About Some Exact and Approximate Formulas for Calculating the Rayleigh Wave Velocity

A generalization of the analytical expression for the Rayleigh wave velocity in algebraic form and formulas with trigonometric and hyperbolic functions that do not contain cubic radicals are obtained. Their application is considered using the example of calculating the derivative of the Rayleigh determinant in problems of excitation and diffraction of surface acoustic waves in a homogeneous isotropic elastic half-space, allowing solutions for fields of deformations and stresses in the form of quadratures. The results obtained can help in obtaining analytical expressions, as well as approximate formulas, and reduce the calculation time at the stage of numerically solving problems of diffraction and excitation of acoustic waves. Approximate formulas of L. Bergmann, E.G. Nesvijski, P.C. Vinh and P.G. Malischewsky are also considered and their more optimal variants are proposed. The results obtained can help in obtaining and analyzing analytical expressions, reduce the calculation time at the stage of numerical modeling of the problem of excitation and propagation of acoustic waves, and significantly reduce the measurement error in flaw detection and non-destructive material quality control.