On a class of non-smooth oscillators

摘要

The aim of this paper is to provide a unifying framework for several models of non-smooth oscillators with hysteresis which have attracted considerable interest in the engineering literature over the past three decades. By using the theory of maximal monotone operators in conjunction with a relatively recent result of Haraux and Otani (1990, Journal of the Mathematical Society of Japan, 42: 277-294) we are able to characterize the attractors of these systems; in particular, it is shown that the study of their bounded orbits lies at the heart of understanding their possible dynamics. The interplay between material nonlinearity and viscous damping is analysed for a special case of the original model and some new features of this problem are revealed.