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Open AccessArticle

An Analysis of the Dynamical Behaviour of Systems with Fractional Damping for Mechanical Engineering Applications

Department of Mechanics, Design and Industrial Management, University of Deusto, Avenida de las Universidades 24, 48007 Bilbao, Spain
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1499;
Received: 21 November 2019 / Revised: 4 December 2019 / Accepted: 8 December 2019 / Published: 11 December 2019
(This article belongs to the Special Issue Symmetry in Mechanical Engineering)
Fractional derivative models are widely used to easily characterise more complex damping behaviour than the viscous one, although the underlying properties are not trivial. Several studies about the mathematical properties can be found, but are usually far from the most daily applications. Thus, this paper studies the properties of structural systems whose damping is represented by a fractional model from the point of view of a mechanical engineer. First, a single-degree-of-freedom system with fractional damping is analysed. Specifically, the distribution of the poles and the dynamic response to several excitations is studied for different model parameter values highlighting dissimilarities from systems with conventional viscous damping. In fact, thanks to fractional models, particular behaviours are observed that cannot be reproduced by classical ones. Finally, the dynamics of a machine shaft supported by two bearings presenting fractional damping is analysed. The study is carried out by the Finite Element method, deriving in a system with symmetric matrices. Eigenvalues and eigenvectors are obtained by means of an iterative method, and the effect of damping is visualised on the mode shapes. In addition, the response to a perturbation is computed, revealing the influence of the model parameters on the resulting vibration. View Full-Text
Keywords: fractional damping; vibration; dynamic behaviour fractional damping; vibration; dynamic behaviour
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Zarraga, O.; Sarría, I.; García-Barruetabeña, J.; Cortés, F. An Analysis of the Dynamical Behaviour of Systems with Fractional Damping for Mechanical Engineering Applications. Symmetry 2019, 11, 1499.

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