Resonant nonlinear response of a nanomechanical system with broken symmetry

TL;DR

This paper investigates how broken symmetry in a nanomechanical resonator causes unique nonlinear responses, including vibrations at twice the drive frequency, and develops a theory to accurately describe these effects and determine nonlinearity parameters.

Contribution

It presents a comprehensive theoretical and experimental analysis of nonlinear responses in a nanostring resonator with broken symmetry, extending beyond standard approximations.

Findings

Vibration amplitude depends nontrivially on force parameters.

Emergence of vibrations at twice the drive frequency due to broken symmetry.

Quantitative agreement between theory and experiment, enabling parameter extraction.

Abstract

We study the response of a weakly damped vibrational mode of a nanostring resonator to a moderately strong resonant driving force. Because of the geometry of the experiment, the studied flexural vibrations lack inversion symmetry. As we show, this leads to a nontrivial dependence of the vibration amplitude on the force parameters. For a comparatively weak force, the response has the familiar Duffing form, but for a somewhat stronger force, it becomes significantly different. Concurrently there emerge vibrations at twice the drive frequency, a signature of the broken symmetry. Their amplitude and phase allow us to establish the cubic nonlinearity of the potential of the mode as the mechanism responsible for both observations. The developed theory goes beyond the standard rotating-wave approximation. It quantitatively describes the experiment and allows us to determine the nonlinearity parameters.