Nonlinear response of hysteretic oscillator under evolutionary excitation

In this article a state variable approach for the description of an hystere tic restoring force model is presented. In particular the approach is able to describe the nonlinear behaviour in the force-displacement plane by subs tantial modifications at the basic set of differential equations governing the dynamics of the oscillator and the state equation formulated on the bas is of an endochronic relation. The attention is focussed on the loading-rel oading paths of short amplitude where the effective reproduction of the beh aviour is usually more difficult, as reported in experimental tests. It is observed that the phenomenological nature of the basic model can be respons ible of certain violations to fundamental physical postulates for stable ma terials especially during short amplitude load cycles. The smooth solution to the problem that is proposed here is presented as an implementation of t he existing hysteretic model. In the numerical example a comparison is set up imposing a critical displacement path and the dynamic response under evo lutionary excitations of environmental nature is examined. The basic and th e improved model are compared showing significant differences both in the l ocal and in the global behaviour. (C) 1999 Elsevier Science Ltd and Civil-C omp Ltd. All rights reserved.