Coupled global dynamics of an axially moving viscoelastic beam

Ghayesh, Mergen H., Amabili, Marco and Farokhi, Hamed (2013) Coupled global dynamics of an axially moving viscoelastic beam. International Journal of Non-Linear Mechanics, 51. pp. 54-74. ISSN 0020-7462

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Abstract

The nonlinear global forced dynamics of an axially moving viscoelastic beam, while both longitudinal and transverse displacements are taken into account, is examined employing a numerical technique. The equations of motion are derived using Newton′s second law of motion, resulting in two partial differential equations for the longitudinal and transverse motions. A two-parameter rheological Kelvin-Voigt energy dissipation mechanism is employed for the viscoelastic structural model, in which the material, not partial, time derivative is used in the viscoelastic constitutive relations; this gives additional terms due to the simultaneous presence of the material damping and the axial speed. The equations of motion for both longitudinal and transverse motions are then discretized via Galerkin's method, in which the eigenfunctions for the transverse motion of a hinged-hinged linear stationary beam are chosen as the basis functions. The subsequent set of nonlinear ordinary equations is solved numerically by means of the direct time integration via modified Rosenbrock method, resulting in the bifurcation diagrams of Poincaré maps. The results are also presented in the form of time histories, phase-plane portraits, and fast Fourier transform (FFTs) for specific sets of parameters.

Item Type:	Article
Uncontrolled Keywords:	Axially moving beams; Coupled nonlinear dynamics; Viscoelasticity; Stability; Bifurcation
Subjects:	H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User:	Paul Burns
Date Deposited:	30 Aug 2018 17:19
Last Modified:	11 Oct 2019 19:30
URI:	http://nrl.northumbria.ac.uk/id/eprint/35530

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