Shape optimization of geometrically nonlinear modal coupling coefficients: an application to MEMS gyroscopes

Area of Science:

• Mechanical Engineering
• Nonlinear Dynamics
• Microelectromechanical Systems (MEMS)

Background:

• MEMS and NEMS resonators exhibit complex nonlinear dynamics due to high amplitudes, quality factors, and modal couplings.
• Nonlinear modal couplings are influenced by resonance conditions and coupling coefficients, impacting device performance.
• Geometric nonlinearities are a primary source of these modal couplings in MEMS/NEMS devices.

Purpose of the Study:

• To apply node-based shape optimization for tuning geometrically nonlinear 3-wave coupling coefficients in MEMS gyroscopes.
• To demonstrate the ability to significantly alter individual coupling coefficients through design optimization.
• To explore the potential of shape optimization for controlling nonlinear dynamic properties in MEMS/NEMS.

Main Methods:

• Utilized node-based shape optimization techniques.
• Focused on tuning the geometrically nonlinear 3-wave coupling coefficients.
• Ensured optimized designs met manufacturability and operability constraints.

Main Results:

• Achieved tuning of individual coupling coefficients over several orders of magnitude.
• Optimized designs featured unintuitive geometric features beyond typical human design intuition.
• Demonstrated effective control over nonlinear modal coupling strengths.

Conclusions:

• Shape optimization is a powerful tool for designing MEMS and NEMS resonators with specific nonlinear dynamic characteristics.
• This approach enables the creation of devices with precisely tailored modal couplings.
• The findings suggest new possibilities for advanced MEMS/NEMS device concepts and performance enhancement.