Computing the multimodal stochastic dynamics of a nanobeam in a viscous fluid

TL;DR

This paper presents a finite element computational method to accurately simulate the stochastic multimodal dynamics of nanobeams in viscous fluids, incorporating experimental features like tension and boundary effects, with validation against theory.

Contribution

It introduces a flexible finite-element approach to compute multiple stochastic modes of elastic structures in fluids using only deterministic simulations, including complex experimental conditions.

Findings

Excellent agreement with theoretical predictions for first eleven modes

Quantified effects of tension and boundary proximity on dynamics

Established applicability limits of the computational approach

Abstract

The stochastic dynamics of small elastic objects in fluid are central to many important and emerging technologies. It is now possible to measure and use the higher modes of motion of elastic structures when driven by Brownian motion alone. Although theoretical descriptions exist for idealized conditions, computing the stochastic multimodal dynamics for the complex conditions of experiment is very challenging. We show that this is possible using deterministic finite element calculations with the fluctuation dissipation theorem by exploring the multimodal stochastic dynamics of a doubly-clamped nanobeam. We use a very general, and flexible, finite-element computational approach to quantify the stochastic dynamics of multiple modes simultaneously using only a single deterministic simulation. We include the experimentally relevant features of an intrinsic tension in the beam and the influence of a nearby rigid boundary on the dynamics through viscous fluid interactions. We quantify the stochastic dynamics of the first eleven flexural modes of the beam when immersed in air or water. We compare the numerical results with theory, where possible, and find excellent agreement. We quantify the limitations of the computational approach and describe its range of applicability. These results pave the way for computational studies of the stochastic dynamics of complex 3D elastic structures in a viscous fluid where theoretical descriptions are not available.