四边支承矩形板振形曲线及其正交性

Vibration Mode Curve and Its Orthogonality of the Rectangular Plates with Four Edges Supported

主振方向排序法认为 ,板的振形曲线中振动波形在主振方向上是唯一的 ,在另一方向上是不唯一的 ,由此建立了四边支承矩形板精确的振形曲线表达式 .这种振形曲线可以满足振动微分方程和全部边界条件 ,还具有振形的正交性 .通过推导证明了振形正交性的存在 ,阐明了主振方向排序法的物理含义 。

The arrangement method on the main vibration direction believes the vibration wave number in a vibration mode of the plate is unque at the main vibration direction and is not one at other direction. The accurate expressions of vibration mode curve of the rectangular plates with four edges supported are establishes with the method. The mode shape can satisfy the governing differential equation and all boundary conditions of plate and has the orthogonality relation. In this paper it is proved that the vibration mode is orthogonal and the physical meaning of the arrangement method is clarified.This clearly shows that the arranement method above is theoretically correct.