The elastodynamic finite integration technique for waves in cylindrical geometries

Abstract

This paper deals with the elastodynamic finite integration technique for axisymmetric wave propagation in a homogeneous and heterogeneous cylindrical medium ͑CEFIT͒. This special variant of a finite difference time domain ͑FDTD͒ scheme offers a suitable method to calculate real three-dimensional problems in a two-dimensional staggered grid. In order to test the accuracy of the numerical CEFIT code, problems for which analytical solutions are available are presented. These solutions involve wave propagation in an elastic plate, the scattering of a plane longitudinal wave by a spherical obstacle, and ultrasound generation by a thermoelastic laser source. For the latter problem experimental results are included. The CEFIT code also allows the treatment of more complicated problems. Further possible applications are the investigation of elastic waves generated in an acoustic microscope, the simulation of impact-echo measurements in multi-layer systems, axisymmetric wave propagation in arbitrary bodies of revolution, the calculation of elastic wave fields of longitudinal wave transducers with a circular aperture, and the investigation of multi-layer models for particulates.

Simulation of guided wave interaction with in-plane fiber waviness

“…EFIT is a numerical method similar to staggered-grid finite difference techniques. The technique has been in use since the 1990s with extensive foundational work reported by authors such as Fellinger, Marklein, and Schubert, among others [19][20][21][22]. In this paper EFIT is implemented to study wave interaction with in-plane fiber waviness defects.…”

Microcracking in composite laminates: Simulation of crack-induced ultrasound attenuation

“…The technique has been in use since the early 1990s with extensive foundational work reported by authors such as Fellinger, Marklein, and Schubert, among others [8][9][10]. The discretized EFIT velocity, v, and stress, T, equations for the case of anisotropic composite laminates, made up of orthotropic ply layers, are shown below [11]:…”

An axisymmetric non-hydrostatic model for double-diffusive water systems

“…Examples of applications include the modelling of gas flow past a gravitating body in astronomy (Shima et al, 1985), radiative heat transfer in cylindrical enclosures (Menguc and Viskanta, 1986), the heating of air flowing through a combustion burner (Galletti et al, 2007), and acoustic axisymmetric waves in elastic media (Schubert et al, 1998). The similarity between these examples is that a model calculating in two spatial dimensions models 3-D processes due to axisymmetry.…”