圆截面激光晶体热变形的弹性力学分析

Elastic analysis of thermal distortion of laser crystal with circular cross-section

采用热弹性理论建立了关于激光晶体热变形的微分方程和边界条件;对方程进行简化并利用级数法和伽辽金法进行求解,得到了圆截面激光晶体热变形的解析表达式。分析结果表明:晶体内的热变形是坐标r、z的非线性函数;变形与弹性模量E无关,而与晶体的尺寸、泊松比、热传导系数有关。

The thermal distortion of laser crystals with circular cross-section is studied.The differential equations and boundary conditions of the thermal deformation of a laser crystal are established by the thermo-elasticity theory.Then the equations can be simplified and the series method and the Galerkin method are used for solution.The analytical expressions of the thermal deformation of laser crystals with circular cross-section are obtained.These results are more realistic for the optimal design of solid-state laser crystals.