A Comparison Between the Tiersten Model and O(H) Boundary Conditions for Elastic Surface Waves Guided by Thin Layers

In this paper we make a comparison between the boundary conditions (BCs) derived by Tiersten and the so-called O(h) BCs for elastic surface waves guided by thin films. By a thin layer we here mean a layer for which the thickness is much smaller than the wavelengths involved. The advantage of the O(h) model is that it starts with the general three-dimensional equation of motion and derives the boundary conditions in a rational manner keeping all terms linear in the layer thickness. The Tiersten model is obtained from the approximate equations for low frequency and flexure of thin plates by neglecting the flexural stiffness. We consider straight-crested surface waves under plane-strain conditions, so-called Rayleigh-type waves (P-SV), and Love waves (SH). It is shown that for the Rayleigh type waves the O(h) BCs gives a much better approximation of the exact case than the Tiersten BCs. Even for the Tiersten model including flexural stiffness, the O(h) BCs yields more accurate results. Concerning Love waves both the Tiersten model and O(h) model reduces to the same dispersion relation which quite well approximates the exact solution.