Title: Multiple timescale spectral analysis of a linear fractional visco-elastic oscillator under arbitrary stationary input

Authors: Vincent Denoël

Addresses: Structural and Stochastic Dynamics, University of Liège, Belgium

Abstract: This paper studies the structural response of a single degree-of-freedom structure including a fractional derivative constitutive term. Unlike usual existing models for this kind of structure, the excitation is not required to be a Markovian process; however, it is assumed to be slowly varying in time, so that a timescale separation is used. Following the general formulation of the multiple timescale spectral analysis, the solution is developed as a sum of background and resonant components. A specificity of the fractional derivative is that background component is not obtained as the variance of the loading divided by the stiffness of the system, as in standard linear systems. On the contrary the resonant component is expressed as a simple extension of the existing formulation for a viscous system, at least at leading order. The proposed solution is validated by comparison with a stochastic averaging approach.

Keywords: Caputo fractional derivative; Riemann-Liouville fractional derivative; perturbation analysis; stochastic averaging; background component; resonant component.

DOI: 10.1504/IJSMSS.2018.10024415

International Journal of Sustainable Materials and Structural Systems, 2018 Vol.3 No.3/4, pp.189 - 202

Received: 15 May 2018
Accepted: 17 Dec 2018

Published online: 09 Oct 2019 *

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