Asymptotic formula of Rayleigh wave speed in an orthotropic half-space coated by a thin piezoelectric film

Piezoelectric thin films have been widely used in electro-acoustic devices including ones measuring Rayleigh wave speed. The main objective of this work is to find an explicit formula of Rayleigh speed taking into account the effect of the thin piezoelectric film. First the problem of Rayleigh surface waves propagating along an orthotropic substrate coated by a thin piezoelectric film is considered using Stroh's formalism approach. Then, the exact secular equation of Rayleigh wave is obtained in implicit form. In case when the thickness of the thin layer is much smaller than the considering wavelength of Rayleigh waves, an asymptotic formula of Rayleigh speed is derived from the asymptotic form of the exact secular equation. The obtained asymptotic formula is simple enough and could be used in practice when Rayleigh speed is measured by using piezoelectric device. Numerical illustrations are carried out to show the validity of the obtained approximate formulas and its potential application in inverse problem.