@article {, title = {On a technique for deriving the explicit secular equation of Rayleigh waves in an orthotropic half-space coated by an orthotropic layer}, journal = {Waves in Radom and Complex Media}, year = {2016}, abstract = {

The \ secular equation \ of Rayleigh propagating in an orthotropic half-space coated by an orthotropic layer has been obtained by Sotiropolous [Mechanics of Materials 31 (1999), 215-233] and \ Sotiroplous $\&$ Tougelidis [Ultrasonics 36 (1998), 371-374]. However, it \ is not totally explicit and some misprints have been 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.

}, doi = {10.1080/17455030.2015.1132859}, author = {Pham Chi Vinh and Vu Thi Ngoc Anh and Nguyen Thi Khanh Linh} }