Effective model for elastic waves in a substrate supporting a array of plates/beams with flexural and longitudinal resonances
Résumé
In a previous study [1] we have studied the effect of an array of plates or beams over an elastic ground on the propagation of waves hitting the interface. The study was restricted to the low frequency regime where only flexural resonances take place. The present study presents a generalization to higher frequencies which allows us to account for both flexural and longitudinal resonances and to evaluate their interplay. An effective model is obtained using asymptotic analysis and homogenization techniques, which can be expressed in terms of the ground alone with an effective dynamic (frequency-dependent) boundary conditions of the Robin's type. For an inplane wave at oblique incidence, the scattered displacement fields and the reflection coefficients are obtained in closed forms and their effectiveness to reproduce the actual scattering is inspected by comparison with direct numerics in a two-dimensional setting.
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