Elastodynamic response of a periodic layer of spherical particles containing vacancies

This paper is concerned with the influence of vacancies on the elastodynamic response of a periodic (square) array of identical spherical elastic inclusions embedded in an unbounded elastic matrix. A response function of the array is defined as H*(omega) = R*(omega)/T*(omega), where R*(omega) and T*(omega) are, respectively, the reflection and transmission spectra of the lattice. H*(omega) was measured for a "perfect lattice," i.e., one without any vacancies, and was found to be characterized by lattice resonances. H*(omega) was also measured for lattices containing one and three vacancies within the 72 lattice site area insonified by the ultrasonic beam. A counter-intuitive observation is that the presence of even one vacancy significantly reduces the amplitude of the fundamental lattice resonance. Furthermore, in the case of the specimen containing three closely spaced vacancies, the reduction is not three times the reduction due to one vacancy; it is significantly less than that.