The incremental harmonic balance method for nonlinear vibration of axially moving beams

In this paper, the incremental harmonic balance (IHB) method is formulated for the nonlinear vibration analysis of axially moving beams. The Galerkin method is used to discretize the governing equations. A high-dimensional model that can take nonlinear model coupling into account is derived. The forced response of an axially moving strip with internal resonance between the first two transverse modes is studied. Particular attention is paid to the fundamental, superharmonic and subharmonic resonance as the excitation frequency is close to the first, second or one-third of the first natural frequency of the system. Numerical results reveal the rich and interesting nonlinear phenomena that have not been presented in the existent literature on the nonlinear vibration of axially moving media.