An analytical benchmark for a 2D problem of elastic wave propagation in a solid

A two-dimensional problem of elastic wave propagation in a rectangular solid is considered. It is first approached using the classical apparatus of mathematical physics, with a fully analytical model produced as the result. The same system is then analysed numerically using two commercial finite element software packages, COMSOL and ANSYS APDL, with the focus on the bulk and guided wave propagation. The results produced by the numerical models are compared with those produced by the analytical one, and the superiority of the latter in terms of the computational costs is established, while a good overall quantitative agreement is observed. The proposed analytical model is therefore shown to be a very attractive choice as a benchmark for validation of fully-numerical models. A procedure for the inverse use of the model is established and tested as well.