BIE method to analyze wave motion in solids with periodically distributed cavities
type: Item
instance of: scholarly article
title: BIE method to analyze wave motion in solids with periodically distributed cavities
zbMATH Open document ID: 0626.73017
DOI: 10.1016/0045-7825(87)90054-5
author: Jianyong Qiao
author: Sumit K. Garg
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1987-01-01T00:00:00Z
review text: A three-dimensional boundary integral equation method is developed to analyze reflection and transmission of incident waves by a doubly periodic planar array of spherical cavities in an elastic solid. By taking into account the periodicity of the incident field and the geometrical configuration, the system of integral equations is reduced to a system over the surface of a single cavity in a reference cell. The displacements on the cavity surface, which are obtained by solving the system of boundary integral equations, are used to obtain reflection and transmission coefficients via a novel application of the Betti-Rayleigh reciprocal theorem. The dispersion relation for propagation of horizontally polarized transverse waves in a triply periodic three- dimensional array of spherical cavities is subsequently determined with the aid of the Floquet or Bloch theory, and by using the reflection and transmission coefficients for a single planar array of cavities. The dispersion curves show passing and stopping bands. Numerical results are presented for three directions of wave propagation and two geometrical configurations.
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 74S99
zbMATH DE Number: 4018468
zbMATH Keywords: three-dimensional boundary integral equation method
zbMATH Keywords: reflection
zbMATH Keywords: transmission
zbMATH Keywords: incident waves
zbMATH Keywords: doubly periodic planar array of spherical cavities
zbMATH Keywords: Betti-Rayleigh reciprocal theorem
zbMATH Keywords: horizontally polarized transverse waves
zbMATH Keywords: triply periodic three-dimensional array
zbMATH Keywords: Floquet or Bloch theory
zbMATH Keywords: dispersion
MaRDI profile type: Publication
full work available at URL: 0045-7825(87)90054-5
OpenAlex ID: W2059724457
cites work: Dynamic response of 3-d embedded foundations by the boundary element method
cites work: Q3711935
cites work: Q3746974
cites work: On time-harmonic elastic-wave analysis by the boundary element method for moderate to high frequencies
cites work: Q3725666
cites work: Q3719990
cites work: Partial Differential Equations with Periodic Coefficients and Bloch Waves in Crystals
description: scientific article; zbMATH DE number 4018468