A landscape method to unveil high-frequency localized modes in random acoustic metamaterials

Abstract

Mechanical media with randomly fluctuating parameters are fundamentally different from periodic (or homogeneous) media in that, above a certain threshold (and depending on dimensionality), eigenmodes are localized. While that feature may be extremely useful in practice, for any application involving vibration isolation, numerical methods currently lack for the prediction of these localized eigenmodes at a reasonable cost. Recently, the so-called localization landscape method was proposed [1] to predict such localized modes in quantum systems (Schrödinger equation). It allows to predict the locus of all the lowest localized eigenmodes by solving one single (cheap) elliptic problem. Although very elegant, this method is not useful for classical (acoustic) equations because the lower eigenmodes for this equation are de-localized and essentially hide the higher modes, which are of interest. The talk will discuss and compare the operators corresponding to the quantum and classical equations and describe a technique to use the localization landscape method with the acoustic operator.