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J. Bryner, J. Vollmann, L. Aebi and J. Dual, “Wave Propagation in Pyramidal Tip-Like Structures with Cubic Material Properties,” Wave Motion, Vol. 47, No. 1, 2010, pp. 33-44. doi:10.1016/j.wavemoti.2009.07.003

has been cited by the following article:

• TITLE: Analysis of Ringing and Noise in FE and FDTD Calculated Acoustic Pulse Profiles

  AUTHORS: Arthur Every, Laurent Aebi, Jurg Dual

  KEYWORDS: Numerical Dispersion; Wave Field Modelling; FE; FDTD Calculations

  JOURNAL NAME: Applied Mathematics, Vol.3 No.10A, November 1, 2012

  ABSTRACT: Ringing, i.e. the emergence of an oscillatory tail behind a wave pulse as it propagates through a medium, is a pervasive artefact in FE and FDTD calculated waveforms. It is known to be a consequence of numerical dispersion arising from the discretization of the equations of motion. The use of an irregular mesh in a FE code has the further consequence of rendering the displacement field increasingly noisy with distance behind the wave front. In this paper these effects are illustrated using the commercial FE package ABAQUS with square and irregular triangular meshes to calculate the progress of a longitudinally polarized Ricker pulse along the axis of a cylindrically shaped aluminium specimen. We are able to give a precise analytical account of the evolution of ringing on the basis of a low order approximation for the dispersion relation of the discretized equations of motion. A qualitative account is provided of the generation of noise in the use of an irregular triangular mesh.