Influences of gradient profile on the band gap of two-dimensional phononic crystal

Abstract

Propagation characteristics of elastic waves in two-dimensional (2D) phononic crystal consisting of parallel cylinders or cylindrical shells embedded periodically in a homogeneous host are investigated. The cylinders or cylindrical shells with varying material parameters along the radial direction are considered. The influences of the gradient profile on the band gap are the main concern. First, the multiple scattering method and the Bloch theorem are used to derive the dispersive equation. Second, the transfer matrix of graded medium is derived based on the laminated cylindrical shell model. Three cases of combination are considered: (1) Solid cylinders embedded in solid host (solid-solid type). (2) Solid cylinders embedded in liquid host (solid-liquid type). (3) Hollow cylinder filled with liquid embedded in liquid host (liquid-solid-liquid type). Next, the dispersive curves and the band gaps between them are evaluated numerically in the reduced Brillouin zone. Five kinds of typical gradient profiles and two limited cases are considered. At last, the influence of the graded medium with different gradient profiles upon dispersive curves and the band gaps are discussed based on the numerical results.