热冲击作用下非均质圆筒的广义热弹性分析

An analysis on generalized thermoelasticity of inhomogeneous hollow cylinders under thermal shock

基于L-S广义热弹性理论,研究了非均质圆筒在热冲击作用下的广义热弹性问题。利用状态空间技术和有限差分格式,获得了材料性质沿径向任意梯度变化圆筒的一维广义热弹性解。通过算例分析,给出了延迟效应和耦合效应以及材料的梯度形式对圆筒内的温度和应力沿径向分布和随时间变化的影响。分析表明:延迟效应可反映热波以有限速度传播,波前形成巨大的温度梯度,并与弹性波相互作用引起尖峰应力;耦合效应在最初阶段或耦合系数较小时对温度传播影响较小,但会削弱尖峰应力的峰值;改变材料梯度可有效降低热冲击对圆筒内应力的影响。

In this paper, based on the L-S generalized theory of thermoelasticity, the problem of the generalized thermoelasticity is analyzed for inhomogeneous hollow cylinders under thermal shock. By applying the state space technique and the finite difference scheme, a one-dimensional thermoelastic solution is obtained for hollow cylinders with material properties varying arbitrarily in the radial direction. Through an example analysis, the influences of the delay and the coupling effects as well as the gradient profile of materials on the temperature and the stress are presented. The results show that the delay effect may describe the propagation of the thermal wave at a limited speed and gives rise to a huge temperature gradient in front of the thermal wave, and the interaction between the thermal and elastic waves causes sharp stresses. The coupling effect has little influence on the temperature propagation at the initial stage or when the coupling coefficient is small, but it can weaken the peak value of sharp stresses. The effect of thermal shock on the cylinder can be effectively reduced by changing the material gradient.