Acoustical propagation in a prefractal waveguide

Abstract

We present a theoretical study and experimental results for an acoustic multiscattering one-dimensional system made of cylindrical tubes of different diameters whose lengths follow a Cantor-like structure. Homothetic acoustical features and forbidden bands as well as wave trapping phenomena are reported.

Thermal modeling of two-dimensional periodic fractal patterns, an application to nanoporous media

“…deterministic and random, it has also been verified that thermal properties are equivalent provided that the fractal dimensions are the same. This has already been shown for other physical properties [8,9].…”

Wave propagation and localization in randomly disordered layered composites with local resonances

“…However, practical periodic structures are always different from ideal ones because of the randomly distributed material defaults or manufacture errors during production process. Such disordered periodic structures have wave and vibration localization characteristics [8][9][10][11][12][13][14] and one may expect to tune the band structures of phononic crystals by intentionally introducing disorders. Thus, the investigation of randomly disordered systems has attracted increasing interests, such as localization of acoustic waves and electromagnetic waves in disordered media with properties fluctuating randomly [15], and vibration localization of nearly periodic engineering structures such as beams, bars, plates, etc.…”

An Ultrasonic Lens Design Based on Prefractal Structures

“…Lubniewski and Stepnowski [5] developed a simple method of sea bottom identification using elements of fractal analysis. Gibiat et al [6] reported the homothetic acoustical features, forbidden bands, and wave trapping phenomena for an acoustic multiscattering one-dimensional system made of cylindrical tubes of different diameters, whose lengths follow a Cantor-like structure. Castiñeira-Ibañez et al [7,8] presented an acoustic barrier for noise control formed by rigid cylinders arranged in fractal Sierpinski triangle geometry.…”