关键词: Winkler-Pasternak弹性地基, FGM矩形板, 无量纲固有频率, 临界屈曲载荷, 微分变换法(DTM)

Abstract: Based on the classical thin plate theory, a governing differential equation is derived by using the generalized Hamilton principle and the equation is treated to dimensionless. The differential transformation method (DTM) is then utilized to determine first three dimensionless natural frequencies and buckling loads of the equation under different boundary conditions. The solution of the equation is reduced further to two cases: functionally graded plate without foundation and common material plate with foundation. The DTM solution is compared with the solution published in literature, and both results are consistent indicating the applicability and accuracy of DTM. Finally, the effects of boundary conditions, gradient index, elastic stiffness coefficient of the foundation, shear stiffness coefficient as well as aspect ratio of the foundation on the dimensionless natural frequency and critical buckling load of the FGM rectangular plate are analyzed respectively. The results show that: under the boundary conditions studied, the stronger the boundary constraint is, the larger the dimensionless natural frequency is; the increase of elastic stiffness coefficient, shear stiffness coefficient as well as aspect ratio of the foundation will also lead to the increase of the dimensionless natural frequency; the increase of in-plane pressure load may lead to the decrease of the dimensionless natural frequency; the larger the aspect ratio, the smaller the critical buckling load; the larger the gradient index, the smaller the critical buckling load; the larger the gradient index, the smaller the critical buckling load.

Key words: Winkler-Pasternak elastic foundation, FGM rectangular plates, dimensionless natural frequencies, critical buckling loads, differential transform method (DTM)