正交各向异性矩形板受迫振动的三维分析

从正交各向异性三维弹性动力学的控制方程出发，在求得四边简支矩形板自由振动频率和位移振型的基础上，构造了受迫振动的位移函数；利用自由振动位移振型的正交性，将控制方程的空间变量和时间变量分离，得到了广义质量、广义力和频率表示的关于时间的2阶常微分方程，从而得到了正交各向异性弹性矩形板在受迫振动下的位移场和应力场．给出了本文方法与薄板理论的算例．

Three Dimensional Elasticity Analysis of Forced Vibration of Simple Supported Orthotropic Rectangular Plate

For orthotropic rectangular simply supported plate, based on three dimensional dynamic equations of elasticity, frequency spectrum and displacement vibrancy modes of free vibration are obtained. The displacement functions of forced vibration are then constructed. Utilizing the orthogonality of displacement vibrancy mode separates space variable and time variable in the governing equations, a 2nd order differential equation with constant coefficient expressed by generalized mass, generalized force and frequency spectrum is given. Field of displacements and stresses of the plate on forced vibration are also derived. Comparisons are made between the results in this paper and those given by thin plate theory.