Elastodynamic response of layers of spherical particles in hexagonal and square periodic arrangements
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abstract
The effect of particle arrangement on the transmission and reflection of ultrasonic longitudinal waves through a single layer of spherical inclusions is studied. Specimens were manufactured, each consisting of a layer of glass spheres embedded in a polyester matrix arranged in either a square periodic, hexagonal periodic, or random array, with projected layer area fractions ranging from 0.14 to near close-packed. The transmission and reflection coefficient spectra of a normally-incident plane longitudinal wave were measured over a range of wavelengths that are large, equal, and small compared to the two characteristic lengths of the composites, namely, the particle radius and, in the case of the periodic composites, the unit cell dimension. Periodic spectra are characterized by extrema, which are attributed to lattice resonance. Spectra from specimens with random layers of equal area fraction do not exhibit any extrema. Measured resonance frequencies, which may be accurately predicted for low to midrange area fractions using the concept of the reciprocal lattice, are different for square and hexagonal lattice structures of similar area fraction and identical unit cell dimension.
