# Multimode internal resonances in a MEMS self-sustained oscillator

## TL;DR

This paper explores the complex interactions of multiple resonant modes in a MEMS oscillator, demonstrating how internal resonances can generate a multi-mode frequency comb through symmetry-breaking and feedback mechanisms.

## Contribution

It introduces a novel analysis of multimode internal resonances in MEMS oscillators, showing how symmetry-breaking enables coupling and frequency locking of multiple modes.

## Key findings

- Multiple internal resonances occur among the first four flexural and torsional modes.
- Symmetry-breaking induces coupling between even and odd modes.
- A five-mode frequency-locked comb is generated through internal resonances.

## Abstract

We investigate the dynamics of a microelectromechanical (MEMS) self-sustained oscillator supporting multiple resonating and interacting modes. In particular, the interaction of the first four flexural modes along with the first torsional mode are studied, whereby 1:2, 1:3, and 2:1 internal resonances occur. Even and odd modes are induced to couple by breaking the longitudinal symmetry of the structure. Self-oscillations are induced in the second flexural mode via a gain-feedback loop, thereafter its frequency is pulled into a commensurate frequency ratio with the other modes, enabling the oscillator to act as a driver/pump for four modes simultaneously. Thus, by leveraging multiple internal resonances, a five modes frequency-locked comb is generated.