Abstract
The aim of this study is to describe the hysteretic nonlinear characteristic of the strain–stress relationship of a shape memory alloy; a Van-der-Pol hysteretic cycle is applied to simulate the hysteretic loops. Then, the model of a simply supported shape memory alloy beam with nonlinear damping was proposed. The stability of the free vibration is studied. The criterion determining the stochastic chaos is obtained by the random Melnikov approach. To verify the theoretical analysis, numerical experiments are carried out. The results totally agreed with the analytical work. Clear fractal boundaries of the system's safe basin are observed.
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