Nonlinear modal interactions in clamped-clamped mechanical resonators

TL;DR

This paper investigates nonlinear interactions between vibration modes in clamped-clamped beams, demonstrating how nonlinear coupling enables mode amplitude detection and modeling complex dynamics through beam extension effects.

Contribution

It introduces a theoretical and experimental framework for intermodal coupling in clamped beams, highlighting a novel self-detection method and a model capturing complex nonlinear behaviors.

Findings

Nonlinear coupling enables mode amplitude measurement.

Complex dynamics are quantitatively modeled.

Beam extension causes Duffing nonlinearity.

Abstract

A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector for the amplitude of another mode, presenting a method to measure the energy stored in a specific resonance mode. Experimentally observed complex nonlinear dynamics of the coupled modes are quantitatively captured by a model which couples the modes via the beam extension; the same mechanism is responsible for the well-known Duffing nonlinearity in clamped-clamped beams.