 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
|
| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 79, Issue 3 / 2015 | Next article >> |
| S.M. Mkhitaryan, "An eigenvalue relation in spheroidal wave functions related to potential theory and its applications to contact problems," J. Appl. Math. Mech. 79 (3), 304-313 (2015) |
| Year |
2015 |
Volume |
79 |
Issue |
3 |
Pages |
304-313 |
| DOI |
10.1016/j.jappmathmech.2015.09.010 |
| Title |
An eigenvalue relation in spheroidal wave functions related to potential theory and its applications to contact problems |
| Author(s) |
S.M. Mkhitaryan (Institute of Mechanics of the National Academy of Sciences, Yerevan, Armenia, smkhitaryan39@rambler.ru) |
| Abstract |
Eigenvalue and related integral relations for an integral operator with a symmetrical kernel, defined in a circular region, in the form of the ratio of an exponential function of the distance between two points to its distance, are established by methods of generalized potential theory, related to the Helmholtz equation, in an orthogonal system of coordinates of an oblate spheroid, where one of the coordinate surfaces is degenerate in a plane doubly covered circular disc. These relations extend corresponding relations for the integral operator with a symmetric kernel in the form of the Weber-Sonin integral and contain spheroidal wave functions. Using the integral relations obtained, an exact solution of the integral equation of the contact problem of the indentation of a punch, circular in plan, into a linearly deformed base of an elastic half-space with a kernel identical with a kernel, which varies exponentially with distance, is constructed. Other applications of the eigenvalue and related integral relations obtained are also indicated. |
| Received |
05 May 2014 |
| Link to Fulltext |
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| << Previous article | Volume 79, Issue 3 / 2015 | Next article >> |
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