The Incremental Harmonic Balance Method for Nonlinear Vibration of Axially Moving Beams

By Kam-Yim Sze, S. H. A. Chen, J. L. Huang. 2005

185 citations recorded by the source corpus.

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.

Subfields: Civil and Structural Engineering, Computational Mechanics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/668ca205268a6ad7dab978338c31646e1fa416d6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Computational Mechanics

In Control and Systems Engineering

Citations in the corpus

Galerkin methods for natural frequencies of high-speed axially moving beams (2010, methodology): “[15] applied the incremental harmonic balance method for transverse and longitudinal motions for nonlinear phenomena of axially moving beams.”
An adaptive harmonic balance method for predicting the nonlinear dynamic responses of mechanical systems—Application to bolted structures (2010, methodology): “[24] who applied HBM on a non linear beam.”
Natural frequencies of nonlinear vibration of axially moving beams (2011, methodology): “[23] applied the incremental harmonic balance method for transverse and longitudinal motions for nonlinear phenomena of axially moving beams.”
The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems (2015, methodology): “The incremental HB applies the incremental procedure to the equations of motion before the harmonic approximation and balance (see [12, 13] or, more recently, [14]).”