On a technique for deriving the explicit secular equation of Rayleigh waves in an orthotropic half-space coated by an orthotropic layer

The secular equation of Rayleigh propagating in an orthotropic half-space coated by an orthotropic layer has been obtained by Sotiropolous Sotiropolous, D. A. (1999), The e®ect of anisotropy on guided elastic waves in a layered half-space, Mechanics of Materials 31, 215–233] and by Sotiropolous & Tougelidis Sotiropolous, D. A. and Tougelidis, G. (1998), Guided elastic waves in orthotropic surface layer, Ultrasonics 36, 371–374]. However, it is not totally explicit and some misprints have occurred in this secular equation in both papers. This secular equation was derived by expanding directly a six-order determinant originated from the traction-free conditions at the top surface of the layer and the continuity of displacements and stresses through the interface between the layer and the half-space. Since the expansion of this six-order determinant was not shown in both two papers, it has been difficult to readers to recognize these misprints. This paper presents a technique that provides a totally explicit secular equation of the wave. The technique makes clear the way from the traction-free and continuity conditions to the secular equation and enables us to recognize the misprints appearing in the reported secular equation. The technique can be employed to obtain explicit secular equations of Rayleigh waves for many other cases. Moreover, the paper introduces a transfer matrix in explicit form for an orthotropic layer that is much simpler in form than the one obtained previously.