 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 55, Issue 7 / 2020 | Next article >> |
| Rasulova N.B. and Rasulov M.B., "New Class of Homogeneous Solutions for Plane Elastodynamic Problems," Mech. Solids. 55 (7), 1057-1061 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
7 |
Pages |
1057-1061 |
| DOI |
10.3103/S0025654420070171 |
| Title |
New Class of Homogeneous Solutions for Plane Elastodynamic Problems |
| Author(s) |
Rasulova N.B. (Institute of Mathematics and Mechanics, National Academy of Science of Azerbaijan, Baku, AZ1141 Azerbaijan, nazila.rasulova@imm.az)
Rasulov M.B. (Institute of Mathematics and Mechanics, National Academy of Science of Azerbaijan, Baku, AZ1141 Azerbaijan, rasulova@gmail.com) |
| Abstract |
The paper presents a new type of functionally invariant Smirnov–Sobolev solutions for the
wave equation, which can be used for solving many homogeneous problems of elastodynamics. The
derived solution has a unique property: the double preimage of Laplace and Fourier transforms of this
function with a new argument and coefficient coincides with the function itself. Thus, this property
allows us to find an inversion formula for double integral transformations. The method for obtaining
this formula is demonstrated by solving the Lamb problem for a half-plane under the transition from
the image to the original. |
| Keywords |
homogeneous solutions, Laplace and Fourier transformations, Lamb’s problem, wave equation, Smirnov–Sobolev solutions |
| Received |
25 February 2019 | Revised |
09 September 2019 | Accepted |
16 September 2019 |
| Link to Fulltext |
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