Effective model for elastic waves propagating in a substrate supporting a dense array of plates/beams with flexural resonances. (October 2020)

• Record Type: Journal Article
• Authors: Marigo, Jean-Jacques; Pham, Kim; Maurel, Agnès; Guenneau, Sébastien
• Is Part Of: Journal of the mechanics and physics of solids. Volume 143(2020)
• Publication Date: 2020-10
• Subjects: Asymptotic analysis -- Elastic waves -- Metamaterials -- Metasurfaces -- Multimodal method; 00-01 -- 99-00; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2020.104029
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: We consider the effect of an array of plates or beams over a semi-infinite elastic ground on the propagation of elastic waves hitting the interface. The plates/beams are slender bodies with flexural resonances at low frequencies able to perturb significantly the propagation of waves in the ground. An effective model is obtained using asymptotic analysis and homogenization techniques, which can be expressed in terms of the ground alone with effective dynamic (frequency-dependent) boundary conditions of the Robin's type. For an incident plane wave at oblique incidence, the displacement fields and the reflection coefficients are obtained in closed forms and their validity is inspected by comparison with direct numerics in a two-dimensional setting.