受热冲击时球体的广义热弹性分析

摘要

Following the theory of generalized Green-Lindsay thermoelasticity with two relaxation times,the response of a solid sphere under thermal shock is analyzed.With Laplace transform and its inversion,the asymptotic solutions of the displacement and temperature are obtained by the transient characteristic of thermal shock.Through numerical calculation,the rules of the sphere's displacement and temperature distributions are discovered,and the influences of the thermal relaxation time and the thermoelastic coupling coefficient on the distributions are also revealed.It is found that there are two step points in both displacement and temperature distributions; the step time,the interval and the peak value of step are affected by the thermal relaxation time and the thermoelastic coupling coefficient,which weakens the effect of thermal shock.%基于具有2个热松弛时间的G-L广义热弹性理论,研究了实心球体外表面突然受到均匀热冲击时的广义热弹性问题.由于控制方程复杂,到目前为止此类问题的解析解还没有得到.文中利用拉普拉斯正、反变换技术和热冲击的瞬时特征对该问题进行求解,最终得到了位移场和温度场的渐近表达式;通过数值计算,获得了热冲击下实心球体的位移与温度分布规律,以及热松弛时间和耦合系数对位移及温度分布的影响.结果表明:位移及温度分布中存在2个阶跃点;热松弛时间和耦合系数对位移及温度的阶跃时间、阶跃间隔和阶跃峰值均产生影响,对热冲击的作用效果也有一定的抑制作用.