Shock and Vibration

Shock and Vibration / 2013 / Article
Special Issue

Nonlinear Vibrations in Elastic Structures: Dynamics and Control

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Open Access

Volume 20 |Article ID 126735 | 10 pages |

Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation

Received08 Oct 2013
Accepted08 Oct 2013


The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann – Liouville fractional derivative of order 0 α ⩽ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann – Liouville fractional derivative with lower terminal at −∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order α and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.

Copyright © 2013 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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