COUPLED STRUCTURAL DYNAMIC RESPONSE USING PASSIVE DAMPERS

1. COUPLED STRUCTURAL DYNAMIC
RESPONSE USING PASSIVE
DAMPERS
Luis Alejandro Pérez, Suzana Avila, Graciela Doz.
7th International Symposium on Dynamic Problems of
Mechanics

2. The impacts between two adjacent buildings during major earthquakes in the past have caused
significant damage and great loss of life.
Based on this fact, in last years the so called structural coupling method has been proposed, it is
an efficient structural control technique.
It consists of connecting two neighboring buildings through a coupling device, with the aim of
reducing the undesirable dynamic effects, taking advantage of the mechanical properties of each
structure. In this way it is possible to control both structural responses simultaneously, that is
specifically attractive for this technique.
1. Introduction

3. Due to the coupling technique potential, this work evaluates the effectiveness of a passive
control working as a coupling device on mitigating dynamics response of two neighboring
structures.
This connecting device is represented through a spring and a linear damper, which mechanical
properties (stiffness and damping values) were varied in each analysis.
The acceleration time history of El Centro earthquake (north-south component) was used as an
horizontal excitation.
All the analysis were performed with MATLAB.
1. Introduction

4. 2. Coupled structures models
Starting from two buildings with mechanical and physical parameters identical, or the
same mass and stiffness, with the same number of floors and height.
Structure Mass (mj
i) [kg] Stiffness (kj
i) [MN/m] ζ [%]
1 30000 12.58 3
2 30000 12.58 3
Table 1 – Parameters of the structures used in numerical modeling
Figure 1 – Uncoupled symmetric structures.
Figure 2 – Uncoupled structures with different heights.

5. 2. Coupled structures models
The structures with different heights are coupled generating several combinations, resulting on a
total of nine possible combinations, illustrated on Figure 3.
Figure 3 – Coupled models varying the floor numbers of the two neighboring structures

6. Figure 4 – 2DOF coupled system
2. Coupled structures models
In order to reduce the data processing time, the multiple-degree-of freedom (MDOF) models are
reduced to two degree of freedom models (2DOF) using modal analysis (Soong e Dargush,
1997).
To obtain the system reduced models shown on Figure 3, a modal analysis of the uncoupled
structures was performed. For each one of them, natural frequencies, mode vibrations and the
associated effective modal mass (Mi
*) were obtained.
iiii
MC **
2
2**
iii
MK 
(1)
(2)

7. 3. Mathematical formulation
The equation of motion for the structure of Figure 5 is given by:
Figure 5 – 2DOF coupled system
       tGttt gxxKxCxM  





























1
1
,,,
0
0
3
*
23
33
*
1
3
*
23
33
*
1
*
2
*
1
MCKM G
cCc
ccC
kKk
kkK
M
M
• M, C and K are the mass, stiffness and damping matrices
of the coupled structure.
• x(t) the vector (n+m,1) of story displacements with respect
to the ground.
• The k3 and c3 values represent the passive device
mechanical properties.

8. 4. Numerical analysis
First, it was calculated the rms dynamics response of the uncoupled reduced structures.
Model Structures xrms [m] vrms [m/s] arms [m/s²]
1
1 0.00437 0.08573 1.73199
2 0.00437 0.08573 1.73199
2
1 0.00437 0.08573 1.73199
2 0.01382 0.17391 2.22766
3
1 0.00437 0.08573 1.73199
2 0.02409 0.22198 2.10129
5
1 0.01382 0.17391 2.22766
2 0.01382 0.17391 2.22766
6
1 0.01382 0.17391 2.22766
2 0.02409 0.22198 2.10129
9
1 0.02409 0.22198 2.10129
2 0.02409 0.22198 2.10129
Table 2 – Rms dynamics response of uncoupled reduced structures

9. 4. Numerical analysis
Next, coupled models dynamics responses were calculated varying the connection device
properties k3 and c3 in order to obtain the better response reduction;
The rms dynamics responses obtained are compared with those of the uncoupled structures in
order to evaluate advantages and disadvantages of this technique and the effectiveness of the
coupling device.

10. • Coupled models with different mechanical and physical properties

11. • Coupled models with different mechanical and physical properties

12. • Coupled models with different mechanical and physical properties

13. • Coupled models with different mechanical and physical properties

14. • Coupled models with different mechanical and physical properties

15. • Coupled models with different mechanical and physical properties

16. • Coupled models with same mechanical and physical properties
That indicates that the coupling technique in this case is not effective, being necessary a
difference on the mechanical and physical properties of the neighboring structures to harness the
potential of this technique.
As a result, independently of considered k3 and c3 values, the passive connecting device loses its
effectiveness. Thus, the results for these models are disregarded.

17. The developed analysis showed that the effectiveness of the control method through coupling
depends mainly on the neighboring buildings properties as mass, stiffness, number of floors
beside the connecting device properties.
In the analyzed models, it was found that to get a better performance of the coupling technique,
the relation between heights should be less than two, in other words the higher structure cannot
overcome twice the short structure.
A height ratio higher or equal two implies on a reduction on the response of the higher structure,
increasing, however, the response amplitudes of the other structure, being advisable to install an
additional control device in this structure.
5. Conclusions

18. Thanks for your attention!!