磁热冲击下非均质圆筒的动态响应分析

Dynamic response analysis of heterogeneous hollowcylinders under magnetothermal shock

文章基于轴对称平面应变问题的运动方程和应力-位移关系,借助状态空间技术和Newmark法,对受热冲击和轴向磁冲击下,材料性质沿径向任意梯度变化的圆筒进行动态响应分析,得到位移和应力随时间变化的半解析解;对均质圆筒、双层均质材料组合圆筒及含功能梯度材料(functionally graded material,FGM)的双层圆筒进行分析,检验解的正确性和有效性。算例分析表明:适当地延迟热冲击时间,可大幅降低磁热冲击下双层均质材料组合圆筒的动应力振幅;将双层圆筒内层材料替换成FGM,并选取合适的梯度分布因子,可有效降低圆筒内动应力的峰值。研究结果可为受磁热冲击的非均质空心圆筒结构强度评价和优化设计提供理论参考。

Based on the equation of motion and stress-displacement relation for the axisymmetric plane-strain problem,the dynamic response analysis for the hollow cylinder with material properties changing along the radial direction arbitrarily under thermal shock and axial magnetic shock is carried out,by means of the state space technology and Newmark method.The semi-analytical solution of displacement and stress varying with time is obtained.Through the analyses of a homogeneous hollow cylinder,a double-layered cylinder combined by two homogeneous layers,and a double-layered cylinder by a homogeneous layer and a functionally graded material(FGM)layer,the correctness and effectiveness of the solution in this paper are examined.The numerical results show that the proper delay of thermal shock time may sharply reduce the oscillation amplitude of the dynamic stress in double-layered homogeneous cylinders under magnetothermal shock;by replacing the inner layer with an FGM and selecting an appropriate gradient distribution factor,the peak value of the dynamic stress decreases effectively in the cylinder.The research results can provide theoretical reference for the strength evaluation and optimization design of heterogeneous hollow cylinders subjected to magnetothermal shock.