Elastodynamic response of a periodic layer of spherical particles containing vacancies

This paper is concerned with the influence of vacancies on the elastodynami c response of a periodic (square) array of identical spherical elastic incl usions 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 l attice. H*(omega) was measured for a "perfect lattice," i.e., one without a ny vacancies, and was found to be characterized by lattice resonances. H*(o mega) was also measured for lattices containing one and three vacancies wit hin the 72 lattice site area insonified by the ultrasonic beam. A counter-i ntuitive observation is that the presence of even one vacancy significantly reduces the amplitude of the fundamental lattice resonance. Furthermore, i n the case of the specimen containing three closely spaced vacancies, the r eduction is not three times the reduction due to one vacancy; it is signifi cantly less than that.