S. Yu. Gurevich, D. G. Kozhevnikov, E. V. Golubev, “The roots of the Rayleigh characteristic equation for rational values of the parameter”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2024, Volume 16, Issue 1,Pages <nobr>56

Short communications

The roots of the Rayleigh characteristic equation for rational values of the parameter

S. Yu. Gurevich, D. G. Kozhevnikov, E. V. Golubev

South Ural State University, Chelyabinsk, Russian Federation

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.

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

UDC: 534.2

Received: 12.11.2023

DOI: 10.14529/mmph240107