Equivalent Linearization and Parameter Optimization of the Negative Stiffness Bistable Damper

Abstract

The negative stiffness bistable damper (NSBD) was proposed to suppress structural dynamic responses in our previous study. The vibration mitigation performance of the NSBD is influenced by its design parameters, including negative stiffness, cubic stiffness, and damping coefficients. However, it is extremely challenging to directly acquire the ideal design parameters of the NSBD owing to its inherent nonlinearity. To address this disadvantage, the optimal design approach for the NSBD, based on the equivalent linearization method (ELM) and genetic algorithm (GA), is presented in this paper. The nonlinear NSBD system can be transformed to a linear system utilizing the ELM based on the pseudo-excitation method (PEM). The linearization model that corresponds to the nonlinear NSBD is fairly accurate in its approximation and can be indicated from the numerical results. Then, the main structure’s peak response is minimized through the optimization of the design parameters of the NSBD using the H∞ norm and GA. Moreover, the proposed approach’s effectiveness is assessed using the optimal parameters to calculate the displacement responses of a tall building equipped with the NSBD during various seismic excitations. As revealed by the numerical results, the displacement of the tall building can be effectively restrained by the optimized NSBD.