# 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 language English 867-877 11 Journal of Applied Mathematics and Mechanics 65 5 https://doi.org/10.1016/S0021-8928(01)00092-2 Published - 1 Dec 2001

### Fingerprint

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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title = "Diffraction of a flexural wave by a short joint of semi-infinite elastic plates",
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.",
author = "Andronov, {I. V.}",
year = "2001",
month = "12",
day = "1",
doi = "10.1016/S0021-8928(01)00092-2",
language = "English",
volume = "65",
pages = "867--877",
journal = "Journal of Applied Mathematics and Mechanics",
issn = "0021-8928",
publisher = "Elsevier",
number = "5",

}

In: Journal of Applied Mathematics and Mechanics, Vol. 65, No. 5, 01.12.2001, p. 867-877.

Research output

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AU - Andronov, I. V.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - 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.

AB - 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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