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Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation

Danilo Karlicic Orcid Logo, Predrag Kozić, Milan Cajić

European Journal of Mechanics - A/Solids, Volume: 72, Pages: 66 - 78

Swansea University Author: Danilo Karlicic Orcid Logo

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DOI (Published version): 10.1016/j.euromechsol.2018.02.014

Abstract

In this paper, we analyzed the stochastic stability of a single-layer graphene sheet resting on a viscoelastic foundation and influenced by the in-plane magnetic field. The mechanical model of a graphene sheet is given as an orthotropic and viscoelastic nanoplate while the viscoelastic foundation is...

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Published in: European Journal of Mechanics - A/Solids
ISSN: 0997-7538
Published: Elsevier BV 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa49827
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spelling 2020-06-16T15:32:40.9085314 v2 49827 2019-03-29 Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation d99ee591771c238aab350833247c8eb9 0000-0002-7547-9293 Danilo Karlicic Danilo Karlicic true false 2019-03-29 EEN In this paper, we analyzed the stochastic stability of a single-layer graphene sheet resting on a viscoelastic foundation and influenced by the in-plane magnetic field. The mechanical model of a graphene sheet is given as an orthotropic and viscoelastic nanoplate while the viscoelastic foundation is of the Kelvin-Voigt type. We assume that the graphene sheet is influenced by the in-plane random forces variable with time and exerted in-plane magnetic field. Based on the Eringen's nonlocal continuum theory and Kirchhoff – Love plate theory, the governing equation of motion is derived by considering the influence of the Lorentz forces obtained from the classical Maxwell relations. In order to investigate the stochastic stability of such system, the maximal and moment Lyapunov exponents are considered by using the perturbation method. The predicted approximated analytical results for the p-th moment Lyapunov exponents are validated by the Monte Carlo method. Moreover, the boundaries of almost-sure and moment stability of the viscoelastic nanoplate are determined as functions of different system parameters. The influences of the nonlocal and magnetic field parameters, stiffness and damping coefficients and spectral density on the moment Lyapunov exponents are investigated through several numerical examples. Presented results reveal that the applied in-plane magnetic field could be successfully used to improve stability performances of nano-electromechanical systems based on graphene sheets. Journal Article European Journal of Mechanics - A/Solids 72 66 78 Elsevier BV 0997-7538 Nonlocal elasticity theory; Stochastic stability; Monte Carlo simulation; Magnetic field; Graphene sheet 30 11 2018 2018-11-30 10.1016/j.euromechsol.2018.02.014 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2020-06-16T15:32:40.9085314 2019-03-29T21:41:40.5062907 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Danilo Karlicic 0000-0002-7547-9293 1 Predrag Kozić 2 Milan Cajić 3
title Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation
spellingShingle Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation
Danilo Karlicic
title_short Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation
title_full Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation
title_fullStr Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation
title_full_unstemmed Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation
title_sort Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation
author_id_str_mv d99ee591771c238aab350833247c8eb9
author_id_fullname_str_mv d99ee591771c238aab350833247c8eb9_***_Danilo Karlicic
author Danilo Karlicic
author2 Danilo Karlicic
Predrag Kozić
Milan Cajić
format Journal article
container_title European Journal of Mechanics - A/Solids
container_volume 72
container_start_page 66
publishDate 2018
institution Swansea University
issn 0997-7538
doi_str_mv 10.1016/j.euromechsol.2018.02.014
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 0
active_str 0
description In this paper, we analyzed the stochastic stability of a single-layer graphene sheet resting on a viscoelastic foundation and influenced by the in-plane magnetic field. The mechanical model of a graphene sheet is given as an orthotropic and viscoelastic nanoplate while the viscoelastic foundation is of the Kelvin-Voigt type. We assume that the graphene sheet is influenced by the in-plane random forces variable with time and exerted in-plane magnetic field. Based on the Eringen's nonlocal continuum theory and Kirchhoff – Love plate theory, the governing equation of motion is derived by considering the influence of the Lorentz forces obtained from the classical Maxwell relations. In order to investigate the stochastic stability of such system, the maximal and moment Lyapunov exponents are considered by using the perturbation method. The predicted approximated analytical results for the p-th moment Lyapunov exponents are validated by the Monte Carlo method. Moreover, the boundaries of almost-sure and moment stability of the viscoelastic nanoplate are determined as functions of different system parameters. The influences of the nonlocal and magnetic field parameters, stiffness and damping coefficients and spectral density on the moment Lyapunov exponents are investigated through several numerical examples. Presented results reveal that the applied in-plane magnetic field could be successfully used to improve stability performances of nano-electromechanical systems based on graphene sheets.
published_date 2018-11-30T04:01:03Z
_version_ 1763753133245202432
score 11.03559

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