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

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.