Acoustic wave propagation in a one-dimensional layered system

Abstract

Propagation of acoustic waves in an one-dimensional water duct containing many air filled blocks is studied by the transfer matrix formalism. Energy distribution and interface vibration of the air blocks are computed. For periodic arrangement band structure and transmission rate are calculated analytically, whereas the Lyapunov exponent and its variance are computed numerically for random situations. A distinct collective behavior for localized waves is found. The results are also compared with optical situations.

Statistics of the Lyapunov exponent in one-dimensional layered systems

“…Before the discussion of the numerical results we first summarize the relevant results of our previous study [17]. There both LE and its variance as functions of frequency were studied.…”

“…In the special case of layered media considered in [17], ρ and c are all constants in a single layer. Across an interface that separate two layers either ρ or c jump to a diferent value but pressure p and media vibration velocity u = 1 iωρ dp dx…”

“…In a recent study of acoustic (AC) waves propagation in a one dimensional randomly layered system [17] we have found that the statistics relation between Lyapunov exponent (LE) γ and its variance var(γ) do not follow the preditions of single parameter scaling (SPS). However, in an earlier study on 1D localization behaviors of electromagnetic (EM) waves [15], the author claimed that the non-universal bahaviors of LE will disappear and SPS will be restorted while the randomness of the system exceeds a critical value.…”

Asymmetric transmission of acoustic waves in a layer thickness distribution gradient structure using metamaterials

“…In addition to metamaterials, periodicity in material arrangement has proven another feasible tool for eliminating undesired waves in acoustic systems. [27][28][29][30][31][32][33][34] With proper mismatched impedances of the constituent materials, the wave propagation over specified frequency ranges can be easily manipulated. Typical examples of such acoustic constructions are two-dimensional periodic arrays of cylinders immersed in air or water.…”

Theoretical Investigation of Acoustic Band Gaps in Cylindrical Periodically Layered Structure

“…The existence of absolute band gaps where sound and vibration are all prohibited has been demonstrated by theoretical and experimental work. Up to now, most attention has been given to composites composed of periodic arrays of inclusions embedded in a matrix in a Cartesian coordinate system [1][2][3][4], including planar layered media (1D), composites composed of cylinders embedded in a host (2D) [5][6][7][8][9][10][11] or of spheres embedded in a host (3D) [12][13][14][15][16][17]. A few works considered cylindrical periodically layered media, which are suitable for certain situations e.g.…”