Jump and Pull-in Instability of a MEMS Gyroscope Vibrating System

Area of Science:

• Nonlinear Dynamics
• Micro-electro-mechanical Systems (MEMS)

Background:

• Jump and pull-in instability are critical nonlinear phenomena affecting electrostatic micro gyroscope performance and safety.
• Understanding these initial-sensitive behaviors is crucial for enhancing device reliability.

Purpose of the Study:

• To explore the global dynamics of micro gyroscope systems with nonlinear stiffness and electrostatic forces.
• To investigate the conditions leading to static and dynamic pull-in instability.

Main Methods:

• Static and dynamic analyses were performed to determine pull-in voltage thresholds.
• Analysis of primary resonance and 1:1 internal resonance in driving and detecting modes.
• Application of the Melnikov method to analyze pull-in instability conditions (heteroclinic bifurcation).

Main Results:

• High driving AC voltage amplitude can induce bistable periodic responses via saddle-node bifurcation.
• Initial condition disturbances can cause jumps between attractors, evidenced by basins of attraction.
• Pull-in instability is linked to heteroclinic bifurcation and is exacerbated by increased driving AC voltage amplitude.

Conclusions:

• The study provides a global perspective on micro gyroscope nonlinear dynamics.
• Pull-in instability is directly related to driving AC voltage amplitude and nonlinear system behavior.
• Findings offer insights for improving the performance reliability and structural safety of electrostatic micro gyroscopes.