三边支承一边自由矩形板自由振动分析

Free Vibration Analysis of Rectangular Plates with Three Edges Supported and One Edge Free

板自由振动振形必须具有正交性,采用主振方向排序法建立三边支承一边自由矩形板振形函数表达式可以满足振动微分方程和全部边界条件,又具有振形的正交性.该振形曲线中的振动波形数在主振方向上是唯一的,在另一方向上是不唯一的,振形曲线形状符合板边界条件所能限定的变形形态.通过证明振形正交性的存在,分析振形函数表达式的结构形式,推导不同边界条件矩形板的频率方程,计算板的自振频率及相应振形,并与前人的结果进行了比较,从理论上说明了该方法的正确性.

Mode shapes of plate must possess orthogonality under free vibration The mode shape expressions of the rectangular plates with three edges supported and one edge free established by the arrangement method on the main vibration direction can satisfy the governing differential equation and all boundary conditions and the mode shape enforcing all boundary conditions can possess orthogonality The vibration wave number in expression is unique at the main vibration direction and is not unique at the other direction The waveform used in the mode shape is in aggrement with the deformation pattern permitted by the edge supportIn this paper it proves that the mode shape is orthogonality, the meaning of the arrangement method is clarified by analyzing the structure of mode shape expression, the free vibration frequency equations of rectangular plates with different boundary conditions are deduced, and twenty-five free vibration frequencies and corresponding nodal line diagrams per plate are calculated,which clearly show the method above is theoretically correct.