Fractional damping: Stochastic origin and finite approximations

Singh, Satwinder Jit and Chatterjee, Anindya (2007) Fractional damping: Stochastic origin and finite approximations. In: 2nd Symposium on Fractional Derivatives and Their Applications (FDTAs, SEP, 2005, Long Beach, CA.

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Abstract

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

Item Type:	Conference Paper
Publisher:	Springer
Additional Information:	Copyright of this article beongs to Springer.
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	30 Mar 2010 10:55
Last Modified:	19 Sep 2010 05:57
URI:	http://eprints.iisc.ac.in/id/eprint/26267

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