Coupled systems mechanics

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Internal resonance and nonlinear response of an axially moving beam: two numerical techniques

  • Ghayesh, Mergen H. (Department of Mechanical Engineering, McGill University) ;
  • Amabili, Marco (Department of Mechanical Engineering, McGill University)
  • Received : 2012.06.21
  • Accepted : 2012.09.08
  • Published : 2012.09.25
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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).

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References

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