受热冲击时球体的广义热弹性分析
首发时间:2013-03-04
摘要:基于具有两个热松弛时间的G-L广义热弹性理论,针对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进行研究。由于控制方程的复杂,到目前为止,此类问题的精确解还没有得到。本文利用Laplace 正、反变换技术和热冲击的瞬时特征对该问题进行求解,最终得到位移场和温度场的解析解。通过数值计算,发现热波以有限速度在弹性体中进行传播,位移及温度分布中存在两个阶跃点;热松弛时间与耦合系数对位移和温度的阶跃时间、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着一定的抑制作用。
关键词: G-L广义热弹性理论 Laplace变换 热松弛时间 热弹性耦合系数
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Analytical Study of the Generalized Thermoelastic Problem of a Solid Sphere Subjected to Thermal Shock
Abstract:Based on the theory of Green-Lindsay generalized thermoelasticity with two relaxation times, the problem of a solid sphere subjected to thermal shock is studied. So far, there is no analytical solution for this problem as the governing equation is so complex. With the Laplace transform and 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 influence of the thermal relaxation time and the thermoelastic coupling coefficient effects on these distributions are also obtained. It is found that the outer surface displacement of the sphere gradually increases as time goes on, and there are two step points in temperature distributions; the step time, the interval and the peak value of step are influenced by the thermal relaxation time and the thermoelastic coupling coefficient, which can weaken the influence of thermal shock.
Keywords: G-L generalized thermoelasticity Laplace transform thermal relaxation time thermoelastic coupling constant
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