The transmission of a longitudinal wave through a layer of spherical inclusions with a random or periodic arrangement

Abstract

The transmission of a normally incident plane longitudinal wave through a single layer of spherical inclusions embedded in a polyester matrix is measured. Area fraction of inclusions is varied from 0.05 (a very dilute suspension) to 0.86 (densely packed). Two specimens are manufactured for each area fraction: in the first, the spheres are distributed in a random manner; in the second, they are arranged in a periodic (square) array; otherwise, the two are identical. The transmission spectra are measured at wavelengths that are large, equal or small compared to the two characteristic lengths of the composites, namely, the particle radius and, in the case of the periodic composites, the inter-particle distance. The transmission spectra are characterized by several resonances; the first of these corresponds to the excitation of the rigid-body translation resonance. It also happens to be the most dominant resonance for both the periodic and the random composites. In the case of the periodic composites, the transmission spectra are characterized by at least one additional resonance that can be unambiguously attributed to the periodicity of the lattice.