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

Area of Science:

• Nonlinear Dynamics
• Mechanical Engineering
• Micro-Electro-Mechanical Systems (MEMS)

Background:

• Micro ring structures with low damping ratios are ideal for sensitive dynamic behavior detection.
• Geometric nonlinearities in support beams influence system dynamics.

Purpose of the Study:

• Investigate the nonlinear dynamics of a micro ring structure under harmonic base excitation.
• Explore the potential for 1:3 internal resonance activation and its impact on dynamic response.
• Analyze complex nonlinear phenomena for enhanced MEMS sensor and switch applications.

Main Methods:

• Derivation and simplification of nonlinear differential equations into a reduced-order model.
• Analysis of coupled nonlinear Duffing-type equations.
• Examination of natural frequencies by varying support beam lengths.
• Frequency response curve analysis and bifurcation analysis.

Main Results:

• Tunable frequency ratios enabling 1:3 internal resonance near primary resonance.
• Demonstrated efficient energy transfer between modes due to internal resonance.
• Uncovered complex nonlinear phenomena: modal interactions, torus bifurcations, quasi-periodic motion, and cyclic fold bifurcations.

Conclusions:

• The micro ring structure effectively exploits nonlinear dynamics for enhanced sensitivity and robustness.
• Internal resonance and observed bifurcations offer novel operational mechanisms for MEMS devices.
• Findings pave the way for next-generation MEMS mass sensors and bifurcation-based switches.