Shock and Vibration

Shock and Vibration / 2012 / Article

Open Access

Volume 19 |Article ID 321421 | https://doi.org/10.3233/SAV-2010-0634

R. Abu-Mallouh, I. Abu-Alshaikh, H.S. Zibdeh, Khaled Ramadan, "Response of Fractionally Damped Beams with General Boundary Conditions Subjected to Moving Loads", Shock and Vibration, vol. 19, Article ID 321421, 15 pages, 2012. https://doi.org/10.3233/SAV-2010-0634

Response of Fractionally Damped Beams with General Boundary Conditions Subjected to Moving Loads

Received14 Dec 2009
Revised01 Nov 2010

Abstract

This paper presents the transverse vibration of Bernoulli-Euler homogeneous isotropic damped beams with general boundary conditions. The beams are assumed to be subjected to a load moving at a uniform velocity. The damping characteristics of the beams are described in terms of fractional derivatives of arbitrary orders. In the analysis where initial conditions are assumed to be homogeneous, the Laplace transform cooperates with the decomposition method to obtain the analytical solution of the investigated problems. Subsequently, curves are plotted to show the dynamic response of different beams under different sets of parameters including different orders of fractional derivatives. The curves reveal that the dynamic response increases as the order of fractional derivative increases. Furthermore, as the order of the fractional derivative increases the peak of the dynamic deflection shifts to the right, this yields that the smaller the order of the fractional derivative, the more oscillations the beam suffers. The results obtained in this paper closely match the results of papers in the literature review.

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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