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.
Exact Closed-Form Fractional Spectral Moments for Linear Fractional Oscillators Excited by a White Noise
Manuscript received June 17, 2016; final manuscript received December 10, 2016; published online June 12, 2017. Assoc. Editor: Mario Di Paola.
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Artale, V., Navarra, G., Ricciardello, A., and Barone, G. (June 12, 2017). "Exact Closed-Form Fractional Spectral Moments for Linear Fractional Oscillators Excited by a White Noise." ASME. ASME J. Risk Uncertainty Part B. September 2017; 3(3): 030901. https://doi.org/10.1115/1.4036700
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