One single static measurement predicts wave localization in complex structures

TL;DR

This study demonstrates that a single static measurement of a complex structure's deformation can accurately predict vibrational localization regions and eigenfrequencies, enabling control of vibrational modes without detailed structural data.

Contribution

First experimental validation of the localization landscape concept using holographic static deformation measurements to predict vibrational modes in complex structures.

Findings

Static deformation measurement predicts localization regions.

Maxima of landscape match eigenfrequencies.

Landscape minima indicate transition to extended modes.

Abstract

A recent theoretical breakthrough has brought a new tool, called \emph{localization landscape}, to predict the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures the localization landscape and demonstrates its predictive power. Holographic measurement of the static deformation under uniform load of a thin plate with complex geometry provides direct access to the landscape function. When put in vibration, this system shows modes precisely confined within the sub-regions delineated by the landscape function. Also the maxima of this function match the measured eigenfrequencies, while the minima of the valley network gives the frequencies at which modes become extended. This approach fully characterizes the low frequency spectrum of a complex structure from a single static measurement. It paves the way to the control and engineering of eigenmodes in any vibratory system, especially where a structural or microscopic description is not accessible.