Wave Propagation in Two Dimensional Periodic Composites

In this paper we present theoretical calculations and experimental results concerning acoustic wave propagation in a 2-D periodic composite. It is known that the microstructure below the length scale of the wavelength affects the macroscale wave and makes the composite dispersive [1,2]. This dispersion manifests as frequency dependent phase and group velocities. We present a mixed variational formulation originally proposed by Nemat-Nasser for the evaluation of the dispersive characteristics of periodic composites. We employ the formulation to calculate the dispersion relation for a two-dimensional composite consisting of brass rods embedded in epoxy. The method allows for the calculation of the band structure of the composite and the identification of the relevant modes through mode shape information. We finally present experimental results on a fabricated sample for the 2-D composite. The experiments include longitudinal and shear wave propagation through the sample. The transmitted energy of the longitudinal and shear waves are used to evaluate the location of the pass-bands and stop-bands and to compare the results with the numerical predictions.