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On the existence of weakly nonlocal Rayleigh waves with impedance boundary condition
Arch. Mech. 76 (4), 295-310, 2024, DOI: 10.24423/aom.4502
Keywords: Rayleigh waves; weakly nonlocal elasticity; incompressible; impedance boundary condition; existence of Rayleigh waves
Abstract
In this paper, the existence of Rayleigh waves propagating in weakly nonlocal incompressible isotropic elastic half-spaces subject to the tangential impedance boundary condition (TIBC) (at the surface of half-spaces, the tangential stress is proportional to the horizontal displacement and the normal stress is zero) is investigated. It is shown that for the negative values of the dimensionless tangential impedance parameter and the values of the dimensionless nonlocality parameter belong to the interval (0, 0.5), there exist exactly two Rayleigh waves. The first wave is the counterpart of the Rayleigh wave in local incompressible isotropic elastic half-spaces and the second is a new Rayleigh mode appearing due to the presence of nonlocality. Formulae for their velocities have been derived. Remarkably, the second wave can travel with very high velocity.