有角点支座矩形板自振分析

PDF(838 KB)

振动与冲击 ›› 2013, Vol. 32 ›› Issue (17) : 84-89.

论文

有角点支座矩形板自振分析

许琪楼

作者信息 +

FREE VIBRATION ANALYSIS OF RECTANGULAR PLATE WITH CORNER POINT SUPPORT

Xu Qilou

Author information +

文章历史 +

摘要

撤去角点支座代之以角点力得板自由振动分析的基本结构。原结构振形函数表达式由基本结构所固有的基本振形和角点力所激发的附加振形组成，它应满足振动微分方程和板挠度与角点力间的微分关系。为表示板双向振动规律，基本振形在二个坐标轴方向上有各自独立的振形曲线，分别符合相应方向边界所限定的、与微分方程直接关联的变形和受力特征：在支承边界上振幅为零而剪力分布不为零值；在自由边界上振幅不为零而剪力分布为零值；在自由角点处对应的振幅不为零而角点力为零值。附加振形在角点处要满足振幅与角点力的微分关系，在每条边界上要符合边界所限定的振幅与剪力分布的振动特征。文中导出二邻边和对角点支承矩形板，一边支承和一角点或二角点支承矩形板的振形曲线，并计算了不同边长比时板的自振频率。

Abstract

Replace the corner point support by a force, it is the free vibration analysis basic structure of the plate. The vibration mode expression of the original plate is composed of the two parts: the first is the basic intrinsic mode of the basic structure, the second is the addition mode aroused by the corner force. The vibration mode function must satisfy the vibration differential equation and the differential relation between the corner force and the bending deflection. For to indicate the bi-directional vibration the basic mode has the alone expression along the two coordinate axis respectively, which accord with the load-deformation characteristic limited by relevant edges and direct connected with the differential equation.The character is the zero shear force and the non-zero amplitude at the relevant free edges, the zero amplitude and the nor-zero shear force at the relevant supported edge, and the zero corner forces and the non-zero amplitude at the free corner. The addition mode must satisfy the differential relation between the corner force and the bending deflection at the corner, and accord with the above amplitude and shear force character at every edge. In this paper the mode expressions are presented for the plates having two adjacent supported edges with one corner point support and having one supported edge with one or two corner point supports, the vibration frequencies of this plates are listed with the change of edge length ratio.