导电圆柱壳体磁弹性二阶谐波共振响应分析

 研究了磁场环境中受机械载荷作用圆柱壳体的二阶谐波共振响应问题。首先给出了电磁场环境中导电圆柱壳体的非线性磁弹性振动方程和电磁场方程，并应用伽辽金积分法导出了相应的无量纲化非线性振动微分方程。然后采用多尺度法对系统的二阶超谐波和亚谐波共振问题进行求解，得到了稳态运动下关于定常解的幅值响应方程及解的稳定性判别式。最后通过数值算例，给出了共振幅值随磁感应强度和外激励力等参量变化的特征曲线图，分析了解的稳定性、奇点性态及分岔特性。结果表明，通过电磁或机械参数的适当选取，能够达到激发或抑制系统共振现象的目的。

Magnetoelastic Second Order Harmonic Resonance Analysis of a Conductive Cylindrical Shell

The nonlinear second-order harmonic resonances of a thin cylindrical shell in a magnetic field subjected to mechanical loadings are studied. First, the electromagnetic field equations and nonlinear magnetoelastic vibration equations of the cylindrical shell are derived respectively. The Galerkin method is used to derive the non-dimensional differential equation of the nonlinear vibration. Then, the second-order superharmonic and subharmonic resonances of the system are analyzed by the method of multiple scales. The resonance equations for the steady state solutions of amplitudes and the stability discriminant of the solutions are obtained respectively. Diagrams of the resonance amplitudes which change with magnetic intensity, excitation amplitude and other parameters are given respectively via the analysis of a numerical example. The stabilities of solutions, characteristics of singularity points and bifurcation are discussed. Numerical results show that the target of exciting or controlling the resonances of the system can be realized by selecting appropriate electromagnetic and mechanical parameters.