Response characteristics of inelastic 2-DOF primary-secondary system

Dynamic analysis of primary-secondary systems with consideration of inelastic response has recently become an important issue in the design of civil engineering structures. The purpose of this paper is to develop a fundamental understanding of the response of such systems to wide-band input. Previous research on linear response has shown that two-degree-of-freedom (2-DOF) primary-secondary systems contain most of the essential properties of more general systems, yet are sufficiently simple to allow derivation of analytical expressions that mathematically quantify and characterize these properties. In this paper, these results are combined with nonlinear random vibrations theory to examine how nonlinear response differs from linear response. By assuming moderately small nonlinearities, perturbation methods are used to develop analytical expressions for wide-band nonlinear response. The results show that small nonlinearities results in significant reduction of the response. In the final section of the paper, the results are extended to degrading systems subjected to nonstationary excitation.