摘要
本文基于 Ｖｏｎ Ｋａｒｍ ａｎ 变形理论和 Ｈａｍ ｉｌｔｏｎ 变分原理，建立了作大范围运动弹性梁包括了中面变形之间的相互耦合的动力学控制方程。利用 Ｓｃｈｗ ａｒｚ 不等式和 Ｆｒｏｂｅｎｉｕｓ 方法分析了该系统解的周期性和模态解析解，比较了静边界条件下和大范围运动作用时弹性梁振动模态的差别，当大范围转动角速度大于它的基频时，用静边界条件下的模态来离散该连续系统，将存在较大的误差。
Based on Von Karman′s theory and Hamiton′s principle, this paper intends to establish the dynamic equations of elastic beam considering the coupling between deformations of middle surface in large overall motions. Employing Schwarz′s and Frobenius′s methods, the periodic and modal solution of this kind of system are also analyzed. The result shows that the frequency of the system is increased with the raise of rotational velocity and there is great difference between the mode of system when the rotational velocity is greater than the first frequency.
出处
《振动与冲击》
EI
CSCD
1999年第1期12-16,共5页
Journal of Vibration and Shock
基金
国家自然科学基金
博士点专项基金
关键词
弹性梁
大范围运动
耦合变形
模态
振动频率
elastic beams, large overall motions, coupling between deformation of middle surface, mode and frequency, difference
