 | | 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: | | 12977 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8096
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| In English (Mech. Solids): | | 4881 |
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| V.V. Saurin, "Dynamic Bending of a Beam," Mech. Solids. 59 (5), 2706-2718 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
5 |
Pages |
2706-2718 |
| DOI |
10.1134/S0025654424603422 |
| Title |
Dynamic Bending of a Beam |
| Author(s) |
V.V. Saurin (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, saurin@ipmnet.ru) |
| Abstract |
The article discusses problems of dynamic bending for beams of semi-infinite length.
To solve such problems, the article uses a method based on the implementation of the conservation
laws, namely, the law of energy conservation, the law of change in momentum and the law of change
in angular momentum. The results obtained are compared with the analytical solution for the problem
of a semi-infinite beam motion loaded at the free end with a transverse force. The peculiarity of this
solution is that the change in the stress-strain state of the rod is characterized by a wave front. It is considered that all changes in the state of the beam occur at an infinite speed. All designed solutions are
characterized by the presence of a wave front in the beam. It is shown that, in contrast to the transfer
of longitudinal disturbances along the length of the beam, which occur at a constant speed, bending
disturbances propagate at a variable speed, and, with increasing time, this speed decreases and tends
to zero at an infinitely distant point of the beam. It was discovered that the propagation velocity of the
wave front during the transfer of concentrated force and concentrated moment differs from each other.
In this case, the speed of transverse force transfer is almost twice as high as the speed of the wave front from the bending moment. |
| Keywords |
elastic rod, initial boundary value problem, conservation laws, wave front |
| Received |
18 April 2024 | Revised |
28 May 2024 | Accepted |
03 June 2024 |
| Link to Fulltext |
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