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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

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 Science and Business Media LLC 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa69575
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 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.
Keywords: Nonlinear dynamics; Internal resonance; Micro ring; MEMS; Duffing oscillator; Bifurcation
College: Faculty of Science and Engineering
Funders: 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.

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