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Sound Waves: Resonance

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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

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Controlling Resonator Nonlinearities and Modes through Geometry Optimization.

Amal Z Hajjaj¹, Nizar Jaber²

¹Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough LE11 3TU, UK.

|November 27, 2021

Summary

This study presents a novel hybrid micro-electro-mechanical system (MEMS) resonator design for controlling nonlinearities. Geometry optimization and axial stress tuning enable precise control over resonator dynamics for advanced applications.

Keywords:

MEMS resonators geometry optimization nonlinearity tailoring

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Area of Science:

Micro-Electro-Mechanical Systems (MEMS)
Nonlinear Dynamics
Resonator Design

Background:

Controlling nonlinearities in MEMS resonators is crucial for applications like sensing, signal conditioning, and filtering.
Existing methods may lack sufficient control over the complex dynamical behavior of these devices.

Purpose of the Study:

To develop a passive technique using geometry optimization to control MEMS resonator nonlinearities and dynamics.
To explore active tuning of axial stress as a complementary control method.
To investigate a novel hybrid resonator shape for enhanced control.

Main Methods:

Proposed a hybrid microbeam design combining straight and initially curved sections.
Employed the Galerkin method to solve the beam equation and analyze design parameters.
Investigated the effects of geometry on frequency ratios, nonlinearities, symmetry breaking, and linear coupling phenomena (crossing, veering, mode hybridization).

Main Results:

Demonstrated the ability to achieve strong quadratic or cubic effective nonlinearities by selecting appropriate structural parameters.
Showcased control over symmetry breaking and various linear coupling phenomena.
Confirmed the possibility of tuning vibration mode frequencies to achieve commensurate ratios for internal resonance activation.

Conclusions:

The proposed hybrid resonator design offers a simple, fabricable, and highly controllable approach to managing MEMS resonator nonlinearities.
This method provides a wide range of tunability for sensor nonlinearities and dynamical response.
Enables precise control over resonator behavior for advanced MEMS applications.