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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,
Enna 94100, Italy
e-mail: valeria.artale@unikore.it

Giacomo Navarra

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

Angela Ricciardello

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

Giorgio Barone

School of Civil and Building Engineering,
Loughborough University,
Loughborough, Leicestershire LE11 3TU, UK
e-mail: g.barone@lboro.ac.uk

1Corresponding author.

Manuscript received June 17, 2016; final manuscript received December 10, 2016; published online June 12, 2017. Assoc. Editor: Mario Di Paola.

ASME J. Risk Uncertainty Part B 3(3), 030901 (Jun 12, 2017) (6 pages) Paper No: RISK-16-1091; doi: 10.1115/1.4036700 History: Received June 17, 2016; Revised December 10, 2016

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 behavior of many complex mechanical systems, e.g., the nonlocal or nonviscous 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 expressions 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 orders (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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References

Figures

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Fig. 2

Fractional oscillator

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Fig. 3

FSMs for classic linear oscillators with varying damping ratios

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Fig. 4

Existence dominion for FSMs of fractional oscillators

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Fig. 5

Real-order FSMs for fractional oscillators

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Fig. 6

SMs of order 0, 1, and 2 for fractional oscillators

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