Natural and forsed osculations of pipelines in contact with the Wincler medium
In this paper, the pipeline is modeled as a curved rod in contact with the Winkler medium. Linear oscillations of a curved viscoelastic rod lying on the Winkler base are considered. The general formulation of the problem of free oscillations of a spatially curved viscoelastic rod with variable param...
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| Published in: | E3S web of conferences Vol. 411; p. 1005 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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EDP Sciences
01-01-2023
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| Abstract | In this paper, the pipeline is modeled as a curved rod in contact with the Winkler medium. Linear oscillations of a curved viscoelastic rod lying on the Winkler base are considered. The general formulation of the problem of free oscillations of a spatially curved viscoelastic rod with variable parameters is reduced to a boundary value problem for a system of ordinary integro-differential equations of the 12th order with variable coefficients relative to eigenstates; it can be solved by the method of successive approximations. The relations allowing to present the solution of the boundary value problem for the rod in an analytical form are formulated. It is established that the dimensionless complex frequencies of natural oscillations of a spatially curved rod, while maintaining the elongation of the rod constant, do not depend on it. The Poisson's ratio has little effect on the dimensionless real and imaginary parts of the natural frequencies. |
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| AbstractList | In this paper, the pipeline is modeled as a curved rod in contact with the Winkler medium. Linear oscillations of a curved viscoelastic rod lying on the Winkler base are considered. The general formulation of the problem of free oscillations of a spatially curved viscoelastic rod with variable parameters is reduced to a boundary value problem for a system of ordinary integro-differential equations of the 12th order with variable coefficients relative to eigenstates; it can be solved by the method of successive approximations. The relations allowing to present the solution of the boundary value problem for the rod in an analytical form are formulated. It is established that the dimensionless complex frequencies of natural oscillations of a spatially curved rod, while maintaining the elongation of the rod constant, do not depend on it. The Poisson's ratio has little effect on the dimensionless real and imaginary parts of the natural frequencies. |
| Author | Boltayev, Z I Safarov, I I Esanov, N Q Teshaev, M Kh Karimov, I M |
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| Cites_doi | 10.1051/e3sconf/202126401027 10.1088/1757-899X/883/1/012100 10.1007/BF02501021 10.1016/j.nucengdes.2013.10.028 10.1016/j.ijpvp.2020.104234 10.1016/j.ymssp.2020.107390 10.1088/1757-899X/1030/1/012073 10.1007/BF02506181 10.1016/j.apm.2020.08.020 10.1016/j.jsv.2020.115891 10.1155/2019/8986010 10.1007/s11071-016-2924-9 10.1007/s10483-020-2646-6 |
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| Editor | Bovtrikova, E. Sadullozoda, S. Morkovkin, D. Gibadullin, A. Uzakov, G. Toshmamatov, B. Abdullozoda, R. |
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| References | Safarov (R11) 2021; 264 Mao (R7) 2016; 86 Mirzaev (R15) 1973; 9 Wang (R3) 2021; 89 R6 Mirsaidov (R18) 2020; 883 Safarov (R16) 2020; 7 Safarov (R12) 2021; 1030 R10 Wu (R20) 2020; 188 Yamashita (R5) 2021; 152 Li (R9) 2014; 266 R14 R13 Abdollahi (R4) 2021; 494 Kudaykulov (R2) 2019; 1019 Mirzaev (R17) 1975; 11 R19 Chen (R8) 2020; 41 R1 |
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