Keywords: interaction, layered-space, parametric, wave modes, FEM.

The characteristic phenomenon of the wave motion in an infinite homogeneous space is the occurrence of the propagating waves, which propagate away from the source of the excitation. These waves mathematically satisfy the radiating (Sommerfeld's) conditions, [1,2]. However, waves in the layered half-space also reflect from the free surface and partially from the contact interfaces between the layers. This makes the wave motion, generated by the half-space structure interaction, very complicated compared to the wave motion in the homogeneous half-space. Nevertheless, these waves have some characteristics, crucial in engineering analysis, which we can express by parameters, that is by the amplitudes, velocities and attenuation of the wave modes. There are two kinds of waves: waves propagating along the surface and waves vanishing into the under-laying homogeneous half-space. The former ones have the smallest attenuation of all the generated waves and are therefore the prevailing ones, particularly in more distant locations from the source of the excitation. That is why engineers pay special attention to these waves.

We are using a procedure, which yields wave modes and their amplitudes, that depend on the excitation, the characteristics of the layers, the under-laying homogeneous half-space, and the structure. We can distinguish also the surface waves. The procedure uses finite element modelling of the considered part of the layered half-space and creates the transparent boundaries of the computational domain. It exploits the advantage of an effective combination of the propagating wave mode analysis, presented by Špacapan & Premrov [3], and the operator method and is performed in the frequency domain. Such a combination renders the approach simple to apply, and at the same time yields the required parametric analysis of wave motion. In addition, it yields a considerably accurate wave field in the considered domain. Such an approach, and the parametric analysis of wave motion in the interaction problem, is, according to our knowledge, a novelty.

We present a brief outline of the theoretical basis of the computational approach and several numerical examples. The simplest one serves the purpose of verifying the correctness of the approach by comparing the numerical results to the theoretical ones. In other examples we present by parameters the effect of the characteristics of the layered half-space, structure and the excitation on the structure half-space interaction. Special attention, in the presented analysis, is paid to the role of the under-laying homogenous half-space and the surface waves.

1

J.D. Achenbach, "Wave Propagation in Elastic Solids", North Holland Publishing Company, Amsterdam, New York and Oxford, 1973.

2

G.R. Baldock, T. Bridgeman, "The Mathematical Theory of Wave Motion", John Wiley & Sons, New York, Chichester, Brisbane, Toronto, 1981.

3

I. Špacapan, M. Premrov, "Wave Motion in Infinite Inhomogeneous Waveguides", Elsevier Ltd, Advances in Engineering Software 34 (2003) 745-752. doi:10.1016/S0965-9978(03)00108-X

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