Characterization by a time-frequency method of classical waves propagation in one-dimensional lattice : effects of the dispersion and localized nonlinearities

TL;DR

This paper applies time-frequency analysis to study how dispersion and localized nonlinearities affect acoustic wave propagation in one-dimensional lattices, revealing nonlinear effects on wave localization and filtering.

Contribution

It introduces a novel application of time-frequency methods to characterize wave dispersion and nonlinear effects in 1D acoustic lattices with Helmholtz resonators.

Findings

Time-frequency methods evaluate wave energy velocity.

Spectral content evolution shows nonlinear harmonic generation.

Nonlinearities disrupt wave localization and filtering effects.

Abstract

This paper presents an application of time-frequency methods to characterize the dispersion of acoustic waves travelling in a one-dimensional periodic or disordered lattice made up of Helmholtz resonators connected to a cylindrical tube. These methods allow (1) to evaluate the velocity of the wave energy when the input signal is an acoustic pulse ; (2) to display the evolution of the spectral content of the transient signal ; (3) to show the role of the localized nonlinearities on the propagation .i.e the emergence of higher harmonics. The main result of this paper is that the time-frequency methods point out how the nonlinearities break the localization of the waves and/or the filter effects of the lattice.