Scattering of hydoacoustic waves by a narrow crack in an elastic plate

I. V. Andronov, B. P. Belinskii

Research output

Abstract

The scattering of waves by an infinite elastic plate, which covers an acoustic half-space and is weakened by a crack in the form of an infinitely long cut of finite width with parallel edges is considered. The scattered field is expressed in terms of the solution of an integro-algebraic system of equations on the crack. The logarithmic characteristic of the kernel enables Bubnov's method with a basis containing Chebvshev polynomials of the first kind to be used for the numerical analysis. Particular attention is given to the asymptotic investigation of the scattering diagram and the amplitudes of the surface waves for a narrow crack and a thin plate. A comparison with the well-known model of a point crack enables the range of parameters of the problem where the point model is applicable to be indicated.

Original languageEnglish
Pages (from-to)195-202
Number of pages8
JournalJournal of Applied Mathematics and Mechanics
Volume61
Issue number2
DOIs
Publication statusPublished - 1 Jan 1997

Fingerprint

Elastic Plate
Crack
Scattering
Cracks
Thin Plate
Surface Waves
Surface waves
Half-space
System of equations
Numerical analysis
Numerical Analysis
Acoustics
Logarithmic
Diagram
Polynomials
Cover
kernel
Polynomial
Model
Range of data

Scopus subject areas

  • Modelling and Simulation
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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AB - The scattering of waves by an infinite elastic plate, which covers an acoustic half-space and is weakened by a crack in the form of an infinitely long cut of finite width with parallel edges is considered. The scattered field is expressed in terms of the solution of an integro-algebraic system of equations on the crack. The logarithmic characteristic of the kernel enables Bubnov's method with a basis containing Chebvshev polynomials of the first kind to be used for the numerical analysis. Particular attention is given to the asymptotic investigation of the scattering diagram and the amplitudes of the surface waves for a narrow crack and a thin plate. A comparison with the well-known model of a point crack enables the range of parameters of the problem where the point model is applicable to be indicated.

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