Transient axisymmetric stress wave propagation in weakly coupled layered structures

The transient response of finite bi-periodic layered structures under axisymmetric loading conditions are analyzed using a double integral transform technique. The effect of the structures of attenuation and propagation zones of the corresponding infinite systems on the transient response is studied. The relation between transformed (frequency and radial wavenumber) and physical (temporal and spatial) variables is emphasized. For verification purposes, a finite element analysis is also performed, and the finite element results are compared with those derived by the double integral transform. It is shown that, in weakly coupled layered systems with narrow propagation zones in the transformed domain, the transient waves are localized close to the circular area where the load is applied. As the coupling between the layers increases, the transmission of stress waves through the layered medium is enhanced, and stress localization diminishes. It is found that weak coupling between layers affects the distribution of the shear stress field more than that of the longitudinal stress field.