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中文摘要：
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。
英文摘要：
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.
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