Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency

We study theoretically the propagation of elastic waves in two-dimensional composite media composed of a square array of hollow steel cylinders embedded in water using the finite-difference time-domain method. These composite media constitute a class of acoustic band gap materials with narrow pass bands in their transmission stop bands. The frequency at which the pass band occurs is tunable by controlling the inner radius of the tubular steel inclusions. The effect of the tube inner radius on the transmission spectrum is semiquantitatively separable from the effect of the composite periodicity. A linear defect formed of a row of hollow cylinders in an array of filled cylinders produces an elastic waveguide that transmits at the narrow pass band frequency. We show that two of these tunable waveguides with different inner radii can be employed to filter and separate two specific frequencies from a broad band input signal.