Modelling of hysteresis using Masing–Bouc-Wen’s framework and search of conditions for the chaotic responses

In the present work hysteresis is simulated by means of internal variables. It was shown that Masing’s imitating mechanism of the energy dissipation presented in the differential equations of Bouc-Wen’s structure allows to simulate hysteresis from very different fields. The constructed analytical models of different types of hysteresis loops are simple, enable major and minor loops reproducing and provide a high degree of correspondence with experimental data. The models of such structure are convenient for the further investigation. Hysteretic systems under harmonic excitation described by models of such structure may reveal chaotic behaviour. Using an effective algorithm based on analysis of the wandering trajectories [1], [2], [3], [4], [22] and [23], an evolution of chaotic behaviour regions of oscillators with hysteresis is presented in various parametric planes. Substantial influence of a hysteretic dissipation value on the form and location of these regions, and also restraining and generating effects of the hysteretic dissipation on a chaos occurrence are ascertained. Conditions for pinched hysteresis are defined.