Natural Oscillations of the Five-Layer Rod Caused by the Initial Deflection
The problem of natural oscillations of a five-layer rod symmetrical in thickness, resulting from the initial deflection, is considered. The three load-bearing layers are assumed to be thin and high-strength. Bernoulli’s hypotheses are accepted for them. In two relatively thick, light fillers, the Ti...
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| Language: | English |
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National Academy of Sciences of Belarus, State Scientific Institution “The Joint Institute of Mechanical Engineering"
2025-06-01
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| Series: | Механика машин, механизмов и материалов |
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| Online Access: | https://mmmm.by/en/readers-en/archive-room-en?layout=edit&id=2033 |
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| author | Eduard I. Starovoitov Darya A. Budnikova |
| author_facet | Eduard I. Starovoitov Darya A. Budnikova |
| author_sort | Eduard I. Starovoitov |
| collection | DOAJ |
| description | The problem of natural oscillations of a five-layer rod symmetrical in thickness, resulting from the initial deflection, is considered. The three load-bearing layers are assumed to be thin and high-strength. Bernoulli’s hypotheses are accepted for them. In two relatively thick, light fillers, the Timoshenko hypothesis is fulfilled, i. e. a displacement in the filler is taken into account. The system of differential equations of natural oscillations is obtained by the variational method, taking into account the transverse inertia forces. For the rod that is symmetrical in thickness, the system is reduced to two partial differential equations with respect to deflection and relative displacement in the fillers. The analytical solution of the corresponding initial boundary value problem is obtained by decomposing the desired displacements into a series according to the constructed system of eigenfunctions. An algebraic equation for determining eigenvalues is given. Graphs of the dependence of the first three frequencies on the thickness of the central bearing layer and fillers are presented. An example of the occurrence of natural oscillations due to the initial deflection is considered. A numerical analysis of the obtained solutions is carried out. |
| format | Article |
| id | doaj-art-3b5340bc4cb34fbba3d0d79f4eaee286 |
| institution | OA Journals |
| issn | 1995-0470 2518-1475 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | National Academy of Sciences of Belarus, State Scientific Institution “The Joint Institute of Mechanical Engineering" |
| record_format | Article |
| series | Механика машин, механизмов и материалов |
| spelling | doaj-art-3b5340bc4cb34fbba3d0d79f4eaee2862025-08-20T02:34:16ZengNational Academy of Sciences of Belarus, State Scientific Institution “The Joint Institute of Mechanical Engineering"Механика машин, механизмов и материалов1995-04702518-14752025-06-012(71)7077https://doi.org/10.46864/1995-0470-2025-2-71-70-77Natural Oscillations of the Five-Layer Rod Caused by the Initial DeflectionEduard I. Starovoitov0https://orcid.org/0000-0002-2550-5377Darya A. Budnikova1Belarusian State University of TransportBelarusian State University of TransportThe problem of natural oscillations of a five-layer rod symmetrical in thickness, resulting from the initial deflection, is considered. The three load-bearing layers are assumed to be thin and high-strength. Bernoulli’s hypotheses are accepted for them. In two relatively thick, light fillers, the Timoshenko hypothesis is fulfilled, i. e. a displacement in the filler is taken into account. The system of differential equations of natural oscillations is obtained by the variational method, taking into account the transverse inertia forces. For the rod that is symmetrical in thickness, the system is reduced to two partial differential equations with respect to deflection and relative displacement in the fillers. The analytical solution of the corresponding initial boundary value problem is obtained by decomposing the desired displacements into a series according to the constructed system of eigenfunctions. An algebraic equation for determining eigenvalues is given. Graphs of the dependence of the first three frequencies on the thickness of the central bearing layer and fillers are presented. An example of the occurrence of natural oscillations due to the initial deflection is considered. A numerical analysis of the obtained solutions is carried out.https://mmmm.by/en/readers-en/archive-room-en?layout=edit&id=2033symmetrical five-layer rodinitial deflectionanalytical solutioneigenvalues and frequenciesnumerical results |
| spellingShingle | Eduard I. Starovoitov Darya A. Budnikova Natural Oscillations of the Five-Layer Rod Caused by the Initial Deflection Механика машин, механизмов и материалов symmetrical five-layer rod initial deflection analytical solution eigenvalues and frequencies numerical results |
| title | Natural Oscillations of the Five-Layer Rod Caused by the Initial Deflection |
| title_full | Natural Oscillations of the Five-Layer Rod Caused by the Initial Deflection |
| title_fullStr | Natural Oscillations of the Five-Layer Rod Caused by the Initial Deflection |
| title_full_unstemmed | Natural Oscillations of the Five-Layer Rod Caused by the Initial Deflection |
| title_short | Natural Oscillations of the Five-Layer Rod Caused by the Initial Deflection |
| title_sort | natural oscillations of the five layer rod caused by the initial deflection |
| topic | symmetrical five-layer rod initial deflection analytical solution eigenvalues and frequencies numerical results |
| url | https://mmmm.by/en/readers-en/archive-room-en?layout=edit&id=2033 |
| work_keys_str_mv | AT eduardistarovoitov naturaloscillationsofthefivelayerrodcausedbytheinitialdeflection AT daryaabudnikova naturaloscillationsofthefivelayerrodcausedbytheinitialdeflection |