功能梯度梁在热冲击下的动态响应  

Dynamic responses of functionally graded material beams under thermal shock

作　　者：李世荣[1] 范亮亮[1,2] 

机构地区：[1]兰州理工大学理学院工程力学系,甘肃兰州730050 [2]西安交通大学航天航空学院,陕西西安710049

出　　处：《振动工程学报》2009年第4期371-378,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(10872083;10602021)

摘　　要：基于Timoshenko梁理论研究了功能梯度材料(FGM)梁在一维热冲击载荷作用下的瞬态动力响应。采用Laplace变换将功能梯度材料中的一维热传导方程转化为拉氏域中的常微分方程进行求解,再进行反变换得到温度场。然后采用微分求积法(DQM)对位移形式的动力学方程及初边值条件进行DQ离散,数值求解离散后的动力学方程,得到了梁在热冲击下的动态位移和应力响应。分析了材料组份指数和几何参数对梁的动力响应的影响,并考察了DQM法对此类问题的有效性。Based on Timoshenko＇s beam theory, transient dynamic response of the beams made of functionally graded material subjected to one-dimensional thermal shock load are studied in this paper. Laplace transform technique is adopted so that the equation of one-dimensional thermal conduction equation in FGMs can be solved in the Laplace domain. Then the inverse transform is performed to determine the responses of temperature field. The dynamic equations in conjunction with the initial and boundary conditions in terms of the beam displacements are discretized into a system of algebraic equations, which are solved by numerical method and the displacement as well as the stress responses are obtained. The effects of material volume fraction index and the geometrical parameter on the dynamic responses of the beam are analyzed. The validity of the DQM on such kind problem is also examined.

关 键 词：TIMOSHENKO梁 功能梯度材料 热冲击 LAPLACE变换 微分求积法 

分 类 号：U441.5[建筑科学—桥梁与隧道工程] U448.21[交通运输工程—道路与铁道工程]