Analytical optimal design of inerter system for seismic protection using grounded element

Compared with classical tuned mass damper (TMD), inerter system has higher damping efficiency and wider vibration control range. The traditional fixed-point theory of TMD have been used in most of the previous optimal parameter designs of inerter system, the optimized parameters obtained are expressed by the inerter-mass ratio, which may not be applicable to some specific inerter systems (such as tuned viscous mass damper, TVMD) or are too cumbersome. In this paper, the optimal parameters of the inerter system based on the characteristics of the grounded element and muti-performances demand are derived, and demand-based global optimal methods of the design parameters of the inerter system are proposed and compared. The correctness, feasibility and applicability of methods are verified by optimization examples and typical excitation including ground motions. The optimal parameters combinations of the inerter system derived based on the grounded element exist unique analytical expressions. When the value of the grounded element and the objective function are determined, the local optimal design of the inerter system can be realized. If the precise displacement vibration control of original structure is needed, the optimal parameters obtained by the stochastic displacement response that is taken as the objective function can be selected. If the demand is that total energy input of original structure requires is minimum, and the requirements for small displacement control effect are not strict, the optimal parameters of the inerter system obtained by the stochastic velocity response can be selected. If it is necessary to minimize the engineering cost and the control the peak and RMS displacement at the mean time, the optimal parameters of the inerter system obtained by deformation enhancement coefficient of damping element can be selected. The analytical expressions of the optimal design parameters of the inerter system based on the grounded element are concise and the processes of optimal design based on multiple performances objectives are simple, which can be applied to a variety of demands in practical engineering.