Reflection and transmission of an obliquely incident wave by an array of spherical cavities

J. D. Achenbach, M. Kitahara

Research output: Contribution to journalArticlepeer-review

61 Scopus citations

Abstract

A plane wave is incident on a doubly periodic array of spherical cavities in an elastic solid. The cavities are of equal radius d, and their centers are located in a single plane, the x1x2plane, at positions x1= ma, x2= nb. The propagation vector of a plane, time-harmonic, incident longitudinal wave is located in the X1, X3plane. The scattering problem is formulated rigorously by taking advantage of the geometrical periodicity. The reflected and transmitted longitudinal and transverse wave motions may be expressed as superpositions of an infinite number of wave modes, each with its own cutoff frequency. Reflection and transmission coefficients have been defined as integrals over a single cavity in terms of the displacement components and auxiliary surface traction terms on the surface of the cavity. The system of singular integral equations for the displacement components has been solved numerically by the boundary integral equation method. Curves show the reflection and transmission coefficients for the reflected and transmitted longitudinal and transverse waves as functions of the frequency.

Original languageEnglish (US)
Pages (from-to)1209-1214
Number of pages6
Journaljournal of the Acoustical Society of America
Volume80
Issue number4
DOIs
StatePublished - Oct 1986
Externally publishedYes

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

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