We designed and characterized a two-dimensional, gradient-index phononic crystal ͑GRIN PC͒ to control the propagation of acoustic waves. The GRIN PC was composed of solid cylinders arranged in a square lattice and immersed in an epoxy. The refractive index along the direction transverse to the phononic propagation was designated as a hyperbolic secant gradient distribution. This distribution was modulated by means of the density and elastic moduli of the cylinders. The effective refractive indices in each row of the GRIN PC were determined from band diagrams obtained via a plane-wave expansion method. The acoustic wave propagation was numerically investigated by a finite-difference time-domain method, and the results were compared to the analytical beam trajectories derived from the hyperbolic secant profile. These results show that the GRIN PC allows acoustic focusing over a wide range of working frequencies, making it suitable for applications such as flat acoustic lenses and couplers.

We provide experimental evidence of the existence of a locally resonant sonic band gap in a two-dimensional stubbed plate. Structures consisting of a periodic arrangement of silicone rubber stubs deposited on a thin aluminium plate were fabricated and characterized. Brillouin spectroscopy analysis is carried out to determine the elastic constants of the used rubber. The constants are then implemented in an efficient finite-element model that predicts the band structure and transmission to identify the theoretical band gap. We measure a complete sonic band gap for the out-of-plane Lamb wave modes propagating in various samples fabricated with different stub heights. Frequency domain measurements of full wave field and transmission are performed through a scanning laser Doppler vibrometer. A complete band gap from 1.9 to 2.6 kHz is showed using a sample with 6-mm stub diameter, 5-mm thickness, and 1-cm structure periodicity. Very good agreement between numerical and experimental results is obtained.

Propagation of acoustic waves in a phononic-crystal plate and related waveguides are analyzed in this paper. A two-dimensional phononic-crystal plate consisting of circular steel cylinders which form a square lattice in an epoxy matrix is studied first using the finite-difference time-domain ͑FDTD͒ method. The Bloch theorem is employed to deal with the periodic condition, and the traction free condition is set on the top and bottom boundaries of the plates. The dispersion curves and displacement fields are calculated to identify the band gaps and eigenmodes. With the existence of a complete band gap in the phononic-crystal plate, an acoustic waveguide is presented accordingly. Eigenmodes of acoustic waves inside the waveguides are indicated, and the modes are affected by the geometry arrangement of waveguides. Inside the phononic-crystal plate waveguides, wave propagation is well confined within the structure.

A two-port ZnO/silicon Lamb wave resonator using phononic crystals Appl. Phys. Lett. 97, 031913 (2010); 10.1063/1.3467145Study of acoustic wave behavior in silicon-based one-dimensional phononic-crystal plates using harmony response analysisIn this letter, we numerically demonstrate focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal ͑PC͒ silicon plate and its application as a beam-width compressor for compressing Lamb wave into a stubbed phononic tungsten/silicon plate waveguide. The results show that beam width of the lowest antisymmetric Lamb wave in the PC thin plate can be compressed efficiently and fitted into tungsten/silicon PC plate waveguide over a wide range of frequency.

In this paper, we adopt the finite-difference time-domain ͑FDTD͒ method to analyze surface acoustic waves propagating in two-dimensional phononic waveguides. To implement the FDTD program for dealing with surface acoustic waves, the Bloch theorem and absorbing boundary conditions are employed to deal with the periodic boundary condition and reflection from a numerical boundary. A phononic crystal consisting of circular steel cylinders that form a square lattice in an epoxy matrix is considered as an example to study phononic crystal waveguides. The dispersion relation and displacement fields are calculated to identify the band gaps and eigenmodes. The result shows the existence of a complete band gap of surface waves and thus an acoustic waveguide is created accordingly. Eigenmodes of surface waves inside the waveguide are indicated and pseudo surface acoustic waves propagating inside the straight waveguide are demonstrated. Further, waveguides with a sharp bend are reported and an improved design is suggested to enhance energy transmission.