Document Type : Research Article

**Authors**

Engineering Department , University of Mohaghegh Ardabili, Ardabil, Iran

**Abstract**

In this paper, designing variable stiffness semi-active tuned mass damper (SATMD) for

mitigating the responses of nonlinear structures under earthquake excitation has been studied. Two semiactive control algorithms based on instantaneous optimal control and clipping control concept as well as

modified balance control have been developed to determine the optimal stiffness of SATMD for nonlinear

structures in each time step. For determining optimal parameters of semi-active control system including

the weighting matrices in performance index of control algorithm as well as the maximum and minimum

values of SATMD stiffness, an optimization problem for minimization of structure maximum response has

been defined where genetic algorithm (GA) has been used for optimization. For numerical simulations, an

eight-story nonlinear shear building with bilinear hysteresis behavior has been subjected to a white noise

excitation and optimal SATMDs have been designed. The results showed that optimal variable stiffness

SATMD using both control algorithms has been effective in suppressing the seismic responses of nonlinear

structure. Also, variable stiffness SATMD shows better performance than TMD and variable damping

SATMD in structural response controlling. Comparing the performance of the variable stiffness SATMD

under testing earthquakes which were different from design record, showed that the efficiency of SATMD

depends on the characteristics of excitation, hence design record needs to be chosen properly.

mitigating the responses of nonlinear structures under earthquake excitation has been studied. Two semiactive control algorithms based on instantaneous optimal control and clipping control concept as well as

modified balance control have been developed to determine the optimal stiffness of SATMD for nonlinear

structures in each time step. For determining optimal parameters of semi-active control system including

the weighting matrices in performance index of control algorithm as well as the maximum and minimum

values of SATMD stiffness, an optimization problem for minimization of structure maximum response has

been defined where genetic algorithm (GA) has been used for optimization. For numerical simulations, an

eight-story nonlinear shear building with bilinear hysteresis behavior has been subjected to a white noise

excitation and optimal SATMDs have been designed. The results showed that optimal variable stiffness

SATMD using both control algorithms has been effective in suppressing the seismic responses of nonlinear

structure. Also, variable stiffness SATMD shows better performance than TMD and variable damping

SATMD in structural response controlling. Comparing the performance of the variable stiffness SATMD

under testing earthquakes which were different from design record, showed that the efficiency of SATMD

depends on the characteristics of excitation, hence design record needs to be chosen properly.

**Keywords**

- Variable stiffness semi-active tuned
- mass damper
- Non-linear structures
- Semi-Active Control
- Clipped optimal control algorithm
- Modified balance control algorithm

**Main Subjects**

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