
Tabas and Gazlı earthquakes for T of 3 and 3.5 s (see Figure
14(a), 14(b)), respectively. It was also proved as 3.28 and 2.67 thanks to "0.15 VD-corner bays"
under Chi-Chi and Tabas earthquakes, respectively. "0.15 VD-mid bay" introduced the lowest
absolute accelerations as 2.46 m/s2
under Salvador earthquake, which was corresponded to the
greatest reduction as 22.78 % with respect to the isolation system of LRB with T of 4 s as shown
in Figure 14(c). It was as 2.48 and 2.55 m/s2
under Tabas and Chi-Chi earthquakes by virtue of
"0.30 VD-corner bays", respectively. When T was reached to 5 s, "0.15 VD-mid bay" testified
the lowest absolute accelerations of 1.96 and 2.01 m/s2
under Tabas and Salvador (see Figure
14(d)), respectively. The latter provided the greatest reduction on the maximum absolute
acceleration as 9.1 %. The distribution of the absolute acceleration over the height of the case
study building with LRB and NFVD considering T, alternatively placement of the control
damper, and α was reflected on Figure 15. The maximum absolute acceleration was enhanced
when utilized LRB with the higher T for the isolation of the case study building without any
control device. The roof absolute acceleration was gradually reduced from 3.51 to 2.77, 2.98,
2.35 m/s2
in case of T increased from 3 to 3.5, 4, and 5 s, respectively. The inclusion of NFVD
partially mitigated the absolute acceleration, which based on the placement and α. The
equipment of NFVD mid or corner bays was much more effective in the reduction of the
absolute acceleration was to be ensured by the greater α. For example, "0.15 VD-corner bays",
"0.7 VD-mid bay", "0.3 VD-corner bays", and "0.7 VD-all bays" reduced the roof absolute
acceleration from 3.51 to 3.28 m/s2
, 2.77 to 2.69 m/s2
, 2.99 to 2.55 m/s2
, and 2.35 to 2.25 m/s2
as
shown in Figure 15(a-d), 15(e-h), 15(ı-l), and 15(m-p), whose σ were occurred as 0.25, 0.14,
0.15, and 0.16 for 3, 3.5, 4, and 5 s, respectively, (see Table 5). They were enabled to be behaved
the most uniform absolute acceleration distribution. Eventually, it was shown that the control
system of NFVD located at mid bay and designed with greater α satisfactorily reduced the
absolute acceleration of the case study building with LRB.
3.5 Base Shear
Time history responses of the base shear for the base-isolated case study building with and
without NFVD were computed under Gazlı earthquake and given in Figure 16. The time history
responses of the base shear for LRB with 3, 3.5, 4, and 5 s were ranged between -1551 and 1420
kN, -1528 and 1290 kN, -1274 and 1153 kN, -962 and 883 kN, whose σ was recognized as 606,
561, 493, and 369, respectively, (see Table 5). It was shown that the base shear was considerably
decreased as well as restrained the fluctuations of the base shear response. The base shear was
substantially mitigated irrespective of α and placement when NFVD installed to the base-isolated
building. As seen in Figure 16(a-p), the use of NFVD in all bays clearly reduced the base shear
demand. For example, the lowest base shears of 662, 551, 489, and 385 kN were recorded by
means of the case of "0.3 VD-all bays" for 3, 3.5, 4, and 5 s, as shown in Figure 16(b), 16(f),
16(j), and 16(n), respectively. Moreover, as given in Table 5, σ of the cases of "0.3 VD-mid
bay", "0.3 VD-corner bays", "0.3 VD-all bays" were as (306, 283, 268) for T of 3 s, (268, 244,
227) for T of 3.5 s, (231, 209, 195) for T of 4 s, (171, 156, 147) for T of 5 s, respectively. In
addition, the moderate α values (i.e., 0.3 and 0.5) were much more effective lessening the base

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shear and fluctuation of the time history response especially in lower T. The time history
responses of the case of "0.7 VD-corner bays" were in the ranges of -817 and 713 kN (σ = 298),
-694 and 634 kN (σ = 257), -568 and 556 kN (σ = 219), -400 and 417 kN (σ = 161) (see Figure
16(c), 16(g), 16(k), 16(o) and Table 5) while "0.5 VD-corner bays" proved as -783 and 694 kN
(σ = 290), -671 and 616 kN (σ = 250), -555 and 541 kN (σ = 213), -387 and 412 kN (σ = 159)
for T of 3, 3.5, 4, and 5 s (see Figure 16(d), 16(h), 16(l), 16(p) and Table 5) respectively.
3.6 Base moment
The maximum base moment of the case study building with and without NFVD were obtained
for each of the earthquakes and presented in Figure 17. The increase of T was effectively
diminished the base moment. The use of LRB with 3, 3.5, 4, and 5 s produced the average values
of the base moment as 26768, 24824, 2278, and 15764 kNm as shown in Figure 17(a), 17(b),
17(c), and 17(d), respectively. The inclusion of NFVD successfully mitigated the base moment
of the case study building when designed with LRB especially T of 3, 3.5, and 4 s. When
considered the response of the base moment under five earthquakes the most notable value of α
and location of NFVD were recognized as 0.7 and mid bay placement except T of 5 s,
respectively. For example, the greatest base moment reductions with respect to the base-isolated
case study building with LRB having T as 3 s proved as 19.9, 10.8, 17.3, and 27.6 % under
Gazlı, Cape, Chi-Chi, and Salvador earthquakes by virtue of "0.7 VD-mid bay" as shown in
Figure 17(a), respectively, additionally it occurred as 16.7 % by "0.15 VD-corner bays" under
Tabas earthquake. When subjected to Gazlı, Chi-Chi, and Salvador earthquakes LRB with T of
3.5 s and "0.7 VD-mid bay" provided the greatest reductions as 24.8, 20.4, and 23.5 % (see
Figure 17(c)), respectively. As for T of 4 s, "0.3 VD-mid bay", "0.7 VD-mid bay", and "0.15
VD-corner bays" executed the base moment reductions as 20.4, 15.2, and 19.8 % under Chi-Chi,
Gazlı, and Tabas earthquakes (see Figure 17(d)), respectively. However, only "0.3 VD-mid bay"
and "0.15 VD-corner bays" were accomplished the attenuation of the base moment of LRB as
21.2 and 17.5 % when T was 5 s under Chi-Chi and Tabas earthquakes (see Figure 17(d)),
respectively. The amplification of T (i.e., 5 s) was not attributed to the significant contribution in
mitigating the base moment demand of the base-isolated case study building with LRB under
Gazlı, Cape, and Salvador earthquakes as shown in Figure 17(d). The response trend of NFVD
was also displayed in the average value of the base moment reductions occurred as 18.0, 17.5,
and 14.1 % by "0.7 VD-mid bay" for T of 3, 3.5, and 4 s, respectively. In essence, it was shown
that each of NFVD was capable of restraining the base moment response of the base-isolated
case study building except T of 5 s, in which the greatest α and mid bay placement namely "0.7
VD-mid bay" was come into prominence.
3.7 Input Energy
Input energy can be defined as exerting the seismic input energy to the structures during the
earthquakes, which was absorbed by inherently damping behaviour of the structural members or
dissipated by additional damping devices [70]. The input energy of the case study building with
LRB and NFVD was computed and presented in Figure 18 where can be seen the average input
energy as 3891, 4376, 4618, and 4099 kJ for T of 3, 3.5, 4, and 5 s, respectively. The input
energy diminished based upon the characteristic of the earthquakes if NFVD was installed to the

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base-isolated case study building with LRB. "0.15 VD-all bays" produced the greatest reductions
on the input energy as 13.4, 16.1, 6.8 % for T of 3 s (see Figure 18(a)), as 16.0, 26.6, 10.3 % for
T of 3.5 s (see Figure 18(b)), as 13.5, 31.5, 9.8 % for T of 4 s (see Figure 18(c)) under Gazlı,
Tabas, Chi-Chi earthquakes, respectively. On average, the lowest input energies of 3586, 3765,
3879, and 3886 kJ were also obtained by "0.15 VD-all bays" corresponded the reductions as 7.9,
14.0, 16.0, and 5.2 % for T of 3, 3.5, 4, and 5 s, respectively. When fixed the placement and
enhanced the α from 0.15 to 0.70 the input energy generally enhanced under Gazlı, Tabas, and
Chi-Chi earthquakes. For example, when NFVD was placed the mid bay and α varied from 0.15
to, 0.30, 0.50, and 0.70 the input energy observed as (5980, 6074, 6425, 6338 kJ) for T of 3 s,
(6879, 6968, 7185, 7285 kJ) for T of 3.5 s, (7835, 7880, 7978, 8073 kJ) for 4 s, (7755, 7660,
7637, 7657 kJ) for T of 5 s under Tabas earthquake, respectively. The latter proved the adverse
trend on the variation of the input energy. In addition, the input energy was mitigated in case of
α was to be constant and placement of NFVD changed from mid to corner and all bays, but Cape
and Salvador earthquakes responded adverse trend based on the characteristic of the earthquakes.
Assumed that α was constant as 0.15, the placement of NFVD was varied from mid to, corner,
and all bays the input energy occurred as (1261, 1204, 1148 kJ) for T of 3 s, (1363, 1271, 1208
kJ) for T of 3.5 s, (1401, 1325, 1249 kJ) for 4 s, (1332, 1330, 1282 kJ) for T of 5 s under Gazlı
earthquake, respectively.
3.8 Hysteretic curves
The hysteretic cycles obtained through the nonlinear time history analyses with Gazlı earthquake
for the base-isolated case study building with and without NFVD having various characteristics
were given in Figure 19 and 20, respectively. The former was represented the hysteresis
behaviours for the outer and inner bearing of LRB with a series of T while the latter described
the force-displacement response of NFVD with various α. Those curves were abided by the
typical idealized hysteretic curve of LRB and NFVD described in Figure 1(b) and 2(a),
respectively. When considered the hysteretic curve of inner LRB whose yield forces (Fy) were
147.9, 131.2, 111.6, 90.1 kN for T of 3, 3.5, 4, 5 s (see Figure 19(b)) confirmed the predesigned
value of 151.1, 129.5, 113.3, 90.6 kN (see Table 2), respectively. As for the inner displacement
of LRB, it varied between -0.280 and 0.196 m for 3 s, -0.326 and 0.261 m for 3.5 s, -0.339 and
0.296 m for 4 s, -0.398 and 0.292 m for 5 s which were almost the same with the determined
maximum isolator displacement values (D) presented in Table 2. Since the greater T increased
the displacement demand of the isolator under same loads (see Figure 19) the structural
performance of the isolated building with LRB was enhanced. Moreover, it was known that the
linear FVD described the hysteresis loop of purely elliptic corresponded to α of 1 while the
friction damper had rectangular loop whose α was almost "0" as shown in Figure 2(c). The
hysteretic loop of FVD was varied between elliptical and rectangular shape as shown in Figure
2(a) [39]. As α increased, the hysteresis loop was obviously tended to the elliptical shape, in
which the displacement was not much more differentiated, but the force considerably dropped as
shown in Figure 20. For example, the forces varied between -184,5 and 181.3 kN, -161.5 and
160.2 kN, -136.7 and 136.3 kN, -116.2 and 117.0 kN for α of 0.15, 0.30, 0.50, 0.70 (see Figure
20(a)), respectively. As seen in Figure 20, the increase of T slightly influenced the force whereas
the significant amplification of displacement was occurred. While the displacements were ranged

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between -0.282 and 0.221 m, -0.280 and 0.222 m, -0.284 and 0.227 m, -0.290 and 0.232 m for T
of 3.5 s (see Figure 20(b)), respectively. It was reached to 0.302 and 0.261 m, -0.296 and 0.259
m, -0.296 and 0.262 m, -0.300 and 0.267 m for α of 0.15, 0.30, 0.50, 0.70 and T of 4 s (see
Figure 20(c)), respectively.
4. Conclusions
This study conducted an analytical investigation on the nonlinear response of the base-isolated
case study building with and without NFVD. The design parameters of LRB used in the isolated
structure varied with the isolation periods (T). The implementation of NFVD characterized with
various damping exponents (α) and placement scenarios. The aim was to reduce the
deformations of the base-isolated building with LRB. The seismic performance of various base-
isolated models with and without NFVD was assessed by the engineering demand parameters
through the nonlinear time history analyses using five earthquakes. Based on the results of
analyses, the main conclusions are presented as follows:
1. The utilization of LRB with the greater T reduced the lateral stiffness of the bearing
thereby the storey displacements effectively enhanced. Compared to LRB with T of 3 s,
on average, the maximum displacement increments occurred as 12.0, 19.8, and 20.8 %
for T of 3.5, 4, and 5 s, respectively. Both "0.15 VD-all bays" and "0.30 VD-all bays"
cases successfully reduced the maximum storey displacements especially T was as 4 s,
which also depicted the most uniform storey displacement.
2. The greatest reductions on the maximum bearing displacements were also provided by
"0.15 VD-all bays" for T of 3, 3.5, and 4 s, "0.70 VD-all bays" for T of 4 and 5 s.
3. The case of "0.15 VD-all bays" was mitigated the maximum relative displacement as
26.0, 20.2, 32.1, and 21.8 % with respect to LRB with T of 3, 3.5, 4, and 5 s,
respectively. It was also described the most uniform relative displacement distribution
compared to the other alternative placements (i.e., mid bay and corner bays).
4. "0.3 VD-all bays" case provided the lowest roof drifts of 0.84, 0.86, 0.87, 0.91 under
Gazlı earthquake for 3, 3.5, 4, and 5 s, respectively. The lower α not only mitigated the
maximum interstorey drift ratio but also described the more uniform drift distribution
especially for the lower T. It was also valid for the greater α as T reached to 4 or 5 s.
5. The utilization of NFVD at mid bay or corner bays with the higher α was much more
reasonable both for mitigating the absolute acceleration and exhibiting the most uniform
distribution. For example, "0.7 VD-mid bay" case was considerably mitigated the
maximum absolute acceleration especially for T of 3, 3.5, and 4 s.
6. The utilization of NFVD with the moderate α (i.e., 0.3 and 0.5) and all bays placement
substantially mitigated the base shear of the isolated case study building with LRB. Also,
the increase of α with the mid bay placement mostly reduced the base moment.
7. The greatest input energy reductions were experienced in case of α decreased and mid
bay placement preferred. For example, "0.15 VD-all bays" case satisfied the greatest
input energy reductions as 7.9, 14.0, 16.0, and 5.2 % for 3, 3.5, 4, and 5 s, respectively.

17/20
8. The hysteretic loop obtained by the nonlinear analyses proved that the greater T increased
the displacement demand of LRB. As α increased, the hysteretic loop of NFVD gained
the elliptical shape displaced much more under the same load.
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Figure 1. Typical configuration and hysteretic behaviour of LRB [9].
Figure 2. a) Typical longitudinal cross section of NFVD [34], b) schematic view of generalized Maxwell
model for NFVD [63], c) idealized force–displacement relationship of NFVD [39], and d) force–
viscoelasticity relationship of NFVD [39].
Figures

2/9
Figure 3. Elevation views of 10-storey frames; a) with LRB, b) LRB with NFVD in mid bay, c) LRB with
NFVD in corner bays, and c) LRB with NFVD in all bays under investigation.
Figure 4. The cross-section view of LRB and NFVD in structure [66].
Figure 5. Elastic acceleration response spectra of the ground motions used.
a) b)
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2 2.5 3 3.5 4
Sa/g
Period (s)
Gazlı Tabas Cape Mendocino
Chi-Chi San Salvador Average
0
30
60
90
120
Gazlı Tabas Cape Chi-Chi Salvador Average
Max.
Storey
Disp.
(cm)
LRB 0.15 VD-mid bay 0.3 VD-mid bay 0.5 VD-mid bay
0.7 VD-mid bay 0.15 VD-corner bays 0.3 VD-corner bays 0.5 VD-corner bays
0.7 VD-corner bays 0.15 VD-all bays 0.3 VD-all bays 0.5 VD-all bays
0.7 VD-all bays
T = 3 s
0
30
60
90
120
Max.
Storey
Disp.
(cm)
0.7 VD-all bays
T = 3.5 s

3/9
c) d)
Figure 6. Maximum storey displacement of isolated frames with and without NFVD having different
characteristics and configurations under earthquakes.
a) b) c) d)
e) f) g) h)
ı) j) k) l)
m) n) o) p)
Figure 7. Variation of storey displacement for isolated frames with and without NFVD having different
characteristics and configurations under Chi-Chi earthquake.
a) b)
0
30
60
90
120
Max.
Storey
Disp.
(cm)
0.7 VD-all bays
T = 4 s
0
30
60
90
120
Max.
Storey
Disp.
(cm)
0.7 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
Storey Displacement (cm)
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
40 50 60 70 80 90 100 110 120 130
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 5 s
0
20
40
60
80
100
Max.
Bearing
Disp.
(cm)
0.7 VD-all bays
T = 3 s
0
20
40
60
80
100
Max.
Bearing
Disp.
(cm)
0.7 VD-all bays
T = 3.5 s

4/9
c) d)
Figure 8. Maximum bearing displacement of isolated frames with and without NFVD having different
a) b)
c) d)
Figure 9. Maximum relative displacement of isolated frames with and without NFVD having different
a) b) c) d)
e) f) g) h)
ı) j) k) l)
0
20
40
60
80
100
Max.
Bearing
Disp.
(cm)
0.7 VD-all bays
T = 4 s
0
20
40
60
80
100
Max.
Bearing
Disp.
(cm)
0.7 VD-all bays
T = 5 s
0
10
20
30
40
Max.
Relative
Disp.
(cm)
0.7 VD-all bays
T = 3 s
0
10
20
30
40
Max.
Relative
Disp.
(cm)
0.7 VD-all bays
T = 3.5 s
0
10
20
30
40
Max.
Relative
Disp.
(cm)
0.7 VD-all bays
T = 4 s
0
10
20
30
40
Max.
Relative
Disp.
(cm)
0.7 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
Relative Displacement (cm)
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 4 s

5/9
m) n) o) p)
Figure 10. Variation of relative displacement for isolated frames with and without NFVD having different
a) b)
c) d)
Figure 11. Maximum roof drift of isolated frames with and without NFVD having different characteristics
and configurations under earthquakes.
a) b)
c) d)
Figure 12. Maximum interstorey drift ratio of isolated frames with and without NFVD having different
a) b) c) d)
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 5 s
0
1
2
3
4
Max.
Roof
Drift
0.7 VD-all bays
T = 3 s
0
1
2
3
4
Max.
Roof
Drift
0.7 VD-all bays
T = 3.5 s
0
1
2
3
4
Max.
Roof
Drift
0.7 VD-all bays
T = 4 s
0
1
2
3
4
Max.
Roof
Drift LRB 0.15 VD-mid bay 0.3 VD-mid bay 0.5 VD-mid bay
0.7 VD-all bays
T = 5 s
0
0.5
1
1.5
2
Max.
Interstorey
Drift
Ratio
(%)
0.7 VD-all bays
T = 3 s
0
0.5
1
1.5
2
Max.
Interstorey
Drift
Ratio
(%)
0.7 VD-all bays
T = 3.5 s
0
0.5
1
1.5
2
Max.
Interstorey
Drift
Ratio
(%)
0.7 VD-all bays
T = 4 s
0
0.5
1
1.5
2
Max.
Interstorey
Drift
Ratio
(%)
0.7 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
Interstorey Drift Ratio (%)
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3 s

6/9
e) f) g) h)
ı) j) k) l)
m) n) o) p)
Figure 13.Variation of interstorey drift ratio for isolated frames with and without NFVD having different
a) b)
c) d)
Figure 14. Maximum absolute acceleration of isolated frames with and without NFVD having different
a) b) c) d)
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
0.0 0.5 1.0 1.5 2.0
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 5 s
0
1
2
3
4
5
Max.
Abs.
Acceleration
(m/s
2
)
0.7 VD-all bays
T = 3 s
0
1
2
3
4
5
Max.
Abs.
Acceleration
(m/s
2
)
0.7 VD-all bays
T = 3.5 s
0
1
2
3
4
5
Max.
Abs.
Acceleration
(m/s
2
)
0.7 VD-all bays
T = 4 s
0
1
2
3
4
5
Max.
Abs.
Acceleration
(m/s
2
)
0.7 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
Absolute Acceleration (m/s2)
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3 s

7/9
e) f) g) h)
ı) j) k) l)
m) n) o) p)
Figure 15. Variation of absolute acceleration for isolated frames with and without NFVD having different
a) b) c) d)
e) f) g) h)
ı) j) k) l)
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3.5 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 4 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 5 s
0
1
2
3
4
5
6
7
8
9
10
1.5 2.0 2.5 3.0 3.5 4.0
Storey
Level
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 5 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 3.5 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 3.5 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 3.5 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 3.5 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 4 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 4 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 4 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 4 s

8/9
m) n) o) p)
Figure 16. Time history response of base shear of isolated frames with and without NFVD having different
characteristics and configurations under Gazlı earthquake.
a) b)
c) d)
Figure 17. Maximum base moment of isolated frames with and without NFVD having different
a) b)
c) d)
Figure 18. Input energy of isolated frames with and without NFVD having different characteristics and
configurations under earthquakes.
a) b)
Figure 19. Typical hysteretic curves of LRB for the base isolated case study frame under Gazlı
earthquake.
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.15 VD-mid bay
0.15 VD-corner bays
0.15 VD-all bays
T = 5 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.3 VD-mid bay
0.3 VD-corner bays
0.3 VD-all bays
T = 5 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.5 VD-mid bay
0.5 VD-corner bays
0.5 VD-all bays
T = 5 s
-1500
-1000
-500
0
500
1000
1500
0 5 10 15 20
Base
Shear
(kN)
Time (s)
LRB
0.7 VD-mid bay
0.7 VD-corner bays
0.7 VD-all bays
T = 5 s
0
0.5
1
1.5
2
2.5
3
Max.
Base
Moment
(kNm)
x
10000
0.7 VD-all bays
T = 3 s
0
0.5
1
1.5
2
2.5
3
Max.
Base
Moment
(kNm)
x
10000
0.7 VD-all bays
T = 3.5 s
0
0.5
1
1.5
2
2.5
3
Max.
Base
Moment
(kNm)
x
10000
0.7 VD-all bays
T = 4 s
0
0.5
1
1.5
2
2.5
3
Max.
Base
Moment
(kNm)
x
10000
0.7 VD-all bays
T = 5 s
0
3000
6000
9000
12000
Input
Energy
(kJ)
0.7 VD-all bays
T = 3 s
0
3000
6000
9000
12000
Input
Energy
(kJ)
0.7 VD-all bays
T = 3.5 s
0
3000
6000
9000
12000
Input
Energy
(kJ)
0.7 VD-all bays
T = 4 s
0
3000
6000
9000
12000
Input
Energy
(kJ)
0.7 VD-all bays
T = 5 s
-650
-450
-250
-50
150
350
550
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Force
(kN)
Displacement (m)
Outer LRB
T=3 s
T=3.5 s
T=4 s
T=5 s
-650
-450
-250
-50
150
350
550
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Force
(kN)
Displacement (m)
Inner LRB
T=3 s
T=3.5 s
T=4 s
T=5 s

9/9
a) b)
c) d)
Figure 20. Typical hysteretic curves of NFVD at mid bay for the base isolated case study frame under
Gazlı earthquake.
-300
-200
-100
0
100
200
300
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Force
(kN)
Displacement (m)
T=3 s
α=0.15
α=0.30
α=0.50
α=0.70
-300
-200
-100
0
100
200
300
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Force
(kN)
Displacement (m)
T=3.5 s
α=0.15
α=0.30
α=0.50
α=0.70
-300
-200
-100
0
100
200
300
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Force
(kN)
Displacement (m)
T=4 s
α=0.15
α=0.30
α=0.50
α=0.70
-300
-200
-100
0
100
200
300
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Force
(kN)
Displacement (m)
T=5 s
α=0.15
α=0.30
α=0.50
α=0.70

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