Equivalent linearization and parameter optimization of isochronous-pendulum tuned mass damper

Abstract

The isochronous-pendulum tuned mass damper (IPTMD) with curved supports was proposed to eliminate the loss of vibration control performance induced by large swing angles in our previous study. However, the nonlinearity caused by the IPTMD leads to difficulty in its parameter optimization. To overcome this issue, an approach based on the equivalent linearization method (ELM) and genetic algorithm (GA) is proposed in this paper to facilitate the optimal design of the IPTMD. First, based on the pseudo excitation method, the nonlinear IPTMD system is equivalent to a linear one using the ELM. The numerical results demonstrate that the equivalent linearization model of the IPTMD is fairly precise to approximate the original nonlinear IPTMD. Then the optimal design based on the H∞ norm and GA is performed to compute the design parameters of the IPTMD, which can minimize the peak response of the main structure. Additionally, to evaluate the effectiveness of the proposed approach, the optimal parameters are applied to compute the dynamic response of a tall building installed with the IPTMD under different earthquakes. The numerical results reveal that the optimized IPTMD can reduce the displacement of the tall building effectively.