Higher-Order Frequency Response Functions for Hysteretic Systems

Abstract

Volterra analysis for nonlinear systems has long been established as an informative means of investigating nonlinear system behaviour; in particular, the Volterra kernels can be directly transformed into Higher-order Frequency Response Functions (HFRFs) which allow direct visualisation of nonlinear frequency interactions in system responses. Unfortunately, Volterra analysis is restricted to certain (smooth, without memory) classes of systems which exclude many which are of major interest in structural dynamics. In the current paper, it is demonstrated that, by considering non-smooth systems as a combination of smooth systems, it is possible to develop a Volterra series representation for such systems. The paper also presents an approach for rewriting the equation of motion of the Bouc-Wen model of hysteresis so as to remove the hidden state thereby permitting further analysis using the Volterra series.