On the velocities of Rayleigh surface waves propagating along boundaries of generalized continua

Vladimir I. Erofeev, Artem M. Antonov, Alexey O. Malkhanov

Mechanical Engineering Research Institute RAS, Branch of Federal Research Center A. V. Gaponov–Grekhov, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russian Federation

Abstract: It is demonstrated that mathematical models of gradient-elastic medium and reduced Cosserat medium, in contrast to the model of classical deformable solid, allow one to describe experimentally observed dispersion of Rayleigh surface wave, i.e., relationship between phase velocity of surface wave and frequency. At the same time, according to the model of gradient-elastic half-space, velocity of surface wave cannot exceed the velocity of shear wave but at certain values of frequency it can reach it. According to reduced Cosserat model, velocity of surface wave exceeds the velocity of shear wave as well as velocity of propagation of surface wave in classical half-space and gradient-elastic half-space.

Keywords: gradient-elastic half-space, reduced Cosserat model, surface wave, dispersion, phase velocity, frequency.

UDC: 534.1

Received: 07.10.2024
Received in revised form: 15.11.2024
Accepted: 24.12.2024

Language: English