圆柱外表面受热冲击问题的广义热弹性分析

RESEARCH ON GENERALIZED THERMOELASTIC PROBLEMS OF A SOLID CYLINDER SUBJECTED TO THERMAL SHOCK

基于L-S广义热弹性理论,针对实心圆柱体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析.利用热冲击的瞬时特征,借助于Laplace正、反变换技术及柱函数的渐近性质,推导了热冲击作用周期内温度场、位移场和应力场的渐近表达式.通过计算,得到了热冲击条件下各物理场的分布规律以及延迟效应和耦合效应对热弹性响应的影响规律.结果表明:当考虑延迟效应和耦合效应时,热扰动将以两组速度不同的波的形式向前传播,延迟效应和耦合效应对各物理场的建立时间,阶跃间隔和阶跃峰值均产生影响,且延迟效应和耦合效应均在一定程度上削弱了热冲击的作用效果.

Based on the L-S generalized thermoelasticity, one dimensional problem of a solid cylinder subjected thermal shock is studied. In accordance with the transient behaviors of thermal shock, the approximate shorttime analytical solutions of the temperature, displacement and stresses are obtained via the Laplace transform and inverse transform. Numerical simulation is conducted for an isotropic solid cylinder, and the distribution of each physical field including the temperature, radial displacement, radial stress, hoop stress and axial stress are obtained, and the influence of the delay and the coupling effects on these distributions are also obtained. The results show that the thermal disturbance propagates forwards with two different velocities when the effects of the delay and coupling are considered, and these effects have influences on the time of each physical field began to establish, the intervals of two jumps and the peak values of jumps.