О корнях характеристического уравнения Рэлея при рациональных значениях параметра

Sergey Yur'evich Gurevich; Dmitriy Grigor'evich Kozhevnikov; Evgeniy Valer'evich Golubev

doi:10.14529/mmph240107

Authors

Sergey Yur'evich Gurevich South Ural State University, Chelyabinsk http://orcid.org/0000-0002-1042-0303
Dmitriy Grigor'evich Kozhevnikov South Ural State University, Chelyabinsk
Evgeniy Valer'evich Golubev South Ural State University, Chelyabinsk http://orcid.org/0000-0002-6641-0702

DOI:

https://doi.org/10.14529/mmph240107

Keywords:

surface waves, Rayleigh wave velocity, roots of the characteristic equation, exact formulas

Abstract

The roots of the Rayleigh characteristic equation for surface waves are obtained under the assumption that the square of the ratio of the velocities of volume waves is a rational number. The exact formulas for the roots contain a minimum of radicals and rational numbers.