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Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under fringing-field electrostatic actuation

Zahra Rashidi, Saber Azizi Azizishirvanshahi, Omid Rahmani

European Journal of Mechanics - A/Solids, Volume: 116, Issue: Part B, Start page: 105941

Swansea University Author: Saber Azizi Azizishirvanshahi

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DOI (Published version): 10.1016/j.euromechsol.2025.105941

Abstract

Achieving low-frequency MEMS resonators while maintaining the compact size of MEMS sensors has long been a challenge in MEMS design and fabrication. This study focuses on the super-harmonic resonance regions and associated bifurcation points of a curved microbeam sandwiched between two piezoelectric...

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Published in: European Journal of Mechanics - A/Solids
ISSN: 0997-7538 1873-7285
Published: Elsevier BV 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa70839
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spelling 2025-12-12T12:11:32.1000445 v2 70839 2025-11-05 Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under fringing-field electrostatic actuation d69732e7f5a3b101651f3654bf7175d0 Saber Azizi Azizishirvanshahi Saber Azizi Azizishirvanshahi true false 2025-11-05 ACEM Achieving low-frequency MEMS resonators while maintaining the compact size of MEMS sensors has long been a challenge in MEMS design and fabrication. This study focuses on the super-harmonic resonance regions and associated bifurcation points of a curved microbeam sandwiched between two piezoelectric layers and subjected to fringing-field electrostatic actuation. The nonlinear equations of motion are derived, and the dependence of the electrostatic force on displacement is analysed using a finite element approach. The microbeam is excited by a combination of DC and AC electrostatic actuation, along with a tuning DC piezoelectric voltage. The influence of the piezoelectric voltage on the variation of the natural frequency under a given DC electrostatic excitation is examined. The frequency response curves are obtained over a broad excitation range, extending from below the primary resonance, through the super-harmonic regime, and beyond the primary resonance region. Bifurcation points are identified using Floquet multipliers. The results indicate that strong quadratic and cubic nonlinearities lead to the emergence of super-harmonic resonance zones of orders 1/2 and 1/3 in the frequency response, enabling the development of low-frequency resonators while retaining the advantages of MEMS-scale sensors. This effect is particularly significant in the design of MEMS energy harvesters, facilitating energy extraction from low-frequency mechanical noise. The simultaneous presence of nonlinearities of orders 1/2 and 1/3 and even higher orders generates multiple resonance zones within the super-harmonic regime, enabling the design of broadband low-frequency energy harvesters and MEMS wide-bandpass filters. Journal Article European Journal of Mechanics - A/Solids 116 Part B 105941 Elsevier BV 0997-7538 1873-7285 Nonlinear Dynamics; Super-harmonic secondary resonance; Low-frequency MEMS resonators; Wide-band; Initially curved microbeam; Fringing-field electrostatic actuation; Piezoelectric actuation 1 3 2026 2026-03-01 10.1016/j.euromechsol.2025.105941 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University SU Library paid the OA fee (TA Institutional Deal) Swansea University 2025-12-12T12:11:32.1000445 2025-11-05T10:36:22.9094510 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 70839__35808__859fb9f763464a3cb8ae8104db922511.pdf 70839.VOR.pdf 2025-12-12T12:09:03.6211149 Output 3428868 application/pdf Version of Record true © 2025 The Authors. This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/
title Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under fringing-field electrostatic actuation
spellingShingle Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under fringing-field electrostatic actuation
Saber Azizi Azizishirvanshahi
title_short Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under fringing-field electrostatic actuation
title_full Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under fringing-field electrostatic actuation
title_fullStr Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under fringing-field electrostatic actuation
title_full_unstemmed Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under fringing-field electrostatic actuation
title_sort Enhanced super-harmonic resonance in piezoelectrically laminated curved microbeam resonators under 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 European Journal of Mechanics - A/Solids
container_volume 116
container_issue Part B
container_start_page 105941
publishDate 2026
institution Swansea University
issn 0997-7538
1873-7285
doi_str_mv 10.1016/j.euromechsol.2025.105941
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 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
document_store_str 1
active_str 0
description Achieving low-frequency MEMS resonators while maintaining the compact size of MEMS sensors has long been a challenge in MEMS design and fabrication. This study focuses on the super-harmonic resonance regions and associated bifurcation points of a curved microbeam sandwiched between two piezoelectric layers and subjected to fringing-field electrostatic actuation. The nonlinear equations of motion are derived, and the dependence of the electrostatic force on displacement is analysed using a finite element approach. The microbeam is excited by a combination of DC and AC electrostatic actuation, along with a tuning DC piezoelectric voltage. The influence of the piezoelectric voltage on the variation of the natural frequency under a given DC electrostatic excitation is examined. The frequency response curves are obtained over a broad excitation range, extending from below the primary resonance, through the super-harmonic regime, and beyond the primary resonance region. Bifurcation points are identified using Floquet multipliers. The results indicate that strong quadratic and cubic nonlinearities lead to the emergence of super-harmonic resonance zones of orders 1/2 and 1/3 in the frequency response, enabling the development of low-frequency resonators while retaining the advantages of MEMS-scale sensors. This effect is particularly significant in the design of MEMS energy harvesters, facilitating energy extraction from low-frequency mechanical noise. The simultaneous presence of nonlinearities of orders 1/2 and 1/3 and even higher orders generates multiple resonance zones within the super-harmonic regime, enabling the design of broadband low-frequency energy harvesters and MEMS wide-bandpass filters.
published_date 2026-03-01T05:30:37Z
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