轴向压应力波下圆柱壳弹性动力失稳的判据与机理

基于动力失稳瞬间能量的转换和守恒，推导提出了受轴向力圆柱壳弹性动力失稳的判据和两个临界条件，由第一个临界条件导出的圆柱壳弹性动力失稳的控制方程、边界条件、屈曲变形连续与利用Hamilton原理的结果完全相同，但不足以确定包含在本问题中的两个特定特征参数（临界载荷参数和动力特征参数），由第二个临界条件导出压缩波前的屈曲变形约束方程，基于控制方程有满足边界条件、变形连续条件和波前约束方程的非平凡解的条件，导出关于两个特征参数的一对特征方程，基于特征方程的解，精确地计算出临界载荷参数和动力特征参数的值以及动力失稳态态，由此建立了轴向力作用下圆桩壳弹性动力失稳的特征值分析方法。

DYNAMIC INSTABILITY MECHANISM OF CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION WAVE

The mechanism of structural bifurcation-instability is th e ins tant course of releasing partially compressive deformation energy. On the basis of the transformation and conservation of energy, two critical conditions compos ing the criterion for the dynamic instability of a cylindrical shell subject to an axial load have been derived. The governing equations, the boundary condition s and the continuity conditions derived by use of the first critical condition a re the same as those obtained by use of Hamiltons principle, but insufficient to determine the two undetermined characteristic parameters, that is, the critic al load parameter and the dynamic characteristic parameter. The supplementary re straint equation at the compression wave front is obtained by use of the second critical condition. A couple of characteristic equations for the two characteri stic parameters are derived from the condition under which the governing equatio ns have a nontrivial solution satisfying the boundary conditions, the continuity conditions and the restraint equation at the wave front. The dynamic buckling m odes, the critical load parameter and the dynamic characteristic parameter are c alculated accurately on the basis of the solutions of the characteristic equatio ns. Thus, the method of characteristic-value analysis is established for the dy namic instability of a cylindrical shell under the action of an elastic compress ion wave.