Frequency-response curves for rate-independent hysteretic mechanical responses of complex shape

Abstract

We illustrate the performances of a brand new hysteretic model, recently proposed and denominated VRM+D, to characterize the nonlinear response of mechanical systems endowed with quite complex hysteretic behaviors. To this end, we combine the VRM+D with a continuation procedure based on Poincaré maps developed by Lacarbonara et al. in 1999. In this way, the steady-state response, as well as stability and bifurcation, of a large class of mechanical systems can be analyzed. In particular, we show the effectiveness of the VRM+D, in conjunction with the Poincaré map-based continuation procedure, in accurately predicting periodic solutions of the above-mentioned systems independently of the form of the hysteresis loop shapes. Furthermore, we draw some general considerations on the potential applications of the proposed approach in different fields of engineering to get an improved understanding of the dynamics of hysteretic mechanical systems subjected to cyclic loading.