Propagation of dilatation and shear waves through a dynamic checkerboard material geometry in 1D space + time

Abstract

AbstractWe study the propagation of dilatational and shear waves through an isotropic elastic material having the dilatation and shear moduli variable in space and time. Two isotropic materials alternate occupying rectangular cells in 1D space + time producing a double periodic checkerboard material assembly. The materials are assumed to differ in their wave velocities (dilatational and shear) and to have pairwise equal values of wave impedances for each type of wave. We show, however, that, for both types of waves traveling normally to spatial interfaces between the materials, the average velocity of propagation is the same for certain ranges of material and structural parameters. Also, the energy is accumulated in those waves, and such accumulation occurs in very narrow pulses. This is unlike the wave propagation in a uniform static material, where both types of waves propagate at different speeds. The coincidence of average speeds of propagation appears to be due to the checkerboard material geometry. It creates the “plateau effect” within the ranges of material and structural parameters mentioned above [3, 4, 6]. These ranges do not include the purely uniform material. In elastodynamics, the concept of dynamic materials has been previously studied in references [2, 7].