Multiple timescale spectral analysis of a linear fractional visco-elastic oscillator under arbitrary stationary input Online publication date: Wed, 09-Oct-2019
by Vincent Denoël
International Journal of Sustainable Materials and Structural Systems (IJSMSS), Vol. 3, No. 3/4, 2018
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.
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