Propagation of acoustic waves in phononic-crystal plates and waveguides using a finite-difference time-domain method

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 (FDTD) 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.