Ray, mode, and hybrid options for source excited propagation in an elastic plate

I. T. Lu, L. B. Felsen

Research output: Contribution to journalArticle

Abstract

Impact excited vibrations in a multiwave layer can be represented in terms of ray fields or of normal mode fields. At early observation times, multiply reflected ray fields can be distinguished by their different arrivals whereas at later times, their collective effect is best expressed by the normal modes. Instead of utilizing rays or modes separately, as has been customary, a recently developed hybrid theory for multiwave layered media permits both to be combined self-consistently, and in convenient proportions [Lu et al. y Wave Motion 6, 435–467 (1984)]. The hybrid formulation is based on a ray-mode equivalent whereby a given slowness spectral interval can be filled either with rays or with modes subject to a spectral remainder. Moreover, the ray proliferation due to wave coupling at each encounter with a boundary is avoided by introduction of “eigenrays,” which are composed of self-similar combinations of the various wave fields. The general theory is applied to the dilatational and shear waves in an elastic plate. High-frequency motion at given range is calculated in terms of ray fields, normal mode fields, eigenrays, and hybrid combinations, using exact generating spectral integrals and also simplified asymptotic approximations. The numerical results confirm the validity of the ray-mode equivalent and establish conditions where the hybrid scheme offers an attractive option.

Original languageEnglish (US)
Pages (from-to)701-714
Number of pages14
JournalJournal of the Acoustical Society of America
Volume78
Issue number2
DOIs
StatePublished - 1985

Fingerprint

elastic plates
rays
propagation
dilatational waves
reflected waves
Ray
encounters
S waves
arrivals
proportion
intervals
formulations
vibration
Waves
approximation

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Arts and Humanities (miscellaneous)

Cite this

Ray, mode, and hybrid options for source excited propagation in an elastic plate. / Lu, I. T.; Felsen, L. B.

In: Journal of the Acoustical Society of America, Vol. 78, No. 2, 1985, p. 701-714.

Research output: Contribution to journalArticle

@article{c28dd286adcf4c6485aaf11d647729be,
title = "Ray, mode, and hybrid options for source excited propagation in an elastic plate",
abstract = "Impact excited vibrations in a multiwave layer can be represented in terms of ray fields or of normal mode fields. At early observation times, multiply reflected ray fields can be distinguished by their different arrivals whereas at later times, their collective effect is best expressed by the normal modes. Instead of utilizing rays or modes separately, as has been customary, a recently developed hybrid theory for multiwave layered media permits both to be combined self-consistently, and in convenient proportions [Lu et al. y Wave Motion 6, 435–467 (1984)]. The hybrid formulation is based on a ray-mode equivalent whereby a given slowness spectral interval can be filled either with rays or with modes subject to a spectral remainder. Moreover, the ray proliferation due to wave coupling at each encounter with a boundary is avoided by introduction of “eigenrays,” which are composed of self-similar combinations of the various wave fields. The general theory is applied to the dilatational and shear waves in an elastic plate. High-frequency motion at given range is calculated in terms of ray fields, normal mode fields, eigenrays, and hybrid combinations, using exact generating spectral integrals and also simplified asymptotic approximations. The numerical results confirm the validity of the ray-mode equivalent and establish conditions where the hybrid scheme offers an attractive option.",
author = "Lu, {I. T.} and Felsen, {L. B.}",
year = "1985",
doi = "10.1121/1.392439",
language = "English (US)",
volume = "78",
pages = "701--714",
journal = "Journal of the Acoustical Society of America",
issn = "0001-4966",
publisher = "Acoustical Society of America",
number = "2",

}

TY - JOUR

T1 - Ray, mode, and hybrid options for source excited propagation in an elastic plate

AU - Lu, I. T.

AU - Felsen, L. B.

PY - 1985

Y1 - 1985

N2 - Impact excited vibrations in a multiwave layer can be represented in terms of ray fields or of normal mode fields. At early observation times, multiply reflected ray fields can be distinguished by their different arrivals whereas at later times, their collective effect is best expressed by the normal modes. Instead of utilizing rays or modes separately, as has been customary, a recently developed hybrid theory for multiwave layered media permits both to be combined self-consistently, and in convenient proportions [Lu et al. y Wave Motion 6, 435–467 (1984)]. The hybrid formulation is based on a ray-mode equivalent whereby a given slowness spectral interval can be filled either with rays or with modes subject to a spectral remainder. Moreover, the ray proliferation due to wave coupling at each encounter with a boundary is avoided by introduction of “eigenrays,” which are composed of self-similar combinations of the various wave fields. The general theory is applied to the dilatational and shear waves in an elastic plate. High-frequency motion at given range is calculated in terms of ray fields, normal mode fields, eigenrays, and hybrid combinations, using exact generating spectral integrals and also simplified asymptotic approximations. The numerical results confirm the validity of the ray-mode equivalent and establish conditions where the hybrid scheme offers an attractive option.

AB - Impact excited vibrations in a multiwave layer can be represented in terms of ray fields or of normal mode fields. At early observation times, multiply reflected ray fields can be distinguished by their different arrivals whereas at later times, their collective effect is best expressed by the normal modes. Instead of utilizing rays or modes separately, as has been customary, a recently developed hybrid theory for multiwave layered media permits both to be combined self-consistently, and in convenient proportions [Lu et al. y Wave Motion 6, 435–467 (1984)]. The hybrid formulation is based on a ray-mode equivalent whereby a given slowness spectral interval can be filled either with rays or with modes subject to a spectral remainder. Moreover, the ray proliferation due to wave coupling at each encounter with a boundary is avoided by introduction of “eigenrays,” which are composed of self-similar combinations of the various wave fields. The general theory is applied to the dilatational and shear waves in an elastic plate. High-frequency motion at given range is calculated in terms of ray fields, normal mode fields, eigenrays, and hybrid combinations, using exact generating spectral integrals and also simplified asymptotic approximations. The numerical results confirm the validity of the ray-mode equivalent and establish conditions where the hybrid scheme offers an attractive option.

UR - http://www.scopus.com/inward/record.url?scp=84953675850&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84953675850&partnerID=8YFLogxK

U2 - 10.1121/1.392439

DO - 10.1121/1.392439

M3 - Article

VL - 78

SP - 701

EP - 714

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 2

ER -