关键词: 磁弹性, 薄壁圆柱壳体, 谐波共振, 稳定性, 分岔, 多尺度法

Abstract: 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.

Key words: magnetoelastic, thin cylindrical shell, harmonic resonance, stability, bifurcation, multiple scales method