 | | 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 54, Issue 2 / 2019 | Next article >> |
| E.E. Lisenkova, "Boundary-Value Problems of the Dynamic Behavior of Two-Dimensional Elastic Systems with Moving Objects," Mech. Solids. 54 (2), 311-318 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
2 |
Pages |
311-318 |
| DOI |
10.3103/S0025654419030178 |
| Title |
Boundary-Value Problems of the Dynamic Behavior of Two-Dimensional Elastic Systems with Moving Objects |
| Author(s) |
E.E. Lisenkova (Mechanical Engineering Research Institute, Russian Academy of Sciences, Nizhny Novgorod, 603024 Russia; Nizhny Novgorod Institute of Management, Branch of Russian Presidental Academy of National Economy and Public Administration, Nizhny Novgorod, 603950 Russia, EELissen@yandex.ru) |
| Abstract |
The interdependent dynamic behavior of a two-dimensional elastic system in the form of a one-dimensional mechanical object moving on a band is considered. The Lagrangian density of the
two-dimensional system depends on the generalized coordinates and their derivatives up to and
including the second order, and the Lagrangian of the moving object as one of the generalized coordinates contains the motion law, which is an unknown function of this problem. The physically and
mathematically correct conditions at the moving boundary have been found as a result of formulating
the self-consistent boundary-value problem based on the Hamilton variational principle. The problem
of the unseparated motion of a rod, which performs bending and torsional vibrations, along a plate
with consideration for the rotational inertia of its components is formulated as an example. The differential and integral laws of the change in energy and wave momentum are derived for both the entire complex system and its isolated parts. The relationships true at the moving boundary are established between
the components of the energy flux density vector and the wave momentum flux density tensor. |
| Keywords |
boundary-value problem, two-dimensional elastic system, moving object, plate, energy, wave momentum |
| Received |
11 November 2017 | Revised |
17 November 2017 | Accepted |
25 November 2017 |
| Link to Fulltext |
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