Elastic waves blocking in a metamaterial with a disordered cascade of doubly-periodic compliant disk-shaped inclusions
摘要
A three-dimensional problem of time-harmonic longitudinal wave propagation in an elastic matrix containing doubly-periodic arrays of disk-shaped compliant inclusions, arranged in a finite set of non-equidistant parallel square lattices, is studied. The calculation of wave reflection and transmission coefficients in such a metamaterial is based on a generalization of the wide-spacing model to account for varying distances between inclusion lattices in a formed cascade. The relevant quantities via the numerical solution of a boundary integral equation defined in the lattice unit cell are obtained. The results pertain to wave incidence on a three-plane cascade of doubly periodic inclusions (with cracks as a particular case) and the identification of suppression zones in the frequency spectrum of wave penetration, including the effect of complete blocking, which depends on the distances in the cascade, lattice compactness, and rigidity of the scatterers.