中文摘要：

根据分离变量法得到了双参数弹性地基上正交各向异性矩形薄板自由振动封闭形式的精确解,其中边界条件为CCCC、SCCC和SSCC情况的精确解过去被认为是难以得到的。在分离变量方法中,利用控制微分方程本征值给出振型函数的解析形式和两个空间本征值和时间本征值的关系,再利用边界条件得到振型函数系数和本征值方程或频率方程的精确形式。数值结果与有限元结果及文献结果吻合较好,验证了本文方法和结果的正确性。

英文摘要：

The close form exact solutions of free vibrations of thin orthotropic rectangular plates on the Pasternak elastic founda- tion or the elastic foundation with two parameters are solved by means of separation of variables method. It is noteworthy that the exact solutions for the plates with boundary conditions CCCC, SCCC and SSCC （S denotes simple support, and C denotes clamp） were considered impossible to be solved. In separation of variables method, the general formulation of the natural mode and the relationship among the two spatial eigenvalues and the temporal eigenvalue are directly obtained from the governing dif- ferential equation, and the coefficients of the exact eigenfunctions and the exact eigenvalue equations are determined on the basis of boundary conditions. The numerical results agree well with those in literature and FEM, this validates the correctness of the present method.