摘要
本文研究了非惯性参考系中弹性薄板的大范围运动与大变形运动相互耦合时的内共振。在建立了该动力系统运动控制方程的基础上，利用多尺度法得到了非惯性参考系中弹性薄板纵横振动强相互耦合和弱相互耦合时产生内共振固有频率所需满足的条件，讨论了弱相互耦合时横向振动产生分岔导致失稳的条件；用数值仿真模拟了系统包括了横向和纵向转动角速度两个分岔参数的空间分岔集，讨论了该动力系统的稳定性，并得到了它的分叉响应曲线。
This paper presented an analysis of dynamics of thin elastic plates in large overallmotions. Based on the established dynamic equations of thin elastic plates in large overallmotions and used the method of multiple scales, the internal resonance of a simply supported thinelastic plate was investigated. The conditions of causing internal resonance which the natUralfrequencies must satisfy are obtained, and three dimensional diagram of set of bifurcation anddifferent diagrams of bifurcation response curves are given in this paper.
出处
《工程力学》
EI
CSCD
北大核心
1999年第3期30-37,共8页
Engineering Mechanics
基金
国家自然科学基金
国家教委博士点专项基金
关键词
非惯性参考系
弹性薄板
纵横振动耦合
内共振
noninertia
thin elastic plate
internal resonance
bifurcation
bifurcation responsecurves
