Coupling and attenuation of waves in plates by randomly distributed attached impedances

Joseph A. Turner, Richard L. Weaver

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The average response of an infinite thin plate with statistically homogeneous attached random impedances is examined. The added impedances, which represent typical heterogeneities that might occur on complex shells, provide light coupling between the extensional, shear, and flexural waves. The mean plate response is formulated in terms of the Dyson equation which is solved within the assumptions of the first-order smoothing approximation, or Keller approximation, valid when the heterogeneities are weak. Scattering attenuations are derived for each propagation mode. It is shown that the attenuation of one wave type due to coupling to another is proportional to the modal density of the other wave type. Thus the attenuation of extensional and shear waves is predominantly due to mode conversion into flexural waves and is proportional to the large modal density of flexural waves. The flexural degrees of freedom serve as a sink for the energy of the membrane modes and constitute for them an effective fuzzy structure. The specific case of delta-correlated springs is considered for purposes of illustration.

Original languageEnglish (US)
Pages (from-to)2167-2175
Number of pages9
JournalJournal of the Acoustical Society of America
Volume99
Issue number4 I
DOIs
StatePublished - Apr 1 1996

Fingerprint

attenuation
impedance
S waves
propagation modes
thin plates
Waves
Attenuation
sinks
approximation
smoothing
degrees of freedom
membranes
scattering
Approximation
Extensional
energy

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

Coupling and attenuation of waves in plates by randomly distributed attached impedances. / Turner, Joseph A.; Weaver, Richard L.

In: Journal of the Acoustical Society of America, Vol. 99, No. 4 I, 01.04.1996, p. 2167-2175.

Research output: Contribution to journalArticle

@article{4c50add6384547cbb0a6fe0d72a3b18f,
title = "Coupling and attenuation of waves in plates by randomly distributed attached impedances",
abstract = "The average response of an infinite thin plate with statistically homogeneous attached random impedances is examined. The added impedances, which represent typical heterogeneities that might occur on complex shells, provide light coupling between the extensional, shear, and flexural waves. The mean plate response is formulated in terms of the Dyson equation which is solved within the assumptions of the first-order smoothing approximation, or Keller approximation, valid when the heterogeneities are weak. Scattering attenuations are derived for each propagation mode. It is shown that the attenuation of one wave type due to coupling to another is proportional to the modal density of the other wave type. Thus the attenuation of extensional and shear waves is predominantly due to mode conversion into flexural waves and is proportional to the large modal density of flexural waves. The flexural degrees of freedom serve as a sink for the energy of the membrane modes and constitute for them an effective fuzzy structure. The specific case of delta-correlated springs is considered for purposes of illustration.",
author = "Turner, {Joseph A.} and Weaver, {Richard L.}",
year = "1996",
month = "4",
day = "1",
doi = "10.1121/1.415404",
language = "English (US)",
volume = "99",
pages = "2167--2175",
journal = "Journal of the Acoustical Society of America",
issn = "0001-4966",
publisher = "Acoustical Society of America",
number = "4 I",

}

TY - JOUR

T1 - Coupling and attenuation of waves in plates by randomly distributed attached impedances

AU - Turner, Joseph A.

AU - Weaver, Richard L.

PY - 1996/4/1

Y1 - 1996/4/1

N2 - The average response of an infinite thin plate with statistically homogeneous attached random impedances is examined. The added impedances, which represent typical heterogeneities that might occur on complex shells, provide light coupling between the extensional, shear, and flexural waves. The mean plate response is formulated in terms of the Dyson equation which is solved within the assumptions of the first-order smoothing approximation, or Keller approximation, valid when the heterogeneities are weak. Scattering attenuations are derived for each propagation mode. It is shown that the attenuation of one wave type due to coupling to another is proportional to the modal density of the other wave type. Thus the attenuation of extensional and shear waves is predominantly due to mode conversion into flexural waves and is proportional to the large modal density of flexural waves. The flexural degrees of freedom serve as a sink for the energy of the membrane modes and constitute for them an effective fuzzy structure. The specific case of delta-correlated springs is considered for purposes of illustration.

AB - The average response of an infinite thin plate with statistically homogeneous attached random impedances is examined. The added impedances, which represent typical heterogeneities that might occur on complex shells, provide light coupling between the extensional, shear, and flexural waves. The mean plate response is formulated in terms of the Dyson equation which is solved within the assumptions of the first-order smoothing approximation, or Keller approximation, valid when the heterogeneities are weak. Scattering attenuations are derived for each propagation mode. It is shown that the attenuation of one wave type due to coupling to another is proportional to the modal density of the other wave type. Thus the attenuation of extensional and shear waves is predominantly due to mode conversion into flexural waves and is proportional to the large modal density of flexural waves. The flexural degrees of freedom serve as a sink for the energy of the membrane modes and constitute for them an effective fuzzy structure. The specific case of delta-correlated springs is considered for purposes of illustration.

UR - http://www.scopus.com/inward/record.url?scp=0029930422&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029930422&partnerID=8YFLogxK

U2 - 10.1121/1.415404

DO - 10.1121/1.415404

M3 - Article

AN - SCOPUS:0029930422

VL - 99

SP - 2167

EP - 2175

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 4 I

ER -