Nonlinear Analysis of Forced Responses of an Axially Moving Beam by Incremental Harmonic Balance Method

Abstract

This article analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces. The governing equation of the beam vibration is developed using Hamilton's Principle. The stable and unstable periodic solutions are obtained by employing the multivariable Floquet theory and incremental harmonic balance (IHB) method. In the solution procedure, 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.