Stationary response of MDOF hysteretic system under random excitation

Hysteretic nonlinearity is a common phenomenon in engineering fields, and many mathematical models have been developed to describe it. In theory, hysteretic restoring forces are generally decomposed into equivalent stiffness and equivalent damping. However, due to the complexity of hysteretic nonlinearity, obtaining analytical expressions for these equivalent components is extremely challenging. In terms of theoretical methods, most existing research focuses on single-degree-of-freedom (SDOF) hysteretic systems, and there are few analytical solutions for multi-degree-of-freedom (MDOF) hysteretic systems. This paper proposes a method for studying the response of stochastically excited MDOF hysteretic systems. Using the Bouc-Wen hysteretic model as an example, the expressions for the equivalent stiffness and damping coefficients are obtained. By applying the stochastic averaging method, the statistics of the system response can be obtained. An example is given to illustrate this method, and the numerical results show that this method can accurately predict the response of MDOF hysteretic systems under random excitation.