二维横观各向同性厚板在空间变化热源及体力作用下的动力学响应

Study of Dynamic Response in a Two Dimensional Transversely Isotropic Thick Plate With Spatially Varying Heat Sources and Body Forces

研究热源和体力作用下的横观各向同性厚板的二维问题,板的上表面无应力作用,但有规定的表面温度作用;板的下表面置于刚性基础之上,并处于绝热状态.采用Green和Naghdi提出的广义热弹性理论,通过Laplace和Fourier双重变换,在Laplace-Fourier变换域中,得到位移和温度场的控制方程.数值求解双重变换的逆变换,采用一个基于Fourier级数展开的方法,数值地求解Laplace变换的逆变换.对材料镁(Mg)进行数值计算,并用图形表示其结果.推演出各向同性材料铜(Cu)的数值结果,并用图形与横观各向同性材料镁进行比较.同时研究了体力的影响.

A two dimensional problem for a transversely isotropic thick plate having heat source and body force was studied. The upper surface of the plate was stress free with prescribed surface temperature while the lower surface of the plate rest on a rigid foundation and was thermally insulated. The study was carried out in the context of generalized thermoelastici- ty proposed by Green and Naghdi. The governing equations for displacement and temperature fields were obtained in Laplace-Fourier transform domain by applying Laplace and Fourier transform techniques. The inversion of double transform had been done numerically. The nu- merical inversion of Laplace transform was done by using a method based on Fourier series expansion teclmique. Numerical computations had been done for magnesium （Mg） and the results were presented graphically. The results for an isotropic material （Cu） had been deduced numerically and presented graphically to compare with those of transversely isotropic material （Mg）. The effect of body force was also studied.