【摘要】 研究处于均布磁场中的理想导体的二维电磁热弹性耦合问题,引入势函数使控制方程转化为3个偏微分方程.运用Laplace变换和Fourier变换得到该问题在变换域内的精确表达式,再通过级数展开和Laplace逆变换法求得在时间较短时的逆变换,得到时间-空间域内问题的解.运用此方法研究了表面受到热冲击的半无限空间问题.给出了电磁热弹性波、膨胀波和横向波传播的速度,并通过数值计算,给出了各个场量的分布图.所得结论与已有的结论一致.更多还原

【Abstract】 The main object of this paper is to give a method for two-dimensional coupled electromagneto-thermoelastic problem under generalized thermoelasticity with relaxation times in a perfectly conducting medium.The model of the two-dimensional equations of electromagneto-thermoelastic with two relaxation times in a perfectly conducting medium is established firstly. Then the potential functions are introduced to make the problem transform into three coupled partial differential equations. The joint Laplace (for time variable) and Fourier (for one space variable) transform methods are used to obtain the exact expressions for field quantities in transform domain. Using the series expansion method and inverse Laplace transform the solutions of the problem valid in small time range are given. The resulting formulations are applied to a half space subjected to a thermal shock at the boundary. The velocities of electromagneto-thermalelastic wave, dilatational wave and transverse wave are given. The graphs of field quantities distributions are given using numerical calculation. Also the effects of relaxation times and magnetic field on the distribution of field quantities can be observed. The conclusion agrees with that obtained before.Increasing attention has been devoted to the interaction between electromagnetic field and strain field in a thermoelastic solid due to its many applications in the fields of geophysics, plasma physics, and related topics. Especially, study of the problem of generalized coupled electomagneto-thermoelastic in microscale domain is very important due to the rapid development of microelectromechanical system (MEMS). So this work has some value in the theoretical analysis and optimization design of the microscale device.更多还原