Scattering of a flexural wave by a finite straight crack in an elastic plate

I. V. Andronov, B. P. Belinskii

Research output

6 Citations (Scopus)

Abstract

The diffraction of flexural waves by a short straight crack in an elastic thin plate is considered. The vibrations of the plate are described by the Kirchhoff model. The Fourier method transforms the problem to integral equations of convolution on an interval. The theorems of existence and uniqueness of solutions for these equations are proved. The numerical procedure is based on the orthogonal polynomials decomposition method. It leads to infinite systems of algebraic equations for the coefficients. The truncation method is proved to be applicable to these systems due to the special choice of the polynomials. A physical interpretation of numerical and asymptotic results obtained for the directivity of the scattered wave and for the stress intensity coefficients near the ends of the crack is suggested.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of Sound and Vibration
Volume180
Issue number1
DOIs
Publication statusPublished - 9 Feb 1995

Fingerprint

elastic plates
Elastic waves
polynomials
cracks
Polynomials
Scattering
Cracks
thin plates
directivity
coefficients
uniqueness
Convolution
scattering
convolution integrals
Integral equations
integral equations
theorems
Diffraction
Decomposition
intervals

Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

Cite this

@article{46ff95bfa0cd4ba882438595dca41b42,
title = "Scattering of a flexural wave by a finite straight crack in an elastic plate",
abstract = "The diffraction of flexural waves by a short straight crack in an elastic thin plate is considered. The vibrations of the plate are described by the Kirchhoff model. The Fourier method transforms the problem to integral equations of convolution on an interval. The theorems of existence and uniqueness of solutions for these equations are proved. The numerical procedure is based on the orthogonal polynomials decomposition method. It leads to infinite systems of algebraic equations for the coefficients. The truncation method is proved to be applicable to these systems due to the special choice of the polynomials. A physical interpretation of numerical and asymptotic results obtained for the directivity of the scattered wave and for the stress intensity coefficients near the ends of the crack is suggested.",
author = "Andronov, {I. V.} and Belinskii, {B. P.}",
year = "1995",
month = "2",
day = "9",
doi = "10.1006/jsvi.1995.0063",
language = "English",
volume = "180",
pages = "1--16",
journal = "Journal of Sound and Vibration",
issn = "0022-460X",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - Scattering of a flexural wave by a finite straight crack in an elastic plate

AU - Andronov, I. V.

AU - Belinskii, B. P.

PY - 1995/2/9

Y1 - 1995/2/9

N2 - The diffraction of flexural waves by a short straight crack in an elastic thin plate is considered. The vibrations of the plate are described by the Kirchhoff model. The Fourier method transforms the problem to integral equations of convolution on an interval. The theorems of existence and uniqueness of solutions for these equations are proved. The numerical procedure is based on the orthogonal polynomials decomposition method. It leads to infinite systems of algebraic equations for the coefficients. The truncation method is proved to be applicable to these systems due to the special choice of the polynomials. A physical interpretation of numerical and asymptotic results obtained for the directivity of the scattered wave and for the stress intensity coefficients near the ends of the crack is suggested.

AB - The diffraction of flexural waves by a short straight crack in an elastic thin plate is considered. The vibrations of the plate are described by the Kirchhoff model. The Fourier method transforms the problem to integral equations of convolution on an interval. The theorems of existence and uniqueness of solutions for these equations are proved. The numerical procedure is based on the orthogonal polynomials decomposition method. It leads to infinite systems of algebraic equations for the coefficients. The truncation method is proved to be applicable to these systems due to the special choice of the polynomials. A physical interpretation of numerical and asymptotic results obtained for the directivity of the scattered wave and for the stress intensity coefficients near the ends of the crack is suggested.

UR - http://www.scopus.com/inward/record.url?scp=0009335004&partnerID=8YFLogxK

U2 - 10.1006/jsvi.1995.0063

DO - 10.1006/jsvi.1995.0063

M3 - Article

AN - SCOPUS:0009335004

VL - 180

SP - 1

EP - 16

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 1

ER -