Diffraction of a flexural wave by a short joint of semi-infinite elastic plates

Research output

Abstract

The problem of the flexural vibrations of two semi-infinite elastic plates connected along a section of the boundary (the joint) that is short compared with the wavelength of the incident wave, is considered. The problem is reduced to solving integral equations on the section. The use of Green's formula leads to an integral equation with a smooth kernel, the solution of which is a function with singularities of order - 32 at the ends of the section. Regularization of this integral equation is carried out. The asymptotic form of the far field over the dimensionless length of the joint is found.

Original languageEnglish
Pages (from-to)867-877
Number of pages11
JournalJournal of Applied Mathematics and Mechanics
Volume65
Issue number5
DOIs
Publication statusPublished - 1 Dec 2001

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Elastic Plate
Elastic waves
Integral equations
Diffraction
Integral Equations
Kernel Smoother
Green's Formula
Far Field
Dimensionless
Regularization
Vibration
Singularity
Wavelength

Scopus subject areas

  • Mechanical Engineering
  • Applied Mathematics

Cite this

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abstract = "The problem of the flexural vibrations of two semi-infinite elastic plates connected along a section of the boundary (the joint) that is short compared with the wavelength of the incident wave, is considered. The problem is reduced to solving integral equations on the section. The use of Green's formula leads to an integral equation with a smooth kernel, the solution of which is a function with singularities of order - 32 at the ends of the section. Regularization of this integral equation is carried out. The asymptotic form of the far field over the dimensionless length of the joint is found.",
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