Nonlinearity in nanomechanical cantilevers

TL;DR

This study rigorously measures the nonlinear dynamics of nanomechanical cantilevers, revealing significant deviations from Euler-Bernoulli beam theory predictions for the fundamental mode, especially related to aspect ratio effects.

Contribution

It provides the first controlled experimental assessment of nonlinear responses in nanocantilevers, highlighting limitations of classical beam theory in the nonlinear regime.

Findings

Euler-Bernoulli theory deviates for fundamental mode nonlinearity

Second mode shows good agreement with theory

Nonlinearity depends systematically on aspect ratio

Abstract

Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro- and nano-cantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultra-linear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation.