Analytical optimization for tuned viscous inerter damper coupled to quasi-zero-stiffness isolation system

Abstract

According to the H_∞ principle, the dynamical performance optimization of a quasi-zero-stiffness (QZS) isolation system with an additional tuned viscous inerter damper (TVID) is studied by using analytical method. The approximate analytical solutions of the QZS system coupled with TVID are solved by using the complexification-averaging method, and the expression of stability conditions for steady-state solutions is derived based on Lyapunov method and Routh-Hurwitz criterion. Based on the fixed-point theory, considering the nonlinear stiffness and weak damping of the primary system, the stiffness and damping ratios of TVID coupled to QZS system are optimized by using the equal-peak method. The detailed analysis is conducted on the impact of TVID parameters and their corresponding optimization parameters on the dynamic behavior of the QZS primary system, including saddle-node (SN) bifurcation, Hopf bifurcation, backbone curve of amplitude-frequency response, and force transmissibility. According to the analysis, it is found that the steady-state motion of the system can enter quasi-periodic motion or even chaotic motion after losing stability through Hopf bifurcation. By optimizing the parameters of TVID, the number of SN bifurcation regions of the QZS main system can be reduced from 2 to 1, the Hopf bifurcation region can be eliminated, and the number of branches of backbone curve can be reduced from 2 to 1, thereby improving the dynamical performance of the QZS system.