摘要
导出作大范围刚体运动弹性薄板包括了几何非线性和中面变形之间的相互耦合（耦合变形）的动力学控制方程．分析了几何非线性和耦合变形各自对系统动力学性质的影响，得到了在传统方法上只考虑几何非线性，系统将通过同宿轨分岔过渡到混沌运动；若在传统方法上考虑耦合变形，系统稳定且数值解收敛，与实际情形相符．
The dynamical equations of thin elastic plates in large overall motions considering theeffects of geometric non-linearity and coupling deformation are obtained in this paper, and whicheffects to the dynamics of this system are analyzed. The plots of phase plane and time historyin case of considering geometric non-linearity and coupling deformation and only considering geometric non-linearity are shown in Fig.2 and Fig.3 respectively, and the plot of displacement oftransverse vibration is shown in Fig.4. The conclusions can obtained that the system is stable andconvergent and the chaotic motions will happen in this system through the bifurcation of homo-climic orbits only considering the effects of non-linearity form Fig.2 and Fig.3, and the system isstable and its numerical result is convergent only considering the effects of coupling deformationwhich spin speed is 3.14 rad/s and spin-up time is 30 s.
出处
《力学学报》
EI
CSCD
北大核心
1999年第2期243-249,共7页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
博士点基金
关键词
弹性薄板
大范围运动
几何非线性
耦合变形
thin elastic plate, large overall motions, geometric non-linearity, coupling deforma- tion, stability
