温度效应下磁电弹圆杆中的孤波分析

Solitary Wave Analysis of Magnetoelectro-Elastic Circular Rod Under Temperature Effect

以无限长磁电弹圆杆为研究对象,建立了横观各向同性磁电弹圆杆的本构关系,通过非线性弹性位移关系和等效泊松比,结合哈密顿原理和欧拉方程,推导出了无限长磁电弹性圆杆的波动方程。采用扩展的Tanh展开法对波动方程进行求解,得到了方程的精确孤波解;采用Matlab进行模拟,得到了磁场强度为50 kA/m,100 kA/m和150 kA/m,电场强度为50 kV/m,100 kV/m和150 kV/m,温差为20℃,60℃和100℃,半径为0.02 m,0.05 m和0.08 m下的波形图。数值分析结果表明,随着磁场强度、电场强度和温差的增大,波速呈现减小趋势;随着杆半径的增加,色散参数和波长会变大。

Taking the infinite length magnetoelectro-elastic circular rod as the research object,the constitutive relation of the transverse isotropic magnetoelectro-elastic circular rod was established,and the wave equation of the infinite length magnetoelectro-elastic circular rod was derived by using the nonlinear elastic displacement relation and the effective Poisson’s ratio,combining the Hamilton’s principle and Euler equation.The wave equation was solved by using the extended Tanh expansion method,and the exact solitary wave solution of the equation was obtained.Matlab simulation was used to obtain the magnetic field intensity of 50 kA/m,100 kA/m and 150 kA/m,electric field intensity of 50 kV/m,100 kV/m and 150 kV/m,temperature difference of 20℃,60℃and 100℃and radius of 0.02 m,0.05 m and 0.08 m waveforms.The numerical results show that the wave velocity decreases with the increase of magnetic field intensity,electric field intensity and temperature difference.With the rod radius increases,the dispersion parameters and the wavelength also increase.