# Spatial modulation of nonlinear flexural vibrations of membrane resonators

## TL;DR

This study investigates the nonlinear vibrational behavior of membrane resonators under strong drive, revealing unique concentric ring patterns and localized overtones, modeled through coupled nonlinear oscillators.

## Contribution

It introduces a phenomenological model capturing complex nonlinear vibrational patterns in membrane resonators, highlighting localized overtones and circular symmetry.

## Key findings

- Membranes exhibit concentric ring deflection patterns at high drive.
- Different membrane regions oscillate at multiples of the drive frequency.
- A coupled oscillator model explains the observed nonlinear phenomena.

## Abstract

We study the vibrational motion of membrane resonators upon strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular siliconnitride membrane resonators and by analyzing the frequency response using optical interferometry, we show that upon increasing the driving strength, the membrane adopts a peculiar deflection pattern formed by concentric rings superimposed onto the drum head shape of the fundamental mode. Such a circular symmetry cannot be described as a superposition of a small number of excited linear eigenmodes. Furthermore, the different parts of the membrane oscillate at different multiples of the drive frequency, an observation that we denominate as 'localization of overtones'. We introduce a phenomenological model that is based on the coupling of a very small number of effective nonlinear oscillators, representing the different parts of the membrane, and that describes the experimental observations.