GN理论下受到移动内热源的半空间问题的研究

运用无能量耗散的热弹性GN理论研究了受到移动内热源的半空间问题.通过势函数法使问题 转化成一组偏微分方程,采用Laplace变换和Fourier变换法得到问题在变换域内表面位移 精确解. 运用级数展开法得到在小时间范围内表面位移的近似解.给出近似解的适用范围,同时给出热 源固定不动和非耦合理论下问题的解.并对铜介质进行了数值计算.

Transient Disturbance In A Half-Space Due To Moving Line Heat Source Using Thermoelasticity Without Energy Dissipation

In this paper transient problem created by a line heat source that suddenly starts moving with a uniform velocity inside isotropic homogeneous thermoelastic half-space are studied using the GN theory of generalized thermoelasicity. The problem is reduced to the solution of three differential equations by introducing the elastic and the thermoelastic potentials. Using the Laplace and Fourier transforms, the solutions are first obtained in the transform domain. Applying the inverse transforms, the approximate solutions, valid in short time range, are then derived. The displacements are calculated at the boundary for short time. Also the approximate region valid for the solutions is given and two special cases, (i) the source is motionless and (ii) the uncoupled theory, are studied. Numerical evaluations are presented for the medium of copper.