均匀热载荷作用下功能梯度圆板的非线性振动

Nonlinear vibration of functionally graded circular plates subjected to uniform thermal loading

基于经典板理论,研究了热载荷作用下功能梯度圆板的大幅振动问题。在经典板理论下利用物理中面概念,导出了功能梯度圆板的非线性运动方程。利用Ritz⁃Kantorovich方法消去时间变量,将非线性运动方程转换成了一组关于空间变量的非线性常微分方程。采用打靶法数值求解所得方程,并利用数值结果研究了热载荷作用下功能梯度圆板静态响应的影响和振幅、材料梯度参数、热载荷以及边界条件等对功能梯度圆板振动行为的影响。研究表明:热变形的存在使周边夹紧与简支FGM圆板的振动响应及线性振动与非线性振动行为均有显著不同。热过屈曲变形板的硬化是有限度的,过大的热过屈曲变形也会降低FGM圆板的刚度。

Based on the classical plate theory,the large-scale vibration problem of functionally graded circular plates subjected to thermal loading is studied.The nonlinear motion equation of the functionally graded circular plate is derived by using the physical neutral surface concept under the classical plate theory.The Ritz-Kantorovich method is used to eliminate the time variable,and the nonlinear motion equation is transformed into a set of nonlinear ordinary differential equations with respect to the spatial vari⁃able.The available equations are solved on the basis of the shooting method,then the static response of the functionally graded cir⁃cular plates under thermal loading and effects of amplitude,material gradient parameters,thermal loads and boundary conditions on the vibration behavior of the functionally graded circular plates are analyzed.The results show that the vibration response of pe⁃ripheral clamping and simply supported FGM circular plates,as well as its linear and nonlinear vibration behaviors,change signifi⁃cantly under the influence of the thermal deformation.The heat-buckling deformation plate hardens within a limited range,and the inflexibility of the FGM circular plates will be reduced by excessive thermal buckling deformation as well.Therefore,the effect of thermal deformation on the vibration response of the FGM circular plate is complicated.