The Study For Nonlinear Harmonic Resonance Of Axailly Moving Rectangular Plate

In nature and engineering practice, the vibration of axially moving systems is a very common phenomenon. It is widespread in the military, aerospace, machinery, electronics, civil engineering, such as power transmission belts, tapes, textile fibers, band saw, paper, and the composite laminated panels of aerospace engineering. Therefore, the study on the vibration characteristics of axially moving systems has important theoretical and practical significance.In this paper, the axially moving rectangular plate subjected to external excitation is studied. Super harmonic resonance and subharmonic resonance of the axially moving rectangular plates in the different boundary conditions are focused discussed. Firstly, according to the classical plate theory and the parameters of axially moving systems, the nonlinear forced vibration equations of axially moving rectangular plates respectively under the harmonic excitation in the different boundary conditions were deduced by using Galerkin method.Secondly, for super harmonic resonance and subharmonic resonance of axially moving plate with four simply supported edges, the amplitude-frequency response equations were respectively derived using multi-scale method. Based on Lyapunov stability theory, the critical conditions of steady-state solutions'stability were gotten; for super harmonic resonance and subharmonic resonance of axially moving plate with two opposite ends simply supported and two opposite ends free, based on the parameters transformation, the analysis of numerical calculation was carried on.Finally, the axially moving rectangular plates in different boundary conditions were analyzed by programming calculation. In the super harmonic resonance and subharmoic resonance, the amplitude-frequency curves, the time history plot, the phase chart, the Poincarémap and the spectrum plot of the axially moving rectangular plate with four simply supported edges were derived under different parameters. In the boundary condition of two opposite ends simply supported and two opposite ends free, the time history plot, the phase chart, the Poincarémap and the spectrum plot for the super harmonic resonance and subharmoic resonance the of the axially moving rectangular plate were also derived under different parameters. The influences of different parameters on nonlinear resonance properties of system,such as load, damping, speed and the width of plate , were discussed.