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Approximate Analytical Mean-Square Response of an Impacting Stochastic System Oscillator With Fractional Damping

[+] Author and Article Information
D. Yurchenko

Institute of Mechanical, Process and
Energy Engineering,
Heriot-Watt University,
Edinburgh EH14 4AS, UK
e-mail: d.yurchenko@hw.ac.uk

A. Burlon

Dipartimento di Ingegneria Civile, dell’ Ambiente,
dell’ Energia e dei Materiali (DICEAM),
Università di Reggio Calabria,
Reggio Calabria 89124, Italy
e-mail: a.burlon91@gmail.com

M. Di Paola

Dipartimento di Ingegneria Civile, Ambientale,
Aerospaziale e dei Materiali (DICAM),
Università degli Studi di Palermo,
Palermo 90128, Italy
e-mail: mario.dipaola@unipa.it

G. Failla

Dipartimento di Ingegneria Civile, dell’ Ambiente,
dell’ Energia e dei Materiali (DICEAM),
Università di Reggio Calabria,
Reggio Calabria 89124, Italy
e-mail: giuseppe.failla@unirc.it

A. Pirrotta

Dipartimento di Ingegneria Civile, Ambientale,
Aerospaziale e dei Materiali (DICAM),
Università degli Studi di Palermo,
Palermo 90128, Italy;
Department of Mathematical Sciences,
University of Liverpool,
Liverpool L69 7ZL, UK
e-mail: antonina.pirrotta@unipa.it

1Corresponding author.

Manuscript received June 22, 2016; final manuscript received October 9, 2016; published online June 12, 2017. Assoc. Editor: Ioannis Kougioumtzoglou.

ASME J. Risk Uncertainty Part B 3(3), 030903 (Jun 12, 2017) (5 pages) Paper No: RISK-16-1093; doi: 10.1115/1.4036701 History: Received June 22, 2016; Revised October 09, 2016

The paper deals with the stochastic dynamics of a vibroimpact single-degree-of-freedom system under a Gaussian white noise. The system is assumed to have a hard type impact against a one-sided motionless barrier, located at the system's equilibrium. The system is endowed with a fractional derivative element. An analytical expression for the system's mean squared response amplitude is presented and compared with the results of numerical simulations.

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References

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Figures

Grahic Jump Location
Fig. 1

Approximation of an absolute value function with n = 2, n = 4, n = 8, and n = 10

Grahic Jump Location
Fig. 2

Mean-square value of the response amplitude for different values of the fractional order α, for three different values of the noise intensity q, q1 = 1, q2 = 5, q3 = 10, for Cα = 1 and for a restitution coefficient r = 1

Grahic Jump Location
Fig. 3

Mean-square value of the response amplitude for different values of the fractional order α, for three different values of Cα, Cα1=5, Cα2=1, Cα3=0.5, for q = 1 and for a restitution coefficient r = 1

Grahic Jump Location
Fig. 4

Mean-square value of the response amplitude for different values of the fractional order α and for a restitution coefficient r = 0.9 and for q = 1, Cα = 1, Ω = 1

Grahic Jump Location
Fig. 5

Mean-square value of the response amplitude for different values of the fractional order α and for a restitution coefficient r = 0.8 and for q = 1, Cα = 1 and Ω = 1

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