周边固支的矩形板的动力耦合热弹性问题分析

A NOTE ON THE DYNAMIC AND COUPLED THERMOELASTIC PROBLEMS OF A PERIPHERY FIXEDTHIN RECTANGULAR PLATE

本文研究的是周边固支的矩形板上表面受均匀分布热流冲击的动力耦合热弹性问题，在热冲击过程中，板的周边温度场保持稳定，下表面绝热。采用算子法将热传导方程由三维降为二维问题，以和二维的热弹性动力方程相协调，二方程相互耦合，故用带补充项的双重富里叶级数消去对坐标的微分项，再用拉普拉斯变换消去方程中对时间的微分项，然后尝试用加权最佳逼近法作数值拉普拉斯逆变换，给出问题在原象空间的解。为防止误差的扩大，本文利用正交齐异分解法求解方程，并对计算结果中动力项和耦合项的影响作出分析。

In this paper,the dynamic and coupled thermo-elastic problem of a periphery fixed thin rectangular plate with its top surface loaded by a step heat flux was studied.During the process of heat impact, the initial temperature was maintained around the periphery of the plate and its lower surface was assumed to be thermally insulated,The operator method was used to degrade the equation of heat conductivity from three dimensions to two dimensions so that it could match with the two dimensional thermoelastic dynamic equation.Since the two equations were coupled, the dual Fourier series with supplementary terms were used to improve the differentiablity and Laplace transforms were used to eliminate the differential terms to time.Using weighted least squarefi.gtocaTyoutthenuaericalinverseofLaplacetrauforasthesolutionsofprobleasin image space are given,In order to improve the precision of computation and avoid ill-conditioning difficulties of equations,singular value decomposition method was employed to solve the equations by taking advantage of the property of orthogonal transform not leading to the expansion of errors.Finally, the analysis of the effects of the dynamic terms and coupled terms are given.