Winkler-Pasternak地基上四边受压FGM矩形板的自由振动与屈曲特性

基于经典薄板理论,利用广义Hamilton原理推导相应的控制微分方程并对方程进行无量纲化;采用微分变换法(DTM)计算不同边界条件下方程的前三阶无量纲固有频率和屈曲载荷,并将方程的求解退化为无地基功能梯度板和有地基普通材料板两种情形,将其DTM解与已有文献的解进行对比,结果一致,表明DTM的适用性和精确性;分析了边界条...

Free vibration and buckling characteristics of four-sides compressed FGM rectangular plates resting on Winkler-Pasternak foundation

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.