两对边简支另两对边任意支承的板内有任意多个点支矩形板横向自振的精确解析解

THE ANALYTICAL SOLUTION OF TRANSVERSE VIBRATION OF RECTANGULAR PLATES WITH TWO OPPOSITE EDGES SIMPLY SUPPORTED AND ARBITRARY NUMBER OF POINT-SUPPORTS INSIDE

本文研究两对边简支另两对边任意支承的板内有任意多个点支矩形板的横向自由振动问题,将点支反力视为作用于板上的待定外力,求得了在待定外力作用下两对边简支矩形板动态响应的解析解,由矩形板另两对边的边界条件确定待定积分常数,利用点支处板位移为零条件决定待求的点支反力,并得到以一阶数等于点支个数的行列式表示的频率方程,由计算机求解各阶频率参数,方法有独特的优越性,本文最后给出了一个数值算例。

This paper studies the transverse vibration of rectangular plates with two opposite edges simply supported, other two edges arbitrarily supported and arbitrary number of point-supports inside. The analytical solution of differential equation of vibration of the rectangular plate which includes the reaction forces of point-supports is given by regarding the reaction forces of point-supports as the unknown external forces acted on the plate. The integral constants are given by the boundary conditions on other two edges. The reaction forces of point-supports are given by the condition of the zero deflection at the point-supports. The frequency equation is derived, which is a determinant whose order is equal to the number of point-supports. The frequency parameters may be obtained by the method of searching roots of determinant by means of computer. The method shows its unique advantage. Finally, a numerical example is given for a square plate with four edges simply supported and a point-support inside.