Two-dimensional nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed

Ghayesh, Mergen H., Amabili, Marco and Farokhi, Hamed (2013) Two-dimensional nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed. Chaos, Solitons & Fractals, 52. pp. 8-29. ISSN 0960-0779

Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.chaos.2013.03.005

Abstract

In the present study, the coupled nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed is investigated employing a numerical technique. The equations of motion for both the transverse and longitudinal motions are obtained using Newton's second law of motion and the constitutive relations. A two-parameter rheological model of the Kelvin-Voigt energy dissipation mechanism is employed in the modelling of the viscoelastic beam material, in which the material time derivative is used in the viscoelastic constitutive relation. The Galerkin method is then applied to the coupled nonlinear equations, which are in the form of partial differential equations, resulting in a set of nonlinear ordinary differential equations (ODEs) with time-dependent coefficients due to the axial acceleration. A change of variables is then introduced to this set of ODEs to transform them into a set of first-order ordinary differential equations. A variable step-size modified Rosenbrock method is used to conduct direct time integration upon this new set of first-order nonlinear ODEs. The mean axial speed and the amplitude of the speed variations, which are taken as bifurcation parameters, are varied, resulting in the bifurcation diagrams of Poincaré maps of the system. The dynamical characteristics of the system are examined more precisely via plotting time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms (FFTs).

Item Type: Article
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 30 Aug 2018 17:26
Last Modified: 30 Aug 2018 17:26
URI: http://nrl.northumbria.ac.uk/id/eprint/35531

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