Low frequency acoustic response of a periodic layer of spherical inclusions in an elastic solid to a normally incident plane longitudinal wave

The influence of particle mass density on the reflection and transmission spectra of a plane longitudinal wave normally incident on a periodic (square) array of identical spherical particles in a polyester matrix are measured at wavelengths which are comparable to the particle radius and the inter-particle distance. The spectra are characterized by several resonances whose frequencies are close to the cut-off frequencies for the shear wave modes, which are analogs of spectral orders in diffraction gratings. Arrays of heavy particles (lead and steel) exhibit a pronounced resonance anomaly which occurs when the lattice resonant frequency is close to the frequency of the rigid body translation (dipole) resonance of an isolated sphere in an unbounded matrix. An approximate low frequency theory is developed which takes into account the multiple scattering effect. The theory shows good comparison with the experimental data for arrays with particle area fractions as high as 32%.