Cascade of Modal Interactions in Nanomechanical Resonators with Soft Clamping

TL;DR

This paper reveals a cascade of nonlinear modal interactions in softly clamped nanomechanical resonators, showing how energy transfers sequentially among modes, leading to broad nonlinear responses and enhanced nonlinearity amplification.

Contribution

It demonstrates the role of soft clamping in enabling cascaded modal interactions and provides analytical and finite element models to explain the mechanism.

Findings

Sequential coupling of five mechanical modes during frequency sweeps

Soft clamping amplifies geometric nonlinearity by an order of magnitude

The phenomenon is generic and can be tailored through design strategies

Abstract

We uncover a chain of nonlinear modal interactions in softly clamped nanostring resonators. The process involves the sequential coupling of five mechanical modes, during frequency sweeps, yielding a broad nonlinear response with nearly constant amplitude. We demonstrate that soft clamping enables this cascaded energy transfer and amplifies the effective geometric nonlinearity of the driven mode by an order of magnitude. Analytical and finite element-based reduced-order models capture the key features of the coupling cascade and clarify its underlying mechanism. The phenomenon is generic in nonlinear vibrational systems and can be tailored through soft-clamping design strategies.