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research-article

Stochastic analysis of a non-local fractional viscoelastic bar forced by Gaussian white noise

[+] Author and Article Information
Gioacchino Alotta

Department of Civil, Environmental, Aerospace, Materials Engineering (DICAM) University of Palermo Viale delle Scienze Ed. 8, 90128 Palermo, Italy
gioacchino.alotta@unipa.it

Giuseppe Failla

Departiment of Civil, Energy, Environment, Materials Engineering (DICEAM) University of Reggio Calabria Via Graziella, Località Feo di Vito, 89124 Reggio Calabria, Italy
giuseppe.failla@unirc.it

Francesco Paolo Pinnola

Engineering and Architecture Faculty University of Enna “Kore” Viale delle Olimpiadi, 94100 Enna, Italy
francescopaolo.pinnola@unikore.it

1Corresponding author.

ASME doi:10.1115/1.4036702 History: Received June 22, 2016; Revised October 16, 2016

Abstract

Recently, a displacement-based non-local bar model has been developed. The model is based on the assumption that non-local forces can be modeled as viscoelastic long-range interactions mutually exerted by non-adjacent bar segments due to their relative motion; the classical local stress resultants are also present in the model. A finite element (FE) formulation with closed-form expressions of the elastic and viscoelastic matrices has also been obtained. Specifically, Caputo's fractional derivative has been used in order to model viscoelastic long-range interaction. The static and quasi-static response has been already investigated. This work investigates the stochastic response of the non-local fractional viscoelastic bar introduced in previous papers, discretized with the FEM, forced by a Gaussian white noise. Since the bar is forced by a Gaussian white noise, dynamical effects cannot be neglected. The system of coupled fractional differential equations ruling the bar motion can be decoupled only by means of the fractional order state variable expansion. It is shown that following this approach Monte Carlo simulation can be performed very efficiently. For simplicity, here the work is limited to the axial response, but can be easily extended to transverse motion.

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