热环境中功能梯度材料圆板的自由振动  

Free vibration of functionally graded circular plates in thermal environment

作　　者：李世荣[1] 范亮亮[1] 

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《振动工程学报》2007年第4期353-360,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(10472039);甘肃省自然科学基金资助项目(3ZS062-B25-018)

摘　　要：基于von Kaman经典板理论,建立了功能梯度材料圆板在升温场内的大挠度动力学控制方程。将控制方程的响应分解为热过屈曲静态解和振动解两部分,得到了功能梯度材料圆板在热过屈曲平衡构形附近小振幅线性自由振动的微分方程。采用打靶法同时求热过屈曲和振动问题的控制方程,得到了随温度载荷变化的热过屈曲平衡路径以及前三阶固有频率的数值解。分析和讨论了板的材料梯度参数、温度场分布参数、边界条件等因素对过屈曲变形和振动响应的影响。分析中考虑了功能梯度板的组份材料的物性参数对温度的依赖性。Based on von Kaman＇s classical plate theory, governing equations for free vibration of FGM circular plates with the large amplitude in a temperature field are formulated. Then, by decomposing the response of the governing equations into two parts, the static thermal post-buckling solution and the dynamic vibration solution, linear differential equations governing small vibration of the plate in the vicinity of the thermal post-bucking configuration are derived. By using shooting method to solve simultaneously the governing equations both for thermal post-buckling and vibration, numerical solutions of thermal post-buckling equilibrium paths and the first three natural frequencies depending on the temperature rise of the FGM circular plates with pinned and fixed boundary conditions are obtained. The effects of the parameters of material gradients, temperature field, and the boundary conditions on the responses of post-bucking and vibration of the plate are examined in detail. The characteristics of nonlinear temperature-dependent material properties of the functionally graded material are considered in the analysis.

关 键 词：功能梯度材料圆板 热后屈曲 自由振动 打靶法 

分 类 号：TU311.3[建筑科学—结构工程]