Surface waves from flexural and compressional resonances of beams

TL;DR

This paper develops a 3D model for elastic wave propagation in soil with cylindrical beams, revealing hybridized Rayleigh waves, bandgaps, and a spoof plasmon polariton analogue, advancing understanding of wave-beam interactions.

Contribution

It introduces a novel 3D model capturing the complex interaction of flexural and compressional resonances in beams affecting surface wave propagation.

Findings

Identification of hybridized Rayleigh waves with bandgaps due to resonances

Discovery of a decoupled wave analogous to spoof plasmon polaritons

Quantitative differences in wave physics between 3D and 2D models

Abstract

We present a three-dimensional model describing the propagation of elastic waves in a soil substrate supporting an array of cylindrical beams experiencing flexural and compressional resonances. The resulting surface waves are of two types. In the sagittal plane, hybridized Rayleigh waves can propagate except within bandgaps resulting from a complex interplay between flexural and compressional resonances. We exhibit a wave decoupled from the hybridized Rayleigh wave which is the elastic analogue of electromagnetic spoof plasmon polaritons. This wave with displacements perpendicular to the sagittal plane is sensitive only to flexural resonances. Similar, yet quantitatively different, physics is demonstrated in a two-dimensional setting involving resonances of plates.