Near field transient axisymmetric waves in layered structures: Effects of weak coupling

Axisymmetric stress wave transmission through the leading layers of layered structures of infinite radial but finite axial extent is numerically studied by employing two different computational approaches: a technique based on the numerical inversion of Double Integral Transformations (DIT), and a Finite Element (FE) analysis. Considering the first approach, careful selections of the limits of the numerical inversions and the sampling rates are required in order to overcome inherent numerical instabilities associated with exponential dichotomy. This type of numerical instability is more evident in layered media with weak coupling. In such systems, direct multiplications of layer transfer matrices are avoided by employing a global scheme to assemble well-conditioned global transfer matrices. Moreover, the specific structure of the propagation and attenuation zones of the structure are taken into account for increasing the efficiency and effectiveness of the transfer matrix manipulations. Satisfactory agreement between the DIT and FE numerical results is observed, at least for early times. Close to the region of application of the external pressure, the FE simulations suffer from the discretization of the applied load, node-to-node oscillations and reflections from infinite elements (silent boundaries). Using the aforementioned numerical techniques, transient wave transmission in two-layered systems (one with weak and one with strong interlayer coupling) is considered, and the effects of weak coupling on the wave transmission is studied. We show that at early times, weak coupling results in stress localization in the region close to the applied pressure, a result which can have potential application in the use of layered media as shock isolators.