Nonlinear analysis of forced responses of an axially moving beam by incremental harmonic balance method

Abstract

This paper analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces by Incremental Harmonic Balance (IHB) method. Attention is paid to the fundamental resonance as the force frequency is close to the first frequencies ω1 of the system. Galerkin method is used to discretize the governing equations and the IHB method is used to illustrate the nonlinear dynamic behavior of the axially moving beam. The stable and unstable periodic solutions for given parameters are determined by the multivariable Floquet theory. Hsu's method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration. © 2010 American Institute of Physics.