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Abstract <p>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 strain and stress fields in 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 proposed by L. Bergmann, E.G. Nesvijski, P.C. Vinh, and P.G.&#xa0;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 substantially reduce the measurement error in flaw detection and nondestructive material quality control.</p>

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

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • E. V. Golubev

摘要

Abstract

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 strain and stress fields in 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 proposed by 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 substantially reduce the measurement error in flaw detection and nondestructive material quality control.