Magnetoelastic simultaneous resonance of axially moving plate strip under a line load in stationary magnetic field

Abstract

This paper studies the primary-internal simultaneous resonance of the moving ferromagnetic thin plate with the action of an alternating line load in a transverse stationary magnetic field. Based on the theory of thin plates, expressions of strain energy and kinetic energy of the thin plate are given. According to the theoretical magnetoelastic model for ferromagnets, the calculation formula for electromagnetic force is derived. The magnetoelastic coupling nonlinear vibration equation is established by using Hamilton’s principle. Duffing-type nonlinear differential equations are obtained for the clamped-hinged plate strip by applying the Galerkin method. The steady-state response of the system with primary resonance and 1:3 internal resonance is given by using the method of multiple scales, and the stability of steady-state solutions are analyzed according to the theory of Lyapunov stability. The primary-internal simultaneous resonance characteristics of the plate strip are presented through numerical examples. Results show that: energy exchange between the first two modes is available and the first mode dominates; jump phenomena exist in amplitude–frequency curves; both the values of steady solutions and the multi-valued regions of amplitude change with varieties of physical parameters; and numerical results agree with analytical results, which verifies the reliability of analytical research method in this paper.