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。
One pre-buckled simply-supported giant magnetostrictive material (GMM) thin film laminated beam model under axial magnetic excitations was proposed. The magnetostrictive force was simplified as a harmonic excitation. Applying Hamilton principle and Galerkin approach, the model was expressed as a one-dimensional vibrating model with parametric excitation. With the help of the undermined natural frequency method and normal form theory, Melnikov approach was improved to calculate more precise threshold value of the amplitude of excitation leading to chaos. The numerical simulations showed that the performance of the new Melnikov approach is much better than the traditional one.
出处
《振动与冲击》
EI
CSCD
北大核心
2013年第17期165-170,共6页
Journal of Vibration and Shock
基金
国家自然科学基金(11272229)
天津市教委科技项目(20120902)
