An Acoustic Model for Wave Propagation in a Weak Layer

Abstract

An acoustic model is developed for transient wave propagation in a weak layer excited by prescribed pressure or prescribed acceleration at the boundary. The validity of the acoustic model is investigated for the two excitations. A comparison of transient response from the acoustic model and a 3D axisymmetric elastic model reveals that for prescribed acceleration the acoustic model fails to capture important features of the elastic model even as Poisson ratio ν approaches 1∕2. However for prescribed pressure, the two models agree since shear stress is reduced. For prescribed acceleration adopting the modal approach, the mixed boundary-value problem on the excited boundary is converted to a pure traction problem utilizing the influence method. To validate the elaborate modal approach a finite difference model is also developed.

Asymmetric transient response of a hollow cylinder enclosing a compressible fluid

“…The r dil response of first arrival retains the character of waves in a solid in that dispersion attenuates stress peaks with distance traveled. The p response of first arrival retains the character of waves in a fluid typified by a sharp unattenuated pre-curser followed by a narrow plateau whose magnitude attenuates with distance (El-Raheb, 2005). At r = r i , r dil in the solid cylinder is approximately three times higher than p in the fluid-filled cylinder (Fig.…”