Axisymmetric elastic waves in weakly coupled layered media of infinite radial extent

The propagation of axisymmetric waves in layered periodic elastic media of infinite radial extent is investigated. Hankel and Laplace transforms are employed, to convert radial and time dependence of displacement and stress within a layer to frequency and radial wavenumber. Continuity of stress and displacement is imposed at the interface between layers yielding transfer matrices. The structure of propagation and attenuation zones (PZ’s and AZ’s) of the system with infinite number of layers is studied. When the ratios of shear and longitudinal mechanical impedances (τ_T, τ_L) of the two layers are large, the PZ’s of the layered system become narrow, approaching certain limiting curves in the frequency-wavenumber plane. For large (τ_T, $τ_L) an asymptotic analysis is employed analytically to approximate the width of the PZ’s. Numerical computations of PZ’s are given, which are in good agreement with the analytical predictions. The spacing of the resonance points of a layered system with finite number of layers is found to depend mainly on the structure of the PZ’s of the corresponding system with an infinite number of layers.