Wave propagation in presence of oscillators on the free surface

This article is devoted to wave propagation in presence of a periodic distribution of oscillators (3D sprung-damped mass) on the surface of an elastic medium. The case of an elastic half space loaded by quasi-periodic surface forces is studied at first. The equivalent boundary conditions at the macro-scale are derived at the first and second order, by assuming the existence of a boundary layer and using a two-dimensional homogenisation method. When the force distribution results from attached oscillators, it is shown that boundary conditions can be expressed in terms of equivalent surface impedance at the first order, with local and non-local correctors at the second order. These results are used to study wave refraction by an oscillator layer. The main phenomena—atypical redistribution of mode and mode conversion, frequency range of efficiency, characteristic time of response—are identified. The first correctors are determined analytically for plane waves of oblique incidence. Finally the validity range of the modelling is discussed.