四边支承矩形板自由振动的精确解法

Accurate Free Vibration Solution of the Rectangular Plates with Four Edges Supported

提出矩形薄板振动主振方向的概念 ,在主振方向上矩形板振动波形是唯一的 ,由此建立了四边支承矩形板统一的振形函数表达式 ,并推导出板自由振动的频率方程及相应的振形曲线 ,除一对边简支、一对边固定矩形板和三边简支、一边固定矩形板仅发生一对边简支方向为主振方向的振动外 。

The idea of the main vibration direction of the rectangular plate is put forward in this paper. The vibration wave number of the plate is unigue in the main vibration direction. The uniform expressions of vibration mode curve of the rectangular plates with four edges supported are established by the method and the free vibration frequency equations and corresponding vibration mode curves of this plates are deduced. The plate with two opposite edges simple supported and two opposite edges clamped and the plate with three edges simple supported and one edge clamped have one main vibration direction that is the direction of the two opposite edges simple supported, and other plates have two main vibration directions.