关键词: 多尺度法, 矩形板, 稳定性, 谐波共振, 轴向运动

Abstract: The nonlinear vibration problem of a thin rectangle plate moving along axial direction is considered here. Based on kinetic energy and strain energy of the thin plate, the nonlinear vibration equation of an axially moving plate considering geometric nonlinearity is deduced by using Hamilton principle. The nonlinear ordinary differential equations of thin plate simply supported on sour sides are gotten by using the given displacement function and stress function and Galerkin method. The multiscale method is used to solve those equations. The frequency-response equation of steady motion under subharmonic responses is obtained, and the stability of solution is analyzed. According to the Liapunov stability theory, the criteria of stability for stable solution are obtained. By the numerical examples, the curves of resonance amplitude changing and the corresponding phase diagrams under different load and speed are obtained. The bifurcation point and doubling time are discussed. The affects of transverse load and axially moving speed on the nonlinear dynamic behaviors of system are discussed in detail.

Key words: Axially moving, Harmonic resonance, Multiple scales method, Rectangular plate, Stability