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Abstract The subharmonic resonance and stability of a ferromagnetic rectangular thin plate with four edges clamped in the air-gap magnetic field are studied. Based on the theory of large deflection of thin plate and the basic theory of electromagnetic field, the boundary conditions satisfying the scalar magnetic potential are given, the distribution of magnetic induction intensity of air-gap magnetic field and the equations for the magnetization force on the surface of the ferromagnetic plate and the electromagnetic torque in the body are solved. Considering the electromagnetic force on the thin plate, the nonlinear magnetoelastic coupled vibration equation of the thin plate with magnetostatic load is established by applying the Hamiltonian variational principle, and the partial differential equation is discretized by using Galerkin integral method. Then, the analytical solution and the amplitude-frequency response equation of the subharmonic resonance of the fixed thin plate are further obtained by the averaging method, and the stability conditions of the system are determined according to Lyapunov stability criterion. By means of examples, the curves of the static deflection and electromagnetic force of the thin plate under the variation of parameters are investigated. Based on the amplitude-frequency response equation and the critical conditions of stability solution, the influence laws of the excitation force, the parameters of air-gap magnetic field and the thickness of plate on the amplitudes and stability regions of the thin plate are obtained. The correctness of the analytical solution of this paper is verified by comparing with the numerical calculation result.
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Received: 15 September 2022
Published: 18 August 2023
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2023, Vol. 44 
