形状记忆合金梁的建模及混沌阈值计算

PDF(1724 KB)

振动与冲击 ›› 2012, Vol. 31 ›› Issue (12) : 103-107,.

论文

形状记忆合金梁的建模及混沌阈值计算

葛根1; 王洪礼2; 许佳2

作者信息 +

Modeling and chaotic motion of a shape memory alloy beam vibration model

Ge Gen1 Wang Hong-li2 ,Xu jia2

Author information +

文章历史 +

摘要

从形状记忆合金（SMA）的等应变拉压实验数据出发，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。并根据弹性理论和Galerkin方法建立了形状记忆合金简支梁在受轴向激励时的振动模型。随后得出了自由振动系统的分岔特性。在利用待定固有频率法研究了模型的非线性参数对系统固有频率的影响后，根据待定固有频率法的计算结果和时间尺度变化提出了系统Melnikov函数的改进表达式，提高了计算形状记忆合金梁模型在参数激励下发生混沌的阈值的精度。数值模拟的结果证明了该途径的有效性。

Abstract

The vanderpol hysteretic cycle was applied to describe the hysteretic nonlinear characteristic of the strain-stress relation of a shape memory alloy （SMA）based on experimental data. A dynamical model with nonlinear damping of a simply supported SMA beam subject to axial excitation was proposed based on elastic theory and Galerkin’s approach. At first, the local bifurcations of the free vibration model were analyzed by the normal form theory. And the global bifurcation was studied Melnikov approach. Secondly, the undermined fundamental frequency and normal form method was utilized to study the influence of the disturbing parameters to the fundamental frequency. Finally, the improved Melnikov expression for the oscillator was built based on the results of the undermined fundamental frequency method and time scale transformation to obtain the approximate threshold value of chaotic motion in the Homoclinicity points of view. The numerical results show the efficiency of the theoretical analysis.

导出引用

葛根;王洪礼;许佳. 形状记忆合金梁的建模及混沌阈值计算[J]. 振动与冲击, 2012, 31(12): 103-107,

Ge Gen Wang Hong-li;Xu jia. Modeling and chaotic motion of a shape memory alloy beam vibration model [J]. Journal of Vibration and Shock, 2012, 31(12): 103-107,