The van-der-pol cycle was adopted to describe hysteretic nonlinear characteristic of stress-strain relation of a shape memory alloy ( SMA). A dynamic model of a simply supported SMA beam subjected to both axial simple harmonic and lateral white noise excitations was proposed based on Galerkin's approach. At first, the stochastic Melnikov process integral was given theoretically to get the necessary condition for the noise-induced chaotic response of the system. To quantify the noise-induced chaos, the boundary of the system's safe basin was studied and it was shown to be inclusively fractal when chaos arised based on the stochastic Melnikov method. The numerical results showed that the theoretical analysis is effective.%利用van-der-pol环模型模拟了形状记忆合金在加载和卸载过程中的应力应变迟滞环特性,根据弹性理论和Galerkin方法建立了形状记忆合金简支梁在受轴向简谐激励和横向白噪声激励时的振动模型.根据随机系统的Melnikov过程方法,得到了系统发生随机混沌的阈值必要条件.用数值方法得到初值对系统安全性的影响及激励参数对系统安全盆边界的侵蚀现象.观察结果发现,随机激励幅值的增大会增强安全盆的内部出现分形特性.
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