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Type: Journal article
Title: Nonlinear stability and bifurcations of an axially moving beam in thermal environment
Author: Ghayesh, M.
Amabili, M.
Citation: Journal of Vibration and Control, 2015; 21(15):2981-2994
Publisher: SAGE Publications
Issue Date: 2015
ISSN: 1077-5463
Statement of
Mergen H Ghayesh and Marco Amabili
Abstract: The thermo-mechanical nonlinear dynamics of an axially moving beam with coupled longitudinal and transverse displacements subjected to a distributed harmonic external force is numerically investigated. This includes a case where the system is tuned to a three-to-one internal resonance between the first two transverse modes and a case where it is not is considered. Two coupled nonlinear partial differential equations for the longitudinal and transverse motions are obtained using Hamilton’s principle and constitutive relations, as well as taking into account the thermal effects. The Galerkin method is then used to discretize these equations into a set of coupled nonlinear ordinary differential equations. Two different techniques are employed to solve the resulting equations; the pseudo-arclength continuation method and direct time integration to investigate the periodic vibrations and the global dynamics of the system, respectively. The effect of different parameters on the dynamics of the system is investigated through the frequency-response curves of the system and the bifurcation diagrams of Poincare´ maps. Furthermore, time histories, phase-plane portraits, and fast Fourier transforms are presented for a few different system parameter sets. It is illustrated that the system shows a broad variety of rich dynamics, depending on system parameters and the temperature rise.
Keywords: Beams; coupled vibrations; nonlinear dynamics; stability; thermo-mechanical vibrations
Rights: © The Author(s) 2014 Reprints and permissions:
DOI: 10.1177/1077546313508576
Appears in Collections:Aurora harvest 8
Mechanical Engineering publications

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