考虑热松弛时间的半无限粘弹性压电杆的热冲击问题

Thermal shock problem for a semi-infinite thermo-viscoelasticpiezoelectric rod with thermal relaxation

基于具有一个松弛时间的广义热粘弹性理论,研究了半无限压电杆热冲击问题。利用现代控制理论中状态空间法求解了偏微分控制方程,获得了拉普拉斯变换域内的精确解。利用数值反变换方法,得到了位移、温度和应力的分布曲线,同时将广义理论和传统耦合理论做了对比。从这些结果来看,当所考察时间的量级短到与材料热松弛时间量级相同时,热松弛影响着所有场变量的分布。材料粘性性质不影响温度分布,但在时间很短时对应力分布影响显著,而对位移分布的影响为时间愈长愈明显。

Based on the theory of generalized thermo-viscoelasticity with one relaxation time,the boundary value problem of one-dimensional semi-infinite piezoelectric rod with its left boundary subjected to a sudden heat is studied. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of the modern control theory. The exact expressions for field quantities are obtained in transform domain. Using numerical inversion transform method,the distributions of the displacement,the temperature and the stress are obtained and the results are shown graphically while the acrylic plastic materials are considered. Also a comparison was made with the results obtained using generalized theory and using conventional coupled theory for all field quantities. From these results we can find that,for the thermal shock problem of viscoelastic-piezoelectric material,the effects of the thermal relaxation and the viscous property are evident in short time(when the order of magnitude of time is the same as that of the thermal relaxation time).