A note on formulas for the Rayleigh wave speed in elastic solids

In the present paper, new analytical, numerical and approximate methods have been presented for the determination of Rayleigh wave speed in isotropic and anisotropic media. The Lagrange's method is used to provide exact expression for the roots of the secular equation for Rayleigh waves in isotropic media. Then, a simple non-iterative type quadrature method is used to numerically determine the Rayleigh wave speed in isotropic and anisotropic media. Further, an approximate method is presented to determine the velocity of Rayleigh waves. The discrete least square approximation on Chebyshev - Gauss - Lobatto nodes is suggested to transform secular equations to quadratic equations, thereby, providing improved approximations to the Rayleigh wave speed. The analysis is complemented with numerical examples.