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Coupled Systems Mechanics Volume 1, Number 3, September 2012 , pages 235-245 DOI: https://doi.org/10.12989/csm.2012.1.3.235 |
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Internal resonance and nonlinear response of an axially moving beam: two numerical techniques |
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Mergen H. Ghayesh and Marco Amabili
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| Abstract | ||
| The nonlinear resonant response of an axially moving beam is investigated in this paper via two different numerical techniques: the pseudo-arclength continuation technique and direct time integration. In particular, the response is examined for the system in the neighborhood of a three-to-one internal resonance between the first two modes as well as for the case where it is not. The equation of motion is reduced into a set of nonlinear ordinary differential equation via the Galerkin technique. This set is solved using the pseudo-arclength continuation technique and the results are confirmed through use of direct time integration. Vibration characteristics of the system are presented in the form of frequency-response curves, time histories, phase-plane diagrams, and fast Fourier transforms (FFTs). | ||
| Key Words | ||
| axially moving beams; vibrations; stability; bifurcation; internal resonance | ||
| Address | ||
| Mergen H. Ghayesh and Marco Amabili : Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada H3A 0C3 | ||
