预屈曲超磁致伸缩材料层合梁的混沌研究

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (17) : 165-170.

论文

预屈曲超磁致伸缩材料层合梁的混沌研究

葛根1 竺致文2 许佳2

作者信息 +

Chaos of a post-buckled Giant- Magnetostrictive thin film laminated beam

GeGen1, ZhuZhiWen2 ,XuJia2

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文章历史 +

摘要

根据基底的柔性力学特性和上下超磁致伸缩材料（GMM）薄膜镀层，考虑梁的几何非线性后用哈密尔顿变分原理建立了两端简支的层合梁在预屈曲情况下的动力学模型，并求得屈曲的挠度。利用Galerkin方法将运动方程离散为一个常微分参数激励模型以梁中点静态挠度为特征尺度对系统无量纲化。利用结合复规范型理论的待定固有频率法研究了轴向激励幅值对系统固有频率的影响，根据待定固有频率法的结果和时间尺度变化改进了系统同宿轨道的表达式，提高了计算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此途径的有效性。

Abstract

One buckled simply supported giant magnetostrictive material (GMM) thin film laminated beam model under axial magnetic excitations is proposed. The magnetostrictive force is simplified as a harmonic excitation. Appling the Hamilton principle and Galerkin approach the model is expressed as a one dimensional vibrating model with parametrical excitation. With the help of the undermined fundamental frequency method and normal form theory the Melnikov approach is improved to calculate more precise threshold value of the amplitude of excitation leading to chaos. The numerical simulation shows the performance of the new Melnikov approach is much better than the traditional way.

导出引用

葛根竺致文许佳. 预屈曲超磁致伸缩材料层合梁的混沌研究[J]. 振动与冲击, 2013, 32(17): 165-170

GeGen;ZhuZhiWen;XuJia. Chaos of a post-buckled Giant- Magnetostrictive thin film laminated beam[J]. Journal of Vibration and Shock, 2013, 32(17): 165-170