Coupled global dynamics of an axially moving viscoelastic beam

Mergen H. Ghayesh*, Marco Amabili, Hamed Farokhi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

79 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)54-74
Number of pages21
JournalInternational Journal of Non-Linear Mechanics
Early online date27 Dec 2012
Publication statusPublished - 1 May 2013


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