Magnetic-Solid Coupling Nonlinear Vibration of Functionally Graded Cylindrical Shell in Magnetic Field

The nonlinear magnetic-solid coupling resonance problem of ferromagnetic functionally graded (FG) cylindrical shell in transverse magnetic field is investigated. Based on the Kirchhoff-Donnell nonlinear theory on physical neutral surface, the expressions of kinetic energy and strain energy are obtained by considering the geometric nonlinear effect. Combined with the theory of electromagnetic elasticity, the expressions of Lorentz force and magnetization force of the FG shell are obtained. The magnetic-solid coupling vibration equations with initial deflection are established by using Hamilton principle. The vibration equations are discretized by Galerkin integral method. The amplitude frequency equation and stability discrimination of steady-state solutions are given by averaging method and Lyapunov stability theory. Through the example analysis, the law curves of the system amplitude with different parameters are drawn. The influences of controlling parameters on the primary resonance response of the system are characterized. The results show that amplitude and position of the excitation force and magnetic field strength have obvious effects on the resonance and stability of the system. In addition, the vibration responses are also influenced by the power-law index and the size of the shell.