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research-article

Exact closed-form Fractional Spectral Moments for linear fractional oscillators excited by a white noise

[+] Author and Article Information
Valeria Artale

Engineering and Architecture Faculty University of Enna “Kore” via delle Olimpiadi, 94100, Enna, Italy
valeria.artale@unikore.it

Giacomo Navarra

Engineering and Architecture Faculty University of Enna “Kore” via delle Olimpiadi, 94100, Enna, Italy
giacomo.navarra@unikore.it

Angela Ricciardello

Engineering and Architecture Faculty University of Enna “Kore” via delle Olimpiadi, 94100, Enna, Italy
angela.riccardello@unikore.it

Giorgio Barone

School of Civil and Building Engineering Loughborough University, Loughborough Leicestershire LE11 3TU, United Kingdom
g.barone@lboro.ac.uk

1Corresponding author.

ASME doi:10.1115/1.4036700 History: Received June 17, 2016; Revised December 10, 2016

Abstract

In the last decades the research community has shown an increasing interest in the engineering applications of fractional calculus, which allows to accurately characterize the static and dynamic behaviour of many complex mechanical systems, e.g. the non-local or non-viscous constitutive law. In particular, fractional calculus has gained considerable importance in the random vibration analysis of engineering structures provided with viscoelastic damping. In this case, the evaluation of the dynamic response in the frequency domain presents significant advantages, once a probabilistic characterization of the input is provided. On the other hand, closed-form expression for the response statistics of dynamical fractional systems are not available even for the simplest cases. Taking advantage of the Residue Theorem, in this paper the exact expressions of the spectral moments of integer and complex order (i.e. fractional spectral moments) of linear fractional oscillators driven by acceleration time histories obtained as samples of stationary Gaussian white noise processes are determined.

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