基于L-S理论的压电球壳广义热冲击分析

基于L-S广义热弹性理论，针对压电球壳受表面球对称热冲击作用下的热弹性问题进行分析.从三维压电弹性理论基本方程出发，利用Laplace变换，建立耦合的6阶状态方程；采用层合近似模型，将状态方程转化为关于径向坐标的常系数状态方程.利用界面连续条件得到球壳内、外状态变量的整体传递关系，结合球壳内、外边界条件，可以确定频域内所有状态变量，通过数值反变换获得时域解.数值算例给出热冲击作用下压电球壳的位移、应力、电势和温度等物理量的分布规律，考察热松弛时间对热冲击作用效果的影响.
Abstract: The spherically symmetric problem of a piezoelectric spherical shell subjected to thermal shock was analyzed based on the L-S generalized thermoelasticity. A sixth-order homogeneous state equation was established by Laplace transform based on the three-dimensional theory of piezoelectricity. The state equation was transferred to the one with constant coefficients using the approximate laminate model. A transfer relation was obtained between the state vectors at the inner and outer surfaces of the spherical shell by using the continuity conditions at each interface between two adjacent layers. Then the state variables were exactly determined by incorporating the prescribed boundary conditions. All time-domain physical variables of the coupled field were obtained by using the numerical inverse Laplace transform. Numerical examples were performed to analyze the distributions of the temperature, stress, displacement, and electric potential, and in particularly, the influences of thermal relaxation time on the thermal shock effects.