Dynamics of pressurized ultra-thin membranes

TL;DR

This paper develops a multi-mode continuum model to accurately predict the nonlinear pressure-frequency response of pressurized ultra-thin 2D membranes, validated by experiments, and demonstrates a method to determine Young's modulus.

Contribution

It introduces a comprehensive multi-mode approach that accounts for shape changes and higher modes, improving upon previous models for pressurized 2D membranes.

Findings

The model accurately predicts nonlinear resonance frequency shifts.

Considering shape change and higher modes is essential for precise predictions.

The method enables determination of Young's modulus of ultra-thin membranes.

Abstract

The resonance frequency of ultra-thin layered two-dimensional (2D) materials changes nonlinearly with the tension induced by the pressure from the surrounding gas. Although the dynamics of pressurized 2D material membranes have been extensively explored, recent experimental observations show significant deviations from analytical predictions. Here, we present a multi-mode continuum approach to capture the nonlinear pressure-frequency response of pre-tensioned membranes undergoing large deflections. We validate the model using experiments conducted on polysilicon drums excited opto-thermally and subjected to pressure changes in the surrounding medium. We demonstrate that considering the effect of pressure on the membrane tension is not sufficient for determining the resonance frequencies. In fact, it is essential to also account for the change in the membrane's shape in the pressurized configuration, the mid-plane stretching, and the contributions of higher modes to the mode shapes. Finally, we show how the presented high-frequency mechanical characterization method can be used to determine Young's modulus of ultra-thin membranes.