三边简支一边固支矩形薄板动力屈曲解析解

摘要

Based on the twin-characteristic-parameter method and stress wave theory, dynamic buckling displacements of a rectangular thin plate with one edge clamped and other three edges simply supported subjected to axial impact in-plane were obtained analytically by solving the dynamic balance equations of a plate with a supplementary restraint-equation in compressive wave front. In the dynamic buckling process of the rectangular thin plate, relations of its thickness-width rate, the amplitude of impulsive loads, buckling modes and critical buckling length were found out. The results indicated that for the existence of transverse inertia effect, the critical load of dynamic buckling is much bigger than that of static buckling.%根据板的动力平衡方程和压缩波前附加约束方程,基于双特征参数法和应力波理论,求解了三边简支一边固支矩形薄板在面内轴向冲击载荷作用下动力屈曲位移的解析解.揭示了矩形薄板动力屈曲过程中板的厚宽比、屈曲模态、冲击载荷大小和临界屈曲长度之间的关系.计算结果表明,由于横向惯性效应的存在,动力屈曲的临界载荷要比静力屈曲的大得多.