Observing off-resonance motion of nanomechanical resonators as modal superposition

TL;DR

This paper visualizes off-resonance modal responses of nanomechanical resonators, demonstrating that their motion can be described as superpositions of resonance modes influenced by driving force distribution and asymmetry.

Contribution

It introduces a method to visualize and analyze off-resonance modal shapes as superpositions, revealing effects of force distribution and asymmetry on modal participation.

Findings

Modal response shapes are superpositions of resonance modes.

Spatial distribution of driving force influences modal weights.

Asymmetry of the drum affects resonance mode shapes.

Abstract

Observation of resonance modes is the most straightforward way of studying mechanical oscillations because these modes have maximum response to stimuli. However, a deeper understanding of mechanical motion could be obtained by also looking at modal responses at frequencies in between resonances. A common way to do this is to force a mechanical object into oscillations and study its off-resonance behaviour. In this paper, we present visualisation of the modal response shapes for a mechanical drum driven off resonance. By using the frequency modal analysis, we describe these shapes as a superposition of resonance modes. We find that the spatial distribution of the oscillating component of the driving force affects the modal weight or participation. Moreover, we are able to infer the asymmetry of the drum by studying the dependence of the resonance modes shapes on the frequency of the driving force. Our results highlight that dynamic responses of any mechanical system are mixtures of their resonance modes with various modal weights, further giving credence to the universality of this phenomenon.