4.7 Article

Subcritical parametric response of an axially accelerating beam

期刊

THIN-WALLED STRUCTURES
卷 60, 期 -, 页码 185-193

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ELSEVIER SCI LTD
DOI: 10.1016/j.tws.2012.06.012

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Axially accelerating beams; Time-dependent velocity; Nonlinear dynamics; Pseudo-arclength continuation technique

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In this paper, the planar nonlinear dynamics of an axially accelerating beam in the subcritical speed regime is examined theoretically, via two different numerical techniques, employing a large enough number of modes in order to investigate modal interactions. The equation of motion is discretized via the Galerkin method which results in a set of coupled nonlinear ordinary differential equations (NODES) with time-dependent coefficients. The set of NODEs is solved by means of the pseudo-arclength continuation technique and some of the results are tested and verified via direct time integration of the NODEs. The analyses include the system tuned to a three-to-one internal resonance, as well as for the case where it is not. Results are illustrated through frequency-response diagrams, time traces, phase-plane portraits, and fast Fourier transforms (FFTs). (C) 2012 Elsevier Ltd. All rights reserved.

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