Thermal effects on nonlinear vibrations of an axially moving beam with an intermediate spring-mass support

Article type: Research Article

Authors: Kazemirad, Siavash | Ghayesh, Mergen H. | Amabili, Marco

Affiliations: Department of Mechanical Engineering, McGill University, Montreal, QC, Canada

Note: [] Corresponding author: Mergen H. Ghayesh, Department of Mechanical Engineering, McGill University, Montreal, QC, Canada H3A 0C3, Tel.: +1 514 398 6290; E-mail: [email protected]

Abstract: The thermo-mechanical nonlinear vibrations and stability of a hinged-hinged axially moving beam, additionally supported by a nonlinear spring-mass support are examined via two numerical techniques. The system is subjected to a transverse harmonic excitation force as well as a thermal loading. Hamilton's principle is employed to derive the equations of motion; it is discretized into a multi-degree-freedom system by means of the Galerkin method. The steady state resonant response of the system for both cases with and without an internal resonance between the first two modes is examined via the pseudo-arclength continuation technique. In the second method, direct time integration is employed to construct bifurcation diagrams of Poincaré maps of the system.

Keywords: Axially moving beams, thermo-mechanical vibrations, spring-mass support, nonlinear dynamics, stability

DOI: 10.3233/SAV-120752

Journal: Shock and Vibration, vol. 20, no. 3, pp. 385-399, 2013