扁球薄壳在大挠度下的非线性动力稳定性  

NONLINEAR DYNAMIC STABILITY OF THE SHALLOW THIN SPHERICAL SHELLS UNDER LARGE DEFLECTION

作　　者：王新志[1] 李林[1] 王钢[2] 顾小妹[1] 邱平[1] 

机构地区：[1]兰州理工大学理学院,兰州730050 [2]兰州理工大学设计艺术学院,兰州730050

出　　处：《工程力学》2008年第10期76-79,85,共5页Engineering Mechanics

基　　金：甘肃省自然科学基金项目(3ZS042-B25-006)

摘　　要：根据薄壳非线性动力学理论,由扁球薄壳大挠度基本方程,在周边固定夹紧的条件下,用修正迭代法求出二次近似解析解,把大挠度解作为扁球薄壳的初挠度处理,推导出扁球薄壳在大挠度下的非线性动力学基本方程。然后给出满足夹紧固定边界条件下的位移模式,求出张力。由动力学势的一阶变分为零得到平衡曲面方程。继之用突变理论给出相应的分岔点集的方程组,同时讨论了扁球薄壳整体的稳定性问题。该文也给出了相应平衡曲面的分岔点集的示意图。Based on nonlinear dynamic theory of thin shells and the basic large deflection equations of the shallow reticulated spherical thin shells, regarding large deflection as the initial deflection, the basic nonlinear dynamic equations are established by using the modified iteration method to obtain the analytical solution of quadratic approximation under the boundary conditions of clamped edges. The tension is obtained according to the displacement model that satisfies the same boundary conditions. The equation of the balanced surface is obtained by set the first variation of the dynamic potential to be zero. Then, the systems of equations of the corresponding bifurcation point set are given in terms of catastrophic theory and the whole stability of the shallow thin spherical shells is discussed. In addition, the sketch map of the corresponding bifurcation point set of the balanced surface is also given in this paper.

关 键 词：大挠度 非线性 稳定性 修正迭代法 动力学势 

分 类 号：O343.5[理学—固体力学] O347.2[理学—力学]