Optimal design of inerter-based isolators minimizing the compliance and mobility transfer function versus harmonic and random ground acceleration excitation

This study is concerned with the problem of analysis and optimization of inerter-based systems. A main inerter system is generally composed of an inerter, a spring, and viscous damper. Series–parallel inerter systems and series inerter systems are two commonly used configurations of inerter-based systems. First, in this study, the H_∞ optimum parameters of inerter-based isolators are derived to minimize the compliance and mobility transfer function of a single-degree-of-freedom system under a harmonic ground acceleration excitation. Under the optimum tuning condition, it is shown that the proposed inerter-based isolators when compared with the traditional dynamic vibration absorber provide larger suppression of the peak value of the magnitude of compliance and mobility transfer functions of the primary system. For the studied cases, more than 40% and 45% improvement can be attained in terms of minimizing the compliance and mobility transfer functions, respectively, as compared with the traditional dynamic vibration absorber for the series–parallel inerter system and 15% and 11% improvement can be attained respectively, for the series inerter system. Finally, further comparison between the inerter-based isolators and traditional dynamic vibration absorber under white noise excitation also shows that the series–parallel inerter system and series inerter systems are superior to the traditional dynamic vibration absorber. The results of the studied systems show that more than 23% and 16% improvement are attained in terms of minimizing the compliance and mobility transfer functions respectively, as compared with the traditional dynamic vibration absorber for the series–parallel inerter system and 26% and 13% improvement can be attained respectively, for the series inerter system. The optimal parameters for different cases are obtained. It is shown that the optimal parameters obtained using the minimized mobility transfer function are smaller than those using the compliance transfer function at all mass ratios or inertance-to-mass ratio. The results of this study can provide theoretical basis for design of the optimal inerter-based isolators in engineering practice.