有角点支座矩形板自振分析  

Free vibration analysis of a rectangular plate with corner point supports

作　　者：许琪楼[1] 

机构地区：[1]郑州大学工学院,郑州450002

出　　处：《振动与冲击》2013年第17期84-89,共6页Journal of Vibration and Shock

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。并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,计算了不同边长比时板的自振频率。The basic structure of a rectangular plate with corner point supports was obtained for its free vibration analysis by replacing a corner point support with a corner force. The modal shape functions of the plate were composed of the basic modal shape functions which were the natural modal shape functions of the basic structure, and the additional ones excited by the corner force. The modal shape functions of the plate had to satisfy the plate's vibration differential equations, its boundary conditions and the differential relation between the corner deflection and the corner force. According to the superposition principle, the basic modal shape functions and the additional ones could be chosen separately. The former were similar to those results in the basic vibration theory of plates, and the latter were selected to satisfy the differential relation mentioned above and other boundary conditions. Here, the modal shape functions were deduced for a plate with two adjacent simply-supported edges and one corner point support and a plate with one simply-supported edge and one or two corner point supports. Their natural frequencies versus edge length ratio were calculated and listed.

关 键 词：弹性振动 矩形板 角点支承 基本振形 附加振形 

分 类 号：O326[理学—一般力学与力学基础] O327[理学—力学]