Abstract

AbstractIn this paper, the principal-internal resonance produced by the principal resonance and the 1:3 internal resonance for an axially moving thin plate with clamped and hinged supports under periodic line load is studied. Based on Kirchhoff’s basic assumption and large deflection theory, the expressions of kinetic energy and potential energy of thin plate are given, the nonlinear vibration differential equation of axially moving thin strip plate is achieved by means of Hamiltonian variational principle. By using Galerkin discretization method, the ordinary differential vibration equations with respect to time variables are derived. The multi-scale method is used to obtain the approximate solution, and the characteristic equation for the steady-state amplitude of the system is obtained. The effects of axial velocity, external excitation position, external excitation amplitude and external excitation frequency on the resonance amplitude are analyzed. The results show that the amplitude of the system may increase with the increase of the axial velocity, excitation amplitude and frequency of the external excitation, respectively.KeywordsStrip plateAxially movingPrincipal-internal resonanceHarmonic line load

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