形状记忆合金梁在简谐和白噪声联合激励下的混沌及安全盆侵蚀现象

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (23) : 1-5.

论文

形状记忆合金梁在简谐和白噪声联合激励下的混沌及安全盆侵蚀现象

葛根1 竺致文2 许佳2

作者信息 +

CHAOS AND FRACTAL BOUNDARY OF SAFE BASIN OF A SHAPE MEMORAY AOLLY BEAM SUBJECTED TO HAMONIC AND WHITE NOSIE EXCITATIONS

GeGen1 ZhuZhiWen2 ,XuJia2

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文章历史 +

摘要

本文利用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。

Abstract

The vanderpol cycle was applied to describe the hysteretic nonlinear characteristic of the strain-stress relation of a shape memory alloy （SMA）.A dynamical model of a simply supported SMA beam subject to both parametrical harmonic and external Gaussian excitation was proposed based on Galerkin’s approach. At first, the stochastic Melnikov integral was given theoretically wich means the necessary rising of noise-induced chaotic response in the system. To quantify the noise-induced chaos, the boundary of the system’s safe basin is firstly studied and it is shown to be inclusively fractal when chaos arises based on the stochastic Melnikov method. The numerical results show the efficiency of the theoretical analysis.

导出引用

葛根竺致文许佳. 形状记忆合金梁在简谐和白噪声联合激励下的混沌及安全盆侵蚀现象[J]. 振动与冲击, 2012, 31(23): 1-5

GeGen ZhuZhiWen ;XuJia. CHAOS AND FRACTAL BOUNDARY OF SAFE BASIN OF A SHAPE MEMORAY AOLLY BEAM SUBJECTED TO HAMONIC AND WHITE NOSIE EXCITATIONS[J]. Journal of Vibration and Shock, 2012, 31(23): 1-5