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This paper presents an application of time-frequency methods to characterizethe dispersion of acoustic waves travelling in a one-dimensional periodic ordisordered lattice made up of Helmholtz resonators connected to a cylindricaltube. These methods allow (1) to evaluate the velocity of the wave energy whenthe input signal is an acoustic pulse ; (2) to display the evolution of thespectral content of the transient signal ; (3) to show the role of thelocalized nonlinearities on the propagation .i.e the emergence of higherharmonics. The main result of this paper is that the time-frequency methodspoint out how the nonlinearities break the localization of the waves and/or thefilter effects of the lattice.

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