摘要
采用Hamilton变分原理建立了大范围运动平板的动力学模型.从理论上证明了不同大范围运动状态下平板中既可存在动力刚化效应,也可存在动力软化效应,且动力软化效应还可使板的平衡状态发生分岔而失稳.采用假设模态法验证了理论分析结果并得到了分岔临界值和近似后屈曲解.
A nonlinear dynamic model of a thin rectangular plate attached to a moving rigid is established by employing the general Hamilton＇ s variational principle. Based on the new model, both phenomena of dynamic stiffening and dynamic softening can occur in the plate was proved theoretically when the rigid undergoes different large overall motions including overall translational and rotary motions. It was also proved that dynamic softening effect even can make the trivial equilibrium of the plate lose its stability through bifurcation. Assumed modes method was employed to validate the theoretical result and analyze the approximately critical bifurcation value and the post-buckling equilibria.
出处
《应用数学和力学》
CSCD
北大核心
2006年第4期495-504,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10272002)
教育部博士点基金资助项目(20020001032)
关键词
柔性多体系统动力学
动力刚化
动力软化
稳定性
分岔
后屈曲
flexible multi-body system
dynamic stiffening
dynamic softening
stability
bifurcation
post-buckling
