87 20 00331.ja.en

Bulletin of the JSME
Proceedings of the Japan Society of Mechanical Engineers
Vol.87, No.894, 2021
Transactions of the JSME (in Japanese)
Attenuation characteristics of two-chamber separate type single-sided granular damper using elastomer particles
(Investigation of damping force angle dependence and its consideration)
Atsushi Toyouchi* 1, * 2， Koji Imon* 1， Yukihiro Iwamoto* 1， Makoto Hanai* 2
Damping force characteristics of a separated dual-chamber single-rod type damper utilizing an
elastomer particle assemblage
(Investigation and consideration of damping force angle dependency)
Atsushi TOYOUCHI* 1, * 2, Yasushi IDO* 1, Yuhiro IWAMOTO* 1 and Makoto HANAI* 2
* 1Nagoya Institute of Technology
Gokiso-cho, Showa-ku, Nagoya-shi, Aichi 466-8555, Japan
* 2 KYB Corporation
2548Dota, Kani-shi, Gifu 509-0298, Japan
Received: 27 September 2020; Revised: 6 December 2020; Accepted: 6 January 2021
Abstract
In this paper, we report the effect of the installation angle of a separated dual chamber single rod type damper using elastomer
particles on the damping force characteristics. The particle assemblage damper uses soft / hard particles and suppresses
vibrations by the compression reaction force of particles and This is attracting attention as a solution to the problem of oil
leakage of oil damper. As a result of calculation using the discrete element method (DEM), in the case of only one chamber is
filled. with particles, when it was found that the mounting angle of the damper is made closer to the vertical from the horizontal,
the particles gather at the bottom of the elastomer due to gravity and the movement of the particles is restricted, so that the
damping force increases. In addition,when both chambers are filled with particles, the damping force that becomes larger by
compressing particles to the bottom side of the damper, however, it is that by the restoring force of the particles already
compressed in the other room is canceled, so it was found that there was no significant change in damping force even if the
installation angle was changed.
Keywords Keywords :: Damper, Damping force, Elastomer, Particle assemblage, Discrete element method
1. O Words
The granular damper is soft instead of the oil of the granular impact damper that obtains the damping effect by using the motion of the granular in the container
installed in the mass part of the vibration system and the oil of the oil damper often used in automobiles. Granules that use hard particles, have a rod that transmits
external force and a piston for flowing the particles filled inside the cylinder, and convert vibration into heat by the frictional force acting between the particles and the wall
surface of the particles. There is a body vibration damper. It is attracting attention as a means to suppress the vibration of structures against vibrations such as
earthquakes, and to solve the temperature dependence of liquid leakage and damping force, which are problems of oil dampers. The advantages of the granular damper
are that the damping force is less dependent on temperature, that liquid leakage does not occur, and that seals are not required. As a result, the granular impact damper
does not require the members / elements and seals that support the damper, which makes it possible to simplify the structure, and the granular vibration damper makes it
possible to simplify the structure by eliminating the need for sealing.
As a previous study of granular impact dampers, the damping effect when the mounting direction of the damper and the number of particles used are changed has
been investigated. Install the damper horizontally and install it horizontally.1 When using individual particles, it has been shown that the optimum parameters can be
calculated numerically by changing the clearance between the particles and the vessel and the excitation wavenumber discretely ().Zahrai and Rod，， 2015)
.. When using multiple particles, increase the mass and coefficient of restitution of the particles, and adjust the particle size and filling rate of the particles appropriately.
No.20-00331 [DOI: 10.1299 / transjsme.20-00331], J-STAGE Advance Publication date: 18 January, 2021
* 1 Full-time member, Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology (〒)466-8555 Gokiso-cho, Showa-ku, Nagoya-shi, Aichi)
* 2 KYB(stock)(〒509-0298 Dota, Kani City, Gifu Prefecture
2548) E-mail of corresponding author: toyouchi-ats@kyb.co.jp
[DOI: 10.1299 / transjsme.20-00331] © 2021 The Japan Society of Mechanical Engineers 1
Translated from Japanese to English - www.onlinedoctranslator.com

Toyouchi, Ido, Iwamoto and Hanai, Transactions of the JSME (in Japanese), Vol.87, No.894 (2021)
It has been shown that a good damping effect can be obtained by combining with (Lu et al.，，2010) .. Gravity damper
When installed in the direction, the resonance peak can be effectively suppressed over a wide frequency range by properly setting the mass ratio of the particles and the
vibration system and the clearance between the particles and the container ().Inoue et al.，，2011) ， Mass ratio is the term of damping and stiffness in the formula
Has been shown to affect (Saeki，，2009) ..
Prior studies on granular dampers other than granular impact dampers have reported damping characteristics when using steel balls or
elastomer particles. It has been shown that the damping characteristics change depending on the filling factor, vibration frequency, and vibration
stroke amount when using steel balls, etc. (Hanai et al.，，2016) .. For steel balls, etc., change the mounting angle of the damper.
It has been shown that the damping force has an angle dependence because the place where the void is formed changes, and this angle dependence can be alleviated by
utilizing the property that the steel balls strongly attract each other when a magnetic field is applied. It has been shown that the decay characteristics can be changed by
changing the applied current value (Imon et al., Et al.2014) .. When elastomer particles are used, the particles are elastically deformed.
A high damping force can be obtained by increasing the filling rate, the voids become smaller when the filling rate is increased, so that the angular dependence of the
damping force can be relaxed, and the damping force depends on the vibration frequency, displacement amount, etc. Has been shown (Morishita et al.，，2016) ..
However, these reports target the damper structure in which the rod protrudes from both sides of the cylinder, and the damping characteristics of
the damper structure in which the rod protrudes from one side of the cylinder, which is often used in dampers such as automobiles, are clarified.
Not.
Therefore, the authors made a prototype of a damper with a linear motion rod single-sided structure using elastomer particles, in which the particle
chamber in the cylinder was separated into two chambers by a piston.DEM((Discrete element method) Was used 3 When a numerical simulation of dimensions
is performed and particles are filled only in a room without a rod (Toyouchi et al.，，2020) ， When both chambers are filled with particles (Toyouchi
et al.，，2021) The damping force generation mechanism was investigated. The damping force characteristics are dominated by the force in the normal direction, and the
damping force increases as the displacement of the piston progresses in the direction of compressing the particles, and the displacement of the piston compresses the
particles. It was confirmed that the damping force became smaller and had hysteresis when the direction changed from the direction to the uncompressed direction. In
addition, the larger the filling rate, vibration frequency, particle hardness, and young rate of the particles, the larger the maximum damping force, hysteresis, and damping
energy. When the stroke center position changes, the maximum damping force changes, but there is a big difference in hysteresis. I confirmed that there was no such
thing. When both chambers are filled with particles, the friction between the rod and the particles increases as the compression progresses in the case of compressing the
particles in the chamber on the side with the rod, compared to the case of the chamber on the side without the rod. It was confirmed that the damping force increases as
the value increases. also,DEM It was confirmed that the numerical simulation using the above was qualitatively and quantitatively in good agreement with the experimental
values. However, in these surveys, the dampers were installed horizontally, and no survey was conducted on the mounting angle of the dampers.
In this research, in the previous survey of the authors DEM Since the results of the numerical simulation using the above and the experimental values are in good
agreement, the damping force of the damper when one chamber and both chambers are filled with elastomer particles with a granular damper with a linear motion rod
single-sided two-chamber separate structure. To clarify the installation angle dependenceDEM Numerical simulation was performed by.
2. Numerical simulation
2·1 Equation of motion
Used for simulation DEM Is a method to calculate the behavior of particles by sequentially calculating the equation of motion for translation and rotation of particles at
each time, considering the contact between particles. In this study, in order to obtain the velocity and position of the particle, the equation of motion for the translation and
rotation of the particle is expressed (1)And expressions (2)It is defined in.
m d2ri
i dt2
= = Fi ((1)
I dΩi
i = = Ti ((2)
dt

here,miIs the particle mass,riIs the particle position vector,t Is the time,FiIs the total contact force vector,IiIs the moment of inertia, ΩiIs an angular
velocity vector,TiIs the total torque applied to the particles. Also, subscriptsi Is the particle number.FiWhen TiFor, considering the contact force for
each particle, the following formula (3)And expressions (Four)It is represented by.
Fi = = Fcn+ Fct+ mig ((3)
Ti = = ri×Fct ((Four)
Contact force Cundall When Strack A model composed of elements of springs, dashpots, and friction sliders, devised byCundall
and Strack，，1979) Is used, and the formula (Five)， (6)It is represented by. Also, the particles at the contact pointi Particles j
Tangent relative velocity vector to VfijAnd the formula (7)It is represented by.
   = (−     −      ·   )    ,, ((Five)
   = −      −         ,, ((6)
    =     − (   ·  )    + 2 ( ) −   ) ×    ,, ((7)
here,KnIs the normal modulus of elasticity,KtIs the tangential modulus of elasticity,CnIs the normal viscosity coefficient,CtIs the tangential viscosity coefficient,δnIs the
amount of displacement in the normal direction with respect to the contact point,δtIs a particle i Particles j Tangent displacement vector at the point of contact with respect
toniIs a particle with respect to the contact point i From particles j Normal direction unit vector towardsVijIs a particle i Particles j Relative velocity vector toa Is the particle
radius,ωi，，ωjIs a particle i，，j It is an angular velocity vector of. The normal modulus of elasticity of a particle isHertz The elastic rebound force and the viscous force
are taken into consideration in the equation based on the contact theory of8)from(11)It is represented by. Regarding the tangential directionMindlin Formula based on the
theory ofMindlin，，1949) Is used, and the formula (12)， (13)It is represented by. It is a viscoelastic model that considers frictional force in addition to elastic rebound
force and viscous force, assuming that there is no slip at the contact point.
    = = Four (( 1 ) √   ,,
3
((8)
2    2
    = = Four ((
3
1
+
) √ , ((9)

= = 1− 2 ,, ((Ten)
2
= = 1− ..
((11 11)
    = = 2√2     0.5
,, ((12)
2-
    = = 8√ 0.5 ,, ((13)
2-
Subscripts in the formula w Represents the wall surfaceKnij Is the elastic modulus when particles come into contact with each other Kn，，Kniw Is the coefficient of elasticity when the
particle and the wall surface come into contact with each other. Kn and,Ei，，EwIs the Young's modulus of particles and walls,Gi Is the modulus of lateral elasticity of the particle，，νi，，ν
j Is the Poisson ratio of particles and walls. also,Cn，，CtFor the formula (14)， (15)It is represented by.

= √
0.25,, ((14)
= √ 0.25 ,, ((15)
Attenuation coefficient α Is the coefficient of viscous force determined so that the coefficient of restitution of the particles obtained in the experiment matches in the analysis. Friction
between particles and between particle walls isThe tangential relative velocity vector on the contact surface 0 If it is larger, or if the contact force in the tangential direction is greater than
the frictional force, it is considered that slip has occurred on the surface of the contact particles.The following formula (16)From the formula (18)It is represented by. | Vfij | = 0 in the case
of,Fct ≤ μ μf | Fcn |time,
Fct= = Fct,, ((16 16)
also,Fct > μ μf | Fcn |time,
Fct= --μf | F | ti.... ((17 17)
cn
| Vfij |> 0 in the case of,
Fct= --μf | F | ti,,.. ((18 18)
cn
However,ti = = Vfij / / |Vfij| And of the particles VfijIt is a unit vector of direction. also,μ μfIs the coefficient of friction of the particles. here, Fcn，，FctIs the contact
force in the normal direction and the tangential direction, and the normal direction at the contact point is subscripted. n， Tangent direction is a subscript t It is
represented by. also,g Is the gravitational acceleration. The simulation is3 It was done in dimension.
2·2 Granule damper overview
figure 1 The schematic diagram of the granular damper used in the simulation is shown in. The damper has a rod protruding from one side of a
cylindrical cylinder. The piston integrated with the rod divides the inside of the cylinder into two chambers.
The particles are enclosed in the room without the rods in the two rooms or in both rooms. The gap between the outer peripheral surface of the piston and
the inner wall surface of the cylinder is sized so that particles do not enter so that particles do not move between the two chambers. The second room is the
one without the rod.Chamber A， The room with the rod Chamber B It was decided. The piston that is integrated with the rodz z It can be displaced in the
axial direction, and when an external force due to forced vibration is applied to the rod, the compressive force generated by the compression of the particles,
or between the particles or between the particles and the piston, cylinder, and rod generated when the particles move. The damping force is obtained by the
frictional force between them. The material property value of each part is carbon steelS45C It is set to the value of. The center of the stroke of the piston isz z
Axial 0 It is a point, and in each room z z From the shaft end face 39mm It is the position of.
(a)
Fig. 1 Schematics of the separated dual-chamber single-rod type damper utilizing an elastomer particle assemblage.
(a) is when one room is filled with particles and (b) is when both chambers are filled with particles. 1. Cylinder,
2. Rod, 3. Piston, 4. Elastomer particles.
(b)
[DOI: 10.1299 / transjsme.20-00331] © 2021 The Japan Society of Mechanical Engineers Four

2·3 Analysis conditions
As for the analysis conditions, the particle size and the material property values of the particles are unified under the same conditions, and only the room for filling the particles, the
filling rate, and the installation angle of the damper are changed values. Here, the filling factor is an index of the amount of granules filled in the damper and is defined by the following
equation.
Total mass of the particles
Volume of the space in the container × Density of the particle
Packing fraction = (19)
The installation angle isz z The state where the axis is installed so that it is horizontal 0 °And when tilted so that the side with the rod comes up z z The angle between the
axis and the horizontal direction was used. Filling rate with basic conditions0.60， Installation angle 0 °It is said. A table that summarizes the conditions1 And table 2 Shown
in. The coefficient of friction is the value of the coefficient of friction between general rubber and rubber.0.5 (Japan Society of Mechanical Engineers,1977)It was adopted.
The displacement of the piston is a sine wave.
Table 1 Numerical conditions.
Material of the elastomer particle Silicone elastomer TSE3466
Diameter of particles [mm] 3
Packing fractions of particles [-] 0.60, 0.65
Chamber A: 1339, Chamber B: No particles
Chamber A: 1451, Chamber B: No particles
Chamber A: 1339, Chamber B: 1125
Number of particles
Stroke of forced vibration [mm] Ten
Frequency of forced vibration [Hz] 1
Installation angle [°] 0, 45, 90
Table 2 Mechanical properties for calculation.
Density of particle [kg / m3] 1.10 × 103
Poisson ratio vi 0.5
Friction coefficient μ μf ((wall-particle) 0.5
Friction coefficient μ μf ((particle-particle) 0.5
Young's modulus of wall Ew [GPa] 210 210
Compressive modulus of particles Ei [MPa] 4.11
Attenuation coefficient α 0.5311
2·Four Validity with analysis results
Filling factor to show the validity of the analysis result 0.65， Installation angle 0 °In this case, we compared the analysis results and the test results when both
chambers were filled with particles. Figure the result2 Shown in. Table for both analysis and experimental results1 Sine and cosine vibration is performed under the
conditions of 2 teeth 1 The cycle data is graphed. Also, the figure2 Since the analysis results and the experimental results are in good agreement qualitatively and
quantitatively, it can be said that the behavior of the particles can be clarified by the analysis.
[DOI: 10.1299 / transjsme.20-00331] © 2021 The Japan Society of Mechanical Engineers Five

Fig. 2 Damping force vs. piston displacement. Comparison of the simulation and experimental results.
3. Results and Discussion
3·1 Particle behavior and damping force characteristics when particles are filled in one chamber Filling rate when particles are filled in one chamber 0.60， Installation angle 0 °
，，45 °，，90 °The particle behavior and damping force characteristics in the case of were investigated. figure3 Installation angle 0 °，，45 °，，90 °Damping force-Displacement
diagram and the result of decomposing the damping force at each angle into a normal component and a tangential component with respect to the piston surface. Four，，Five，，6
Installation angle 0 °，，45 °，，90 °Particle position and compressive force distribution at the time of vibration in the case of 7，，8，，9 Installation angle 0 °，，45 °，，90 °The
velocity vector of the particle in the case of is shown. figure3 (a)From +z z It shows the characteristic of a gradual hardening type in which the damping force increases as the displacement
progresses toward.z z It can be seen that when the elastomer particles are displaced in the direction of, they have a characteristic of having hysteresis due to viscoelastic deformation of
the elastomer particles. Installation angle0 °，，45 °，，90 °Comparing the maximum damping force of0 °Than 45 °Is slightly larger,45 °Than 90 °It can be seen that is larger. Also, the
figure3 (b)， (c)， (d)Therefore, in both the normal direction component and the tangential direction component, the acting force increases as the displacement increases, and the
tangential direction force is smaller than the normal direction, so the normal direction force is dominant. Recognize. Damping force is +z z The characteristics of the gradual hardening
type, which increases as the displacement progresses in the direction of, are shown in the figure. Four，，Five，，6 From the compressive force distribution of, +z z Since the
compressive force of each particle increases as the displacement progresses in the direction of +z z This is because the amount of elastic deformation of each particle increases due to the
displacement in the direction of, that is, the elastic repulsive force increases. ――――z z The characteristic of having hysteresis when displaced in the direction of is because the energy
given to the elastomer particles by compression is lost by being converted into thermal energy by the resistance due to the viscosity of the particles. Also, the figureFour，，Five，，6 So
the particles are +z z In the displacement in the direction of, the compressive force increases from the particles around the piston.
--z It can be seen that the compressive force decreases from around the piston when the displacement is in the direction of. In addition, the figure7，，8，，9 From the
velocity vector diagram of, the particles around the piston have velocities in the direction in which the piston travels, but the particles other than around the piston have
velocities in various directions. It is considered that the frictional force also affects the occurrence of hysteresis. figure3 (a)It is considered that the difference in the
maximum damping force depending on the installation angle is due to the shape of the void in the particle chamber where the piston does not compress the particles
most. figure4 (d)The air gap continues from the piston surface at the upper side of the particle chamber cylinder to the cylinder end surface, whereas in the figure 5 (d)The
gap on the piston surface side is large but does not continue to the cylinder end surface, as shown in the figure. 6 (d)The void is only on the piston surface side. Therefore,
the installation angle0 °Then, even if the displacement progresses, the particles are shown in the figure. 4 (d)The maximum damping force is small because the contact
area between the particles and the cylinder wall surface is small and the frictional force is small, and the space where the particles can escape is narrowed with respect to
the displacement amount by increasing the installation angle. In addition, the contact area between the granules and the cylinder wall surface increases, which increases
the frictional force and the installation angle.90 °Then, after the lower surface of the gap on the piston surface side, there is no space on the cylinder side surface for
particles to escape, and the contact area between the particles and the cylinder wall surface is the largest, so the frictional force is also large and the maximum damping
force is the installation angle. 0 °，，45 °It is thought to be larger. At this time, it is considered that the amount of escape of the particles into the void affects the force in
the normal direction, and the friction between the particles and the side surface of the cylinder affects the force in the tangential direction.3 (b)， (c)， (d)It can be
confirmed that the force in the normal direction and the tangential direction changes depending on the installation angle.

(a) (b)
(c)
Fig. 3 Damping force vs. piston displacement curves of simulation results. (A) is comparison of damping force between 0 °,
45 ° and 90 °. (B) is the normal and tangential force at an installation angle of 0 °. (C) is the normal and tangential force at an
installation angle of 45 °. (D) is the normal and tangential force at an installation angle of 90 °.
(d)
(a) (b)
(c)
Fig. 4 The position of the particles and the distributions of the compressive force acting on the particles. The installation angle is 0 °.
The position of the piston center and time are (a) z z = = 0 mm, t / T = = 0 (compression process), (b) z z = = 5 mm, t / T = = 0.25, (c) z z = = 0
mm, t / T = = 0.50 (non-compression process) and (d) z z = ---5 mm, t / T = = 0.75.
(d)

(a) (b)
(c)
(d)
(a)
(b) (c) (d)

(a) (b)
(c)
Fig. 7 Selected velocity vectors of the particles inside the damper. The installation angle is 0 °. The position of the piston center
and time are (a) z z = = 0 mm, t / T = = 0 (Compression process), (b) z z = = 5 mm, t / T = = 0.25, (c) z z = = 0 mm, t / T = = 0.50
(noncompression process) and (d) z z = ---5 mm, t / T = = 0.75.
(d)
(a) (b)
(c)
(d)

(a)
(b) (c) (d)
3·2 Filling rate 0.65， Installation angle 0 °and 90 °in the case of Verification of the consideration that the shape of the void in the particle chamber where the
piston is the least compressed particles affects the change in the maximum damping force depending on the installation angle, and to increase the filling rate of the
particles and reduce the voids. In order to confirm whether the installation angle of the damper can be relaxed, set the filling rate. 0.60 from 0.65 The analysis was
performed when the value was increased to. figureTen Installation angle 0 °When 90 °Damping force-displacement diagram, figure comparing 11 (a)， (b)Installation angle
0 °When 90 °Shows the position and compression force distribution of the particles in the state where the particles are not compressed most. figureTen From the
installation angle 0 °When 90 °It can be seen that there is no big difference in the maximum damping force and hysteresis. This is a figure11 (a)， (b)From the filling rate
0.60 from 0.65 It is probable that the number of particles increased due to the increase to the above, and the voids inside the damper disappeared, and the particles began
to move in the same way even if the installation angle was changed. From the above, the dependence of the damper installation angle is alleviated by increasing the filling
rate and reducing the voids in the particle chamber, and the filling rate.0.60 from 0.65 It turned out that it disappeared between.
Fig. 10 Damping force vs. piston displacement curves of simulation results of installation angle 0 ° and 90 °.
[DOI: 10.1299 / transjsme.20-00331] © 2021 The Japan Society of Mechanical Engineers Ten

(a)
Fig. 11 The position of the particles and the distributions of the compressive force acting on the particles.
The installation angle is (a) 0 °, the installation angle is (b) 90 °.
(b)
3·3 Particle behavior and damping force characteristics when both chambers are filled with particles Filling rate when particles are filled in both chambers 0.60
And the installation angle 0 °，，90 °The particle behavior and damping force characteristics in the case of were investigated. figure12 (a)Damping force-displacement
diagram, figure 12 (b)， (c)As a result of decomposing the damping force into the normal direction component and the tangential direction component with respect to the
piston surface, the figure is shown. 13，，14 Installation angle 0 °，，90 °Particle position and compressive force distribution during vibration in 15，，16 16 Installation
angle 0 °，，90 °The velocity vector of the particle in is shown. The velocity vector when the piston is stopped is very small as in the result of one-chamber filling, and is
omitted because it is not used for consideration. figure12 (a)From +z z Orientation and-z z It shows the characteristic of a gradual hardening type in which the damping
force increases as the displacement progresses in the direction of +.z z from-z z or-z z From +z z It can be seen that when the displacement is switched in the direction of,
the characteristic has hysteresis due to the viscoelastic deformation of the elastomer particles. figure12 (b)， (c)Therefore, both the normal direction component and the
tangential direction component 0 From the point +z z and-z z It can be seen that the force acting in the normal direction becomes dominant as the displacement progresses
in the direction of, and the force in the tangential direction is smaller than that in the normal direction. Damping force is +z z Orientation and-z z The figure shows the
characteristics of the gradual hardening type that increases as the displacement progresses in the direction of. 13 And figure 14 From the compressive force distribution of,
+ as in the case of filling one chamber with particlesz z and-z z Since the compressive force of each particle increases as the displacement progresses in the direction of +z z
and-z z This is because the amount of elastic deformation of each particle increases due to the displacement in the direction of, that is, the elastic rebound force increases.z
z from-z z or-z z From +z z The characteristic of having hysteresis when the displacement is switched in the direction of is because the energy given to the elastomer
particles by compression is lost by being converted into thermal energy by the resistance due to the viscosity of the particles. Also, the figure13 And figure 14 Because the
piston is +z z When you go in the direction ofChamber A Then, the compressive force increases from the particles around the piston, andChamber B Then, it can be seen
that the compressive force is low from the particles around the piston. Also, the piston is-z z When going in the direction ofChamber A Then, the compressive force
becomes low due to the particles around the piston.Chamber B Then, the compressive force increases from the particles around the piston, but the piston is +z z It can be
seen that the number of particles with high compressive force increases as compared to the direction of. this is,Chamber B This is thought to be because the internal
volume is small and the voids between the particles are small due to the rod volume integral, so the particles are easily affected by compression due to the displacement of
the piston. Also, the figure15 And figure 16 16 From the velocity vector diagram of, the particles around the piston have velocities in the direction of travel of the piston, but
the particles other than around the piston have velocities in various directions, so the elasticity of the particles generated when the particles move. It is considered that the
repulsive force and the frictional force between the particles and between the particle walls also affect the generation of hysteresis. Here, the figure12 (a) From the
installation angle 0 °When 90 °It can be seen that there is no big difference in the damping force. This is + if the particles are filled in only one chamberz z When the
displacement progresses in the direction of Chamber A While only the compressive repulsive force of the particles acts, the particles are filled in both chambers, so that +z z
When the displacement progresses in the direction of Chamber A With the compressive repulsive force of the particles Chamber B Because the restoring force of the
particles ofChamber A The decrease in damping force due to the voids in Chamber B It is considered that the difference in damping force depending on the installation
angle was alleviated by being supplemented by the restoring force of. About this,-z z It is considered that the same effect appears even when the displacement progresses
in the direction of.
[DOI: 10.1299 / transjsme.20-00331] © 2021 The Japan Society of Mechanical Engineers 11 11

(a)
(b)
Fig. 12 Damping force vs. piston displacement curves of simulation results. (A) is comparison of damping force between 0 ° and 90 °.
(b) is the normal and tangential force at an installation angle of 0 °. (c) is the normal and tangential force at an installation
angle of 90 °.
(c)
(a) (b)
(c)
(d)

(a)
Fig. 14 The position of the particles and the distributions of the compressive force acting on the particles. The installation angle is
90 °. The position of the piston center and time are (a) z z = = 0 mm, t / T = = 0 (compression process), (b) z z = = 5 mm, t / T = = 0.25, (c) z z = = 0
(b) (c) (d)
(a)
(b)
(a)
(b)

Four. Conclusion Words
In this study, in order to confirm the dependence of the damping force of the damper on the installation angle of the two-chamber separate type single-
sided granular damper using elastomer particles, elastomer particles are filled in one chamber or both chambers, and the installation angle of the damper.
About the case of changingDEM Numerical simulation was performed by. If only the room on the side without the rod is filled with particles,
If the mounting angle of the damper is moved from horizontal to vertical so that the room on the side with the rod is on the vertical side, the damping force is still
dominated by the force in the normal direction, but the maximum damping force is reached. It was found that the hysteresis became large. As for the behavior of the particles, there is no
big difference in the tendency of the compressive force distribution and velocity vector of the particles depending on the installation angle, but the size of the void on the side of the cylinder
when the particles are not compressed most differs depending on the installation angle. It was confirmed. It was also confirmed that this installation angle dependence can be alleviated or
eliminated by increasing the particle filling rate and increasing the number of particles. When particles are filled in both chambers, there is no significant change in the damping force
characteristics even if the installation angle is changed, and there is a large difference in the tendency of the particle's compressive force distribution and velocity vector depending on the
installation angle in terms of particle behavior. It was confirmed that there was no.
Sentence
Cundall, PA and Strack, ODL, A discrete numerical model for granular assemblies, Géotechnique, Vol. 29, Issue 1 (1979),
pp. 47-65.
Hanai, M., Ido, Y., Iwamoto, Y., Nishizawa, T. and Hayashi, K., Discrete element method simulation of dynamic behavior of
particles in a damper using a steel particle assemblage, Asian Conference on Experimental Mechanics 2016 Abstract PDF
Files, No.160310 (2016), pp. 352-353.
Koji Imon, Koichi Hayashi, Tahiro Higashi, Masashi Yamada, Reduction of installation angle dependence of granular damper damping force using electromagnet, Japan AEM
Academic Journal,Vol. 22, No. 2 (2014), pp.189-194.
Inoue, M., Yokomichi, I. and Hiraki, K., Particle damping with granular materials for multi degree of freedom system, Shock
and vibration, Vol. 18 (2011), pp. 245-256.
Lu, Z., Masri, SF and Lu, X., Studies of the performance of particle dampers attached to a two-degrees-of-freedom system
under random excitation, Journal of Vibration and Control, Vol. 17 (2011), pp. 1454-1471.
Mindlin, RD, Compliance of elastic bodies in contact, Transaction of ASME, Series E, Journal of Applied Mechanics, Vol.
16 (1949), pp. 259-268.
Morishita, Y., Ido, Y., Maekawa, K. and Toyouchi, A., Basic damping property of a double rod type damper utilizing an
elastomer particle assemblage, Advanced Experimental Mechanics, Vol. 1 (2016), pp. 93-98.
Saeki, M., Energy dissipation model of particle dampers, 50th AIAA / ASME / ASCE / ASC Structures, Structural Dynamics, and
Materials Conference (2009), AIAA, 2009-2692. Japan Society of
Mechanical Engineers, Mechanical Engineering Handbook, No. 6 Edition (1977)
，，pp. 3-34， Maruzen.
Toyouchi, A., Hanai, M., Ido, Y. and Iwamoto, Y., Damper force characteristics of a separated dual-chamber single-rod-type
damper using an elastomer-particle assemblage, Journal of Sound and Vibration, Vol. 488 (2020), 115625.
Toyouchi, A., Ido, Y., Iwamoto, Y. and Hanai, M., Damper force characteristics of a separated dual-chamber single-rod type
damper utilizing an elastomer particle assemblage in the case of both chambers containing particles, Journal of Vibration
and Acoustics, Vol. 143, No. 4 (2021), 041008.
Zahrai, SM and Rod, AF, Shake table tests of using single-particle impact damper to reduce seismic response, Asian Journal
of Civil Engineering, Vol. 16, No. 3 (2015), pp. 471-487.
Dedication
References
Cundall, PA and Strack, ODL, A discrete numerical model for granular assemblies, Géotechnique, Vol. 29, Issue 1 (1979),
pp. 47-65.

Hanai, M., Ido, Y., Iwamoto, Y., Nishizawa, T. and Hayashi, K., Discrete element method simulation of dynamic behavior of
particles in a damper using a steel particle assemblage, Asian Conference on Experimental Mechanics 2016 Abstract PDF
Files, No.160310 (2016), pp. 352-353.
Ido, Y., Hayashi, K., Azuma, T. and Yamada, M., Reduction of effect of installation angle of a damper utilizing a particle
assemblage on damping force, Journal of the Japan Society of Applied Electromagnetics and Mechanics, Vol. 22, No. 2 (2014),
pp. 189-194 (in Japanese).
Inoue, M., Yokomichi, I. and Hiraki, K., Particle damping with granular materials for multi degree of freedom system, Shock
and vibration, Vol. 18 (2011), pp. 245-256.
Lu, Z., Masri, SF and Lu, X., Studies of the performance of particle dampers attached to a two-degrees-of-freedom system
under random excitation, Journal of Vibration and Control, Vol. 17 (2011), pp. 1454-1471.
Mindlin, RD, Compliance of elastic bodies in contact, Transaction of ASME, Series E, Journal of Applied Mechanics, Vol.
16 (1949), pp. 259-268.
Morishita, Y., Ido, Y., Maekawa, K. and Toyouchi, A., Basic damping property of a double rod type damper utilizing an
elastomer particle assemblage, Advanced Experimental Mechanics, Vol. 1 (2016), pp. 93-98.
Saeki, M., Energy dissipation model of particle dampers, 50th AIAA / ASME / ASCE / ASC Structures, Structural Dynamics, and
Materials Conference (2009), AIAA, 2009-2692.
The Japan Society of Mechanical Engineers, JSME mechanical engineers' handbook, 6 ed. (1977), pp. 3-34, Maruzen
Publishing Co., Ltd. (in Japanese).
Toyouchi, A., Hanai, M., Ido, Y. and Iwamoto, Y., Damper force characteristics of a separated dual-chamber single-rod-type
damper using an elastomer-particle assemblage, Journal of Sound and Vibration, Vol. 488 (2020), 115625.
Toyouchi, A., Ido, Y., Iwamoto, Y. and Hanai, M., Damper force characteristics of a separated dual-chamber single-rod type
damper utilizing an elastomer particle assemblage in the case of both chambers containing particles, Journal of Vibration
and Acoustics, Vol. 143, No. 4 (2021), 041008.
Zahrai, SM and Rod, AF, Shake table tests of using single-particle impact damper to reduce seismic response, Asian Journal
of Civil Engineering, Vol. 16, No. 3 (2015), pp. 471-487.

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