Dynamical Behaviour of Hysteretic Systems Under Harmonic Forces

Abstract

Abstract The study of the response of hysteretic systems to harmonic forces is formulated in a suitable phase space in which an originally multi-valued restoring force is represented by proper functions. The asymptotic response can thus be studied using an approach which derives from the Poincaré map concept and avoids approximate analytical techniques. On account of the peculiarity of the hysteretic systems considered, based on Masing rules, the dynamics are studied in a reduced dimension phase space using an efficient solution algorithm. Only the periodic response is taken into account, which is described by frequency response curves at various intensities of the excitation and by the frequency content. The results presented mainly refer to a two d.o.f. system with two linear frequencies in a ratio of 1:3 and 1:4. The response is highly complex with numerous peaks corresponding to higher harmonics. The range of frequency in which the effects of internal resonance are evident is much larger than the nonlinear elastic case. In particular the coupling produces a strong modification of the frequency response curves and of the oscillation shape of the structure.