LOW-FREQUENCY BENDING WAVES IN PERIODIC PLATES

An asymptotic approximation is obtained for the dispersion relation of flexural waves propagating in an infinite, flat plate, with material properties periodic in one direction. The approximation assumes that the wave length is long compared with the length of the unit period, but makes no assumption about the magnitude of variation of material parameters. The leading order term corresponds to an effective plate with areal density equal to the mean and bending stiffnesses which could be predicted from purely static considerations. The first departure from the dispersion relation for an effectively uniform plate depends upon a parameter Ω, which is discussed in detail. An expression is found for Ω, for plates with arbitrary periodic variation in material properties. It turns out that Ω vanishes for waves travelling normal to the layering if either the areal density or the bending stiffness is uniform throughout the plate. Numerical comparisons of the exact and asymptotic dispersion relations suggest that the cubic term in the dispersion relation is always small. © 1994 Academic Press Limited.