Random response analysis of nonlinear structures with inerter system

Most researches on inerter focused on the mechanism or deterministic vibration analysis, and some studies lied in the random vibration of linear structures. However, many structures exhibit the nonlinear characteristics under a large excitation, and the effects of inerter system on additional properties and probabilistic distribution of random response of nonlinear structure under random excitation have rarely been considered at present. Based on the enhancement effect of inerter system on nonlinear structure, the influence of various components of inerter system on the response suppression of nonlinear structure is investigated from the probability level, and a developed response analysis method suitable for inerter system is proposed in this paper. The stochastic differential equation of nonlinear structure with inerter is established in this work, in which both the nonlinear structure without hysteresis and the hysteretic structure are considered. The probability density function of structural response is obtained by the exponential polynomial closure (EPC) method combined with the state -space-split technique. In terms of nonstationary random excitation, a scheme of equivalent stationary excitation is proposed to split the state space vector. Meanwhile, the EPC method is developed through the reduction of undetermined coefficients in the probabilistic solution, which significantly improves the efficiency. Numerical results show that the response suppression effectiveness of inerter system is robust to nonlinear structures, and the inerter system mainly provides additional damping for the primary structure, thereby achieving the vibration mitigation. However, an excessively rigid inertia system may lead to a negative additional stiffness for the primary structure and inhibit the vibration mitigation.

Automated summary

This paper investigates the response suppression effectiveness of inerter system on nonlinear structures under random excitation and proposes a response analysis method suitable for inerter system. Numerical results show that the response suppression effectiveness of inerter system is robust to nonlinear structures.