Rayleigh waves in viscoelastic piezoelectric half-space with cladding structures: An analytic Legendre-Laguerre polynomial method

Piezoelectric materials are widely used in surface acoustic wave devices. Many piezoelectric materials themselves have viscoelastic properties, and their surface wave characteristics, especially the attenuation characteristics still needs to be explored. This article proposes a Legendre-Laguerre orthogonal polynomial method to solve the Rayleigh wave problems in a viscoelastic piezoelectric half space with a covering layer. The proposed method compensates for the inherent shortcomings of traditional Laguerre polynomials in solving layered half spaces: the normal stress and electric displacement are discontinuous. The correctness of the method was verified through literature comparison and finite element simulation. At the same time, by utilizing the orthogonality of the Legendre-Laguerre polynomial, the integral analytical formula encountered in the solution process is derived, which improves the computational efficiency by more than ten times. Through the analysis and discussion of the dispersion and attenuation curves, it is found that the piezoelectric effect can suppress the attenuation of Rayleigh waves; the piezoelectric and viscous properties of the covering layer mainly affect attenuation at high frequencies, while those of the half space layer mainly affect attenuation at low frequencies of high-order modes.