由运动内热源引起的磁热黏弹性问题的研究

STUDY ON MAGNETO-THERMOVISCOELASTIC PROBLEM WITH TWO RELAXATION TIMES DUE TO MOVING INTERNAL HEAT SOURCE

在具有两个热松弛时间的广义热弹性理论下,研究了处于定常磁场中的均布各向同性黏弹性半空间中,由以均匀速度运动的线热源引起的瞬态波问题.通过引入黏弹性向量势和热黏弹性标量势,问题退化为求解3个偏微分方程.运用Laplace变换(对时间变量)和Fourier变换(对一个空间变量),得到了变换域内应力和位移的解析表达式.采用级数展开法,得到了边界位移在小时间范围内的近似解,给出了解的近似范围,同时还研究了两种特例:(1)热源静止不动,(2)不考虑热松弛时间的影响.最后对于丙烯酸塑料介质给出了数值结果.

Transient waves created by a line heat source that suddenly starts moving with a uniform velocity inside isotropic homogeneous viscoelastic half-space inside a magnetic field are studied using generalized thermoviscoelsticity with two relaxation times. The problem is reduced to the solutions of three differential equations, one involving the viscoelastic vector potential, and the other two coupled, involving the thermoeviscoelastic scalar potential and the temperature. Using joint Laplace and Fourier transforms the problem is solved and the analytical solution for displacement and stresses are given in transform domain. The expressions for displacements valid in the small time range are obtained and the displacements are calculated at the boundary by using inverse transforms for small time. Also the displacements in the transformed domain indicate the existence of dilatational, transverse and thermoviscoelastic waves inside the medium and the velocities of the three kinds of waves are given in this paper. The approximate region valid for the solution is given and two special cases （1） the source is motionless, （2） for the conventional thermoviscoelasticity, are considered. Also the results are graphically described for the medium of acrylic plastic. The results show that the relaxation times and viscous effects have salient influence on the distribution of boundary displacement at small time range.