Homogenization of Two-Dimensional Clusters of Rigid Rods in Air

Abstract

The scattering of sound waves by circular-shaped clusters consisting of two-dimensional distributions of rigid cylinders in air is studied in the low-frequency limit (homogenization) both theoretically and experimentally. Analytical formulas for the effective density and sound speed are obtained in the framework of multiple scattering. Here, an experimental demonstration is reported in which a cluster of wooden rods acoustically behaves as a cylinder of argon gas. Moreover, evidence is presented indicating the validity of the homogenization in this cluster at frequencies lower than 3 kHz, which corresponds to a wavelength that is only 4 times the parameter of the embedded lattice and is a quarter of the cluster's diameter.

Anomalous sound absorption in lattices of cylindrical perforated shells

“…A lattice of solid rods in air is an example of a two-dimensional (2D) sonic crystal (SC) that has been extensively studied since the nineties. [1][2][3][4] Most of the reported SCs were made of building units with negligible dissipation losses. However, in the last years, 2D SCs consisting of cylinders fabricated with lossy materials are deserving attention due to their potential application as acoustic barrier for broadband noise.…”

Sound focusing by gradient index sonic lenses

“…It has been demonstrated that the homogenization of a SC takes place for wavelengths larger than a certain cutoff given approximately by c Ϸ 4a. 3 Since our fabricated GRIN lenses are based on hexagonal lattices with a = 2 cm, their focusing properties will appear at wavelengths Ն 8 cm, which corresponds to linear frequencies Յ 4.3 kHz. However, let us stress that the onset for the homogenization is not an exact parameter and we report below GRIN lenses working at 4.5 kHz, which is a frequency slightly above the cutoff c = 4.3 kHz.…”

“…1 However, in the range of low frequencies ͑homogenization limit͒ they behave like homogeneous media whose effective acoustic parameters, dynamical mass density, and bulk modulus, basically depend on the lattice filling fraction. [2][3][4] The homogenization properties of SCs have been employed to design refractive devices like, for example, acoustic lenses whose focusing properties are based on their external curved surfaces [5][6][7] or Fabry-Perot type acoustic interferometers. 8 Gradient index ͑GRIN͒ sonic lenses based on homogenized 2D SCs have been proposed.…”

“…The refractive index at row with coordinate y ᐉ is adjusted by taking into account that, in the low frequency limit, a cluster of rigid cylinders embedded in a fluid or gas background behaves like a homogeneous medium whose effective refractive index n eff mainly depends on the fraction of volume occupied by the cylinder in the SC. 3,4 The 2D GRIN SC lenses studied are designed with a profile n͑y͒ as closer as possible to that in Eq. ͑1͒ with n 0 = 1.337 and n h = 1.…”

Transmission character of general function photonic crystals

“…It has been demonstrated theoretically and experimentally that PCs with liquid crystal infiltration exhibit tunability on applying an external electric field [15]or changing the temperature [16][17][18][19][20]. If the constituent materials of PCs have magnetic permeabilities dependent on the external magnetic field, the photonic band gaps [PBGs] can be altered by changing the external magnetic field [21][22][23][24][25][26][27][28]. An electric or magnetic field changes the PBGs easily than the temperature.…”