On harmonic wave propagation in multilayered viscoelastic media

An analytical method is presented to study the propagation of plane harmonic waves in an infinite periodically laminated viscoelastic medium. The dispersion and the damping relations for a periodic layered medium, when the wave propagates in the direction perpendicular to the layers, are illustrated. From these curves, one can establish the static and dynamic characteristics of the homogenized medium. It is shown that when the half of the wave length approaches the periodic length of the medium, the medium becomes extremely dissipative. A comparison between an elastic and a viscoelastic multilayered medium is made. It is illustrated that, in the elastic medium at the zone of forbidden frequencies no waves penetrate into the medium, whereas for the multilayered viscoelastic medium the waves can penetrate but dissipate very fast.