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Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications

Saber Azizi Azizishirvanshahi, Hamed Haddad Khodaparast Orcid Logo, Hadi Madinei Orcid Logo, Mohammad I Younis, Ghader Rezazadeh

Nonlinear Dynamics, Volume: 113, Issue: 18, Pages: 24329 - 24342

Swansea University Authors: Saber Azizi Azizishirvanshahi, Hamed Haddad Khodaparast Orcid Logo, Hadi Madinei Orcid Logo

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DOI (Published version): 10.1007/s11071-025-11379-7

Abstract

This paper presents a novel investigation into the dynamics of a micro ring structure subjected to harmonic base excitation, designed as a highly sensitive MEMS mass sensor or bifurcation-based switch. Leveraging the in-plane nature of the motion, the system exhibits an exceptionally low damping rat...

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Published in: Nonlinear Dynamics
ISSN: 0924-090X 1573-269X
Published: Springer Nature 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa69575
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Leveraging the in-plane nature of the motion, the system exhibits an exceptionally low damping ratio, making it ideal for detecting subtle changes in dynamic behaviour. The governing nonlinear differential equations, incorporating the geometric nonlinearities of the support beams, were derived and simplified into a reduced-order model consisting of coupled nonlinear Duffing-type equations. A key innovation of this study lies in the tunability of the system&#x2019;s frequency ratios, enabling the activation of a 1:3 internal resonance. By varying the length of the support beams while keeping the central ring geometry fixed, the first two natural frequencies were carefully examined, revealing a significant influence on the dynamic response. Frequency response curves confirmed the presence of 1:3 internal resonance near the primary resonance of the first mode, highlighting the potential for efficient energy transfer between modes. 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spelling 2025-11-21T15:38:09.8473042 v2 69575 2025-05-28 Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications d69732e7f5a3b101651f3654bf7175d0 Saber Azizi Azizishirvanshahi Saber Azizi Azizishirvanshahi true false f207b17edda9c4c3ea074cbb7555efc1 0000-0002-3721-4980 Hamed Haddad Khodaparast Hamed Haddad Khodaparast true false d9a10856ae9e6a71793eab2365cff8b6 0000-0002-3401-1467 Hadi Madinei Hadi Madinei true false 2025-05-28 ACEM This paper presents a novel investigation into the dynamics of a micro ring structure subjected to harmonic base excitation, designed as a highly sensitive MEMS mass sensor or bifurcation-based switch. Leveraging the in-plane nature of the motion, the system exhibits an exceptionally low damping ratio, making it ideal for detecting subtle changes in dynamic behaviour. The governing nonlinear differential equations, incorporating the geometric nonlinearities of the support beams, were derived and simplified into a reduced-order model consisting of coupled nonlinear Duffing-type equations. A key innovation of this study lies in the tunability of the system’s frequency ratios, enabling the activation of a 1:3 internal resonance. By varying the length of the support beams while keeping the central ring geometry fixed, the first two natural frequencies were carefully examined, revealing a significant influence on the dynamic response. Frequency response curves confirmed the presence of 1:3 internal resonance near the primary resonance of the first mode, highlighting the potential for efficient energy transfer between modes. Furthermore, a detailed bifurcation analysis uncovered a range of complex nonlinear phenomena, including nonlinear modal interactions, torus bifurcations, quasi-periodic motion, and cyclic fold bifurcations. These bifurcations not only provide deeper insight into the system’s dynamics but also offer additional operational mechanisms for switching applications. The findings demonstrate the system’s capability to exploit nonlinear dynamics for enhanced sensitivity and robustness, paving the way for the development of next-generation MEMS sensors and bifurcation-based devices. Journal Article Nonlinear Dynamics 113 18 24329 24342 Springer Nature 0924-090X 1573-269X Nonlinear dynamics; Internal resonance; Micro ring; MEMS; Duffing oscillator; Bifurcation 1 9 2025 2025-09-01 10.1007/s11071-025-11379-7 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University SU Library paid the OA fee (TA Institutional Deal) This research was supported by the Engineering and Physical Sciences Research Council (EPSRC) under Grant No. EP/Y027914/1. We acknowledge the EPSRC’s support in enabling this work, which addresses key challenges design and fabrication of super sensitive MEMS mass sensors. 2025-11-21T15:38:09.8473042 2025-05-28T13:49:43.8010434 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Saber Azizi Azizishirvanshahi 1 Hamed Haddad Khodaparast 0000-0002-3721-4980 2 Hadi Madinei 0000-0002-3401-1467 3 Mohammad I Younis 4 Ghader Rezazadeh 5 69575__34437__ca89b6b1b6b544aa9eb0d397127f461c.pdf 69575.VoR.pdf 2025-06-09T16:11:42.1468383 Output 2390738 application/pdf Version of Record true © The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License. true eng http://creativecommons.org/licenses/by/4.0/
title Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications
spellingShingle Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications
Saber Azizi Azizishirvanshahi
Hamed Haddad Khodaparast
Hadi Madinei
title_short Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications
title_full Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications
title_fullStr Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications
title_full_unstemmed Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications
title_sort Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications
author_id_str_mv d69732e7f5a3b101651f3654bf7175d0
f207b17edda9c4c3ea074cbb7555efc1
d9a10856ae9e6a71793eab2365cff8b6
author_id_fullname_str_mv d69732e7f5a3b101651f3654bf7175d0_***_Saber Azizi Azizishirvanshahi
f207b17edda9c4c3ea074cbb7555efc1_***_Hamed Haddad Khodaparast
d9a10856ae9e6a71793eab2365cff8b6_***_Hadi Madinei
author Saber Azizi Azizishirvanshahi
Hamed Haddad Khodaparast
Hadi Madinei
author2 Saber Azizi Azizishirvanshahi
Hamed Haddad Khodaparast
Hadi Madinei
Mohammad I Younis
Ghader Rezazadeh
format Journal article
container_title Nonlinear Dynamics
container_volume 113
container_issue 18
container_start_page 24329
publishDate 2025
institution Swansea University
issn 0924-090X
1573-269X
doi_str_mv 10.1007/s11071-025-11379-7
publisher Springer Nature
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 This paper presents a novel investigation into the dynamics of a micro ring structure subjected to harmonic base excitation, designed as a highly sensitive MEMS mass sensor or bifurcation-based switch. Leveraging the in-plane nature of the motion, the system exhibits an exceptionally low damping ratio, making it ideal for detecting subtle changes in dynamic behaviour. The governing nonlinear differential equations, incorporating the geometric nonlinearities of the support beams, were derived and simplified into a reduced-order model consisting of coupled nonlinear Duffing-type equations. A key innovation of this study lies in the tunability of the system’s frequency ratios, enabling the activation of a 1:3 internal resonance. By varying the length of the support beams while keeping the central ring geometry fixed, the first two natural frequencies were carefully examined, revealing a significant influence on the dynamic response. Frequency response curves confirmed the presence of 1:3 internal resonance near the primary resonance of the first mode, highlighting the potential for efficient energy transfer between modes. Furthermore, a detailed bifurcation analysis uncovered a range of complex nonlinear phenomena, including nonlinear modal interactions, torus bifurcations, quasi-periodic motion, and cyclic fold bifurcations. These bifurcations not only provide deeper insight into the system’s dynamics but also offer additional operational mechanisms for switching applications. The findings demonstrate the system’s capability to exploit nonlinear dynamics for enhanced sensitivity and robustness, paving the way for the development of next-generation MEMS sensors and bifurcation-based devices.
published_date 2025-09-01T05:28:33Z
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