Dynamic renormalization group analysis of propagation of elastic waves in two-dimensional heterogeneous media

Abstract

We study localization of elastic waves in two-dimensional heterogeneous solids with randomly distributed Lamé coefficients, as well as those with long-range correlations with a power-law correlation function. The Matin-Siggia-Rose method is used, and the one-loop renormalization group (RG) equations for the the coupling constants are derived in the limit of long wavelengths. The various phases of the coupling constants space, which depend on the value ρ, the exponent that characterizes the power-law correlation function, are determined and described. Qualitatively different behaviors emerge for ρ < 1 and ρ > 1. The Gaussian fixed point (FP) is stable (unstable) for ρ < 1 (ρ > 1). For ρ < 1 there is a region of the coupling constants space in which the RG flows are toward the Gaussian FP, implying that the disorder is irrelevant and the waves are delocalized. In the rest of the disorder space the elastic waves are localized. We compare the results with those obtained previously for acoustic wave propagation in the same type of heterogeneous media, and describe the similarities and differences between the two phenomena.

Transmission spectra of two-dimensional liquid-liquid phononic crystals

“…Since the elastic wave propagation in periodic composite materials was previously investigated by Kushwaha et al [1], Sigalas and Economou [2], a great deal of attention has been focused on these kinds of artificial periodic lattice structures by both theoretical predictions [3,4] and experiments [5,6]. The most interesting and important feature is that such artificial composites (named phononic crystals) can exhibit elastic/acoustic band gaps, in which sound and vibration are all forbidden in all directions.…”

Wave localization in randomly disordered layered three-component phononic crystals with thermal effects

“…In recent years, the elastic wave propagation in periodic composites (called phononic crystals) has been studied extensively [1][2][3][4][5][6][7][8][9][10][11][12][13]. With the band gap property, this kind of system has various potential applications such as the acoustic transducers and filters.…”

Elastic wave band gaps in magnetoelectroelastic phononic crystals

“…Since the pioneer works by Kushwaha et al [1,2] and Sigalas and Economou [3,4] on the elastic wave propagation in periodic composite materials, a great deal of attention is focused on these kinds of artificial periodic lattice and cellular structures by both theoretical predictions [5][6][7][8][9][10][11][12][13][14][15][16] and experiments [17][18][19][20][21][22]. It is known that such structures are called phononic crystals.…”