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Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation

Nikola Nešić, Milan Cajić, Danilo Karlicic Orcid Logo, Goran Janevski

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Volume: 235, Issue: 20, Start page: 095440622093632

Swansea University Author: Danilo Karlicic Orcid Logo

Abstract

This paper investigates the dynamic behavior of a geometrically nonlinear nanobeam resting on the fractional visco-Pasternak foundation and subjected to dynamic axial and transverse loads. The fractional-order governing equation of the system is derived and then discretized by using the single-mode...

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Published in: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
ISSN: 0954-4062 2041-2983
Published: SAGE Publications 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54763
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spelling 2021-12-06T16:13:29.8038537 v2 54763 2020-07-16 Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation d99ee591771c238aab350833247c8eb9 0000-0002-7547-9293 Danilo Karlicic Danilo Karlicic true false 2020-07-16 EEN This paper investigates the dynamic behavior of a geometrically nonlinear nanobeam resting on the fractional visco-Pasternak foundation and subjected to dynamic axial and transverse loads. The fractional-order governing equation of the system is derived and then discretized by using the single-mode Galerkin discretization. Corresponding forced Mathieu-Duffing equation is solved by using the perturbation multiple time scales method for the weak nonlinearity and by the semi-numerical incremental harmonic balance method for the strongly nonlinear case. A comparison of the results from two methods is performed in the validation study for the weakly nonlinear case and a fine agreement is achieved. A parametric study is performed and the advantages and deficiencies of each method are discussed for order two and three superharmonic resonance conditions. The results demonstrate a significant influence of the fractional-order damping of the visco-Pasternak foundation as well as the nonlocal parameter and external excitation load on the frequency response of the system. The proposed methodology can be used in pre-design procedures of novel energy harvesting and sensor devices at small scales exhibiting nonlinear dynamic behavior. Journal Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 235 20 095440622093632 SAGE Publications 0954-4062 2041-2983 Nanobeams, nonlocal elasticity, fractional damping, nonlinear vibration, multiple scales method, incremental harmonic balance 2 7 2020 2020-07-02 10.1177/0954406220936322 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2021-12-06T16:13:29.8038537 2020-07-16T12:37:44.9784758 College of Engineering Engineering Nikola Nešić 1 Milan Cajić 2 Danilo Karlicic 0000-0002-7547-9293 3 Goran Janevski 4 54763__17832__73ad077ffa7248a9b367f39fcabbcaca.pdf 54763.pdf 2020-08-03T13:44:46.6985587 Output 1559509 application/pdf Accepted Manuscript true true English
title Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
spellingShingle Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
Danilo Karlicic
title_short Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
title_full Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
title_fullStr Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
title_full_unstemmed Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
title_sort Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation
author_id_str_mv d99ee591771c238aab350833247c8eb9
author_id_fullname_str_mv d99ee591771c238aab350833247c8eb9_***_Danilo Karlicic
author Danilo Karlicic
author2 Nikola Nešić
Milan Cajić
Danilo Karlicic
Goran Janevski
format Journal article
container_title Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
container_volume 235
container_issue 20
container_start_page 095440622093632
publishDate 2020
institution Swansea University
issn 0954-4062
2041-2983
doi_str_mv 10.1177/0954406220936322
publisher SAGE Publications
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 1
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description This paper investigates the dynamic behavior of a geometrically nonlinear nanobeam resting on the fractional visco-Pasternak foundation and subjected to dynamic axial and transverse loads. The fractional-order governing equation of the system is derived and then discretized by using the single-mode Galerkin discretization. Corresponding forced Mathieu-Duffing equation is solved by using the perturbation multiple time scales method for the weak nonlinearity and by the semi-numerical incremental harmonic balance method for the strongly nonlinear case. A comparison of the results from two methods is performed in the validation study for the weakly nonlinear case and a fine agreement is achieved. A parametric study is performed and the advantages and deficiencies of each method are discussed for order two and three superharmonic resonance conditions. The results demonstrate a significant influence of the fractional-order damping of the visco-Pasternak foundation as well as the nonlocal parameter and external excitation load on the frequency response of the system. The proposed methodology can be used in pre-design procedures of novel energy harvesting and sensor devices at small scales exhibiting nonlinear dynamic behavior.
published_date 2020-07-02T04:31:27Z
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