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Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation

Zahra Rashidi, Saber Azizi Azizishirvanshahi, Omid Rahmani

Nonlinear Dynamics, Volume: 112, Issue: 12, Pages: 9915 - 9932

Swansea University Author: Saber Azizi Azizishirvanshahi

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DOI (Published version): 10.1007/s11071-024-09575-y

Abstract

This paper explores the chaotic dynamics of a piezoelectrically laminated initially curved microbeam resonator subjected to fringing-field electrostatic actuation, for the first time. The resonator is fully clamped at both ends and is coated with two piezoelectric layers, encompassing both the top a...

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Published in: Nonlinear Dynamics
ISSN: 0924-090X 1573-269X
Published: Springer Science and Business Media LLC 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa66206
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spelling v2 66206 2024-04-28 Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation d69732e7f5a3b101651f3654bf7175d0 Saber Azizi Azizishirvanshahi Saber Azizi Azizishirvanshahi true false 2024-04-28 ACEM This paper explores the chaotic dynamics of a piezoelectrically laminated initially curved microbeam resonator subjected to fringing-field electrostatic actuation, for the first time. The resonator is fully clamped at both ends and is coated with two piezoelectric layers, encompassing both the top and bottom surfaces. The nonlinear motion equation which is obtained by considering the nonlinear fringing-field electrostatic force, includes geometric nonlinearities due to the mid-plane stretching and initial curvature. The motion equation is discretized using Galerkin method and the reduced order system is numerically integrated over the time for the time response. The variation of the first three natural frequencies with respect to the applied electrostatic voltage is determined and the frequency response curve is obtained using the combination of shooting and continuation methods. The bifurcation points have been examined and their types have been clarified based on the loci of the Floquet exponents on the complex plane. The period-doubled branches of the frequency response curves originating from the period doubling (PD) bifurcation points are stablished. It's demonstrated that the succession PD cascades leads to chaotic behavior. The chaotic behavior is identified qualitatively by constructing the corresponding Poincaré section and analyzing the response's associated frequency components. The bifurcation diagram is obtained for a wide range of excitation frequency and thus the exact range in which chaotic behavior occurs for the system is determined. The chaotic response of the system is regularized and controlled by applying an appropriate piezoelectric voltage which shifts the frequency response curve along the frequency axis. Journal Article Nonlinear Dynamics 112 12 9915 9932 Springer Science and Business Media LLC 0924-090X 1573-269X Chaotic dynamics; Period-doubling bifurcation; MEMS resonators; Initially curved;microbeam; Piezoelectric actuation; Fringing-field; electrostatic actuation 1 6 2024 2024-06-01 10.1007/s11071-024-09575-y COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University SU Library paid the OA fee (TA Institutional Deal) Swansea University 2024-05-31T16:36:36.0961448 2024-04-28T18:21:16.8951854 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Zahra Rashidi 1 Saber Azizi Azizishirvanshahi 2 Omid Rahmani 3 66206__30312__adc9bc4590264c43a441f2c4e595e96c.pdf 66206.VoR.pdf 2024-05-08T12:16:24.8464325 Output 9224071 application/pdf Version of Record true Copyright: The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License. true eng http://creativecommons.org/licenses/by/4.0/
title Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation
spellingShingle Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation
Saber Azizi Azizishirvanshahi
title_short Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation
title_full Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation
title_fullStr Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation
title_full_unstemmed Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation
title_sort Period-doubling cascade route to chaos in an initially curved microbeam resonator exposed to fringing-field electrostatic actuation
author_id_str_mv d69732e7f5a3b101651f3654bf7175d0
author_id_fullname_str_mv d69732e7f5a3b101651f3654bf7175d0_***_Saber Azizi Azizishirvanshahi
author Saber Azizi Azizishirvanshahi
author2 Zahra Rashidi
Saber Azizi Azizishirvanshahi
Omid Rahmani
format Journal article
container_title Nonlinear Dynamics
container_volume 112
container_issue 12
container_start_page 9915
publishDate 2024
institution Swansea University
issn 0924-090X
1573-269X
doi_str_mv 10.1007/s11071-024-09575-y
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
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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 Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
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description This paper explores the chaotic dynamics of a piezoelectrically laminated initially curved microbeam resonator subjected to fringing-field electrostatic actuation, for the first time. The resonator is fully clamped at both ends and is coated with two piezoelectric layers, encompassing both the top and bottom surfaces. The nonlinear motion equation which is obtained by considering the nonlinear fringing-field electrostatic force, includes geometric nonlinearities due to the mid-plane stretching and initial curvature. The motion equation is discretized using Galerkin method and the reduced order system is numerically integrated over the time for the time response. The variation of the first three natural frequencies with respect to the applied electrostatic voltage is determined and the frequency response curve is obtained using the combination of shooting and continuation methods. The bifurcation points have been examined and their types have been clarified based on the loci of the Floquet exponents on the complex plane. The period-doubled branches of the frequency response curves originating from the period doubling (PD) bifurcation points are stablished. It's demonstrated that the succession PD cascades leads to chaotic behavior. The chaotic behavior is identified qualitatively by constructing the corresponding Poincaré section and analyzing the response's associated frequency components. The bifurcation diagram is obtained for a wide range of excitation frequency and thus the exact range in which chaotic behavior occurs for the system is determined. The chaotic response of the system is regularized and controlled by applying an appropriate piezoelectric voltage which shifts the frequency response curve along the frequency axis.
published_date 2024-06-01T16:36:34Z
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