Modelling of hysteresis using Masing-Bouc-Wen’s framework and search of conditions for the chaotic responses. (English) Zbl 1221.70027

Summary: Hysteresis is simulated by means of internal variables. It is shown that Masing’s imitating mechanism of energy dissipation present in the differential equations of Bouc-Wen’s structure allows one to simulate hysteresis phenomena arising in very different fields. The constructed analytical models of different types of hysteresis loops are simple, allow one to reproduce major and minor loops and provide a high degree of agreement with experimental data. The models of such a structure are convenient for further investigation. Hysteretic systems under harmonic excitation described by models of such a structure may reveal chaotic behaviour. Using an effective algorithm based on the analysis of wandering trajectories, the evolution of regions of chaotic behaviour 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 occurrence of chaos are ascertained. Conditions for pinched hysteresis are defined.


70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics
34C28 Complex behavior and chaotic systems of ordinary differential equations
34C55 Hysteresis for ordinary differential equations
Full Text: DOI


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