# Structural health monitoring of single degree of freedom flexible structure having active mass damper under seismic load

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## Abstract

In this research, the application of active mass damper (AMD) has been experimentally tested using electromagnetic uniaxial shake table. The characteristic of an active damper has been presented. A state-feedback controller has been introduced for single flood active mass damper (AMD) using numerical modeling. The model was built and experiment was performed in laboratory having AMD to discuss the effect of model parameters and the development of parameters by inputting the data obtained from most severe earthquake on Oct 8 2005 in Pakistan. The system model, control design and observer were tested on shake table having 46 cm × 46 cm dimensions in real time vibrations. The shake table used has capability of running with powerful actuator having scaled accelerograms of real time earthquakes. The setup to operate the controller on real experimental work was discussed. It was observed that about 40% reduction in vibration can be achieved using active mass damper.

## Keywords

Seismic simulation Active mass damper Shake table test## Introduction

The use of active and passive control system, e.g., tuned mass dampers, viscous dampers etc. is increased now a day to prevent earthquake damages in high-rise buildings using controller, e.g., linear quadratic regulators [6, 7, 8, 9, 10].

In this research, the application of active mass damper (AMD) has been experimentally tested using electromagnetic uniaxial shake table. The characteristic of an active damper has been presented. A state-feedback controller has been introduced for single floor active mass damper (AMD) using numerical modeling [11, 12, 13, 14, 15]. Shake Table Test of earthquakes signal obtained from strong motions Centre at Nilore and Abbotabad during Oct 8, 2005 earthquake obtained from Pakistan Atomic Energy Commission (PAEC) and the observed damping was compared for active control cases [16].

## Research performed before 2005 earthquake

The earthquake data obtained from PAEC was not used previously for any vibration control experiments, although many researchers suggested various control techniques to be used in buildings and bridges [17, 18]. The probability of reducing stress has been investigated on single floor experimental system. To input the desired earthquake loading various simulations were produced using SIMULINK/MATLAB. Various cases were analyzed, and the module was amplified to obtain desirable results [19, 20, 21].

## Approach

### Active mass damper system

The upper part of the structure fitted with the shaft and support used to function with cart having mass which is controllable. The structure is moved along the same direction of the cart. Particularly, it is an accurate form of solid aluminum cart operated by DC motor having gearbox [22, 23, 24].

Once the motor started, the output shaft generated the torque by gear and track function which results in force control to run the cart. A multi-*I*/*O* panel is used to develop controller same as real time control function. SIMULINK is used to develop the controller of the system.

### Analytical model

*M*

_{c}) = 0.68 kg, floor mass (

*M*

_{f}) = 0.7 kg,

*K*

_{f}is floor stiffness constant which is 6

*EI*/

*l*

^{3}= 520 N/m,

*x*

_{f}(

*t*) is floor position at time ‘

*t*’,

*x*

_{c}(

*t*) is cart position at time ‘

*t*’,

*E*= 200 GPa,

*I*= 3.599 × 10

^{−12}m

^{4},

*J*

_{m}is cart rotor moment of inertia = 0.038 10

^{−5}kg m

^{2},

*K*

_{g}is cart gear ratio = 3.71,

*r*

_{mp}is pinion radius = 0.00625 m,

*F*

_{c}is linear force applied to cart and the Lagrangian is defined as

*A*,

*B*,

*C*and

*D*and state vector

*X*and output vector

*Y*:

The analytical model shown in Fig. 2. The total mass of structure is 3 kg, the height is 500 mm, natural frequency is 2.6 Hz, and linear stiffness is 520 N/m.

### Observer system

*G*(

*Y*−

*Y*

_{o}) multiplied by the observer gain matrix. The obtain estimated state vector can then be used for state-feedback law, as expressed Eqs. (9) and (10)

*X*_{e} is the estimation error it will asymptotically go to zero if (*A *− *GC*) is stable.

### Seismic excitation

The faulting mechanism solution indicated that it was thrusting fault and damages were recorded to structures of the area.

As there was a limit ± 7.62 cm maximum stroke of the shaking table. To simulate an earthquake on the shaking table system, the ground motion data was scaled to ± 3 cm. The gravitational acceleration with units (g) has been recorded and the method was produced in MATLAB which was used to compute the desired positions such that the measured accelerations yielded on the STII are equivalent to the recorded values.

### Simulation

## Vibration control

## Conclusion

Application of shake table test for presenting the earthquake engineering and structural dynamic concept is convenient. The mathematical and experimental aspects have been demonstrated with hands on experiment using real time earthquake ground motions having active mass damper. Public awareness of seismic hazards using the Shake Table experiment may be used. The earthquake ground motions were used to analyze the structure using controlled response of the buildings. The use of active mass damper is an effective tool to control the severe damage to the structure. After various experimental work, the control model for real time earthquake has been proposed using active mass damper. The experiments were successful. The model will be expanded for future research.

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