COUPLED STRUCTURAL DYNAMIC

RESPONSE USING PASSIVE

DAMPERS

Luis Alejandro Pérez, Suzana Avila, Graciela Doz.

7th International Symposium on Dynamic Problems of

Mechanics

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

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

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 (mji) [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.

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

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.

iiiiMC ** 2

2**

iiiMK

(1)

(2)

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

*

1MCKM 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.

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]

11 0.00437 0.08573 1.73199

2 0.00437 0.08573 1.73199

21 0.00437 0.08573 1.73199

2 0.01382 0.17391 2.22766

31 0.00437 0.08573 1.73199

2 0.02409 0.22198 2.10129

51 0.01382 0.17391 2.22766

2 0.01382 0.17391 2.22766

61 0.01382 0.17391 2.22766

2 0.02409 0.22198 2.10129

91 0.02409 0.22198 2.10129

2 0.02409 0.22198 2.10129

Table 2 – Rms dynamics response of uncoupled reduced structures

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.

• Coupled models with different mechanical and physical properties

• Coupled models with different mechanical and physical properties

• Coupled models with different mechanical and physical properties

• Coupled models with different mechanical and physical properties

• Coupled models with different mechanical and physical properties

• Coupled models with different mechanical and physical properties

• 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.

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

Thanks for your attention!!