UDC 533.6.013.42
1 State Scientific and Research Institute of Engineering Structures, Kyiv, Ukraine, and Institute of Telecommunication and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 kalyukh2002@gmail.com
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2 Institute of Telecommunication and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine
o.g.lebid@gmail.com
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APPLICATION OF ASYMPTOTIC AND NUMERICAL METHODS FOR DETERMINING
THE STABILITY BOUNDARIES OF DISTRIBUTED SYSTEMS IN A FLOW
Abstract. The reasons and the set of parameters leading to aeroelastic flutter oscillations in distributed systems (DS) are investigated on the basis of asymptotic and numerical methods. The instability is caused by the combined influence of three factors: the drift of disturbances along the DS along the flow, bending stiffness, and the influence of the inertial force, which is a distributed load moving along the DS. An increase in the tensile force and bending stiffness of the DS shifts the instability to a higher frequency range of vibrations. An increase in the relative flux density and the relative length of the DS expands the region of instability. The presence of the angle of inclination of the DS to the flow introduces peculiarities in the balance of forces acting on the DS, and in the formation of the boundary of the regions of stability and instability. However, it is not possible to correctly assess its influence within the framework of the considered model and requires more detailed further consideration. The configuration of the DS in the unstable region indicates the concentration of stresses near its upper end. The results obtained for small angles of inclination of the DS to the flow agree with the known results of other authors.
Keywords: waves, aeroelasticity, asymptotic methods, flutter, bladeless wind turbine.
FULL TEXT
REFERENCES
- AN/ALE-50 Towed Decoy System. URL: https://www.raytheon.com/capabilities/products/ale50.
- Mechanical behavior of submarine cable under coupled tension, torsion and compressive loads. URL: https://www.sciencedirect.com/science/article/abs/pii/S0029801819304470.
- Электродинамические связки — «ЭДС». URL: http://galspace.spb.ru/index116.html.
- Chen B., Su F., Huo C., Zhang R., Yao B., Lian L. Numerical investigation of the dynamics for low tension marine cables. Journal of Shanghai Jiaotong University (Science). 2015. Vol. 20, Iss. 3. P. 257–264. https://doi.org/10.1007/s12204-014-1559-6.
- Navrose, Mittal S. Vibrations of a cylinder in a uniform flow in the presence of a no-slip side-wall. J. Fluid. Struct. 2015. Vol. 57. P. 185–195. https://doi.org/10.1016 /j.jfluidstructs.2015.06.009.
- Selezov I.T., Kryvonos Yu.G., Gandzha I.S. Wave propagation and diffraction. Mathematical methods and applications. Ser. Foundations of Engineering Mechanics. Springer, 2018. 237 p. https://doi.org/10.1007/978-981-10-4923-1.
- Gladkiy A.V., Sergienko I.V., Skopetsky V.V. Numerical-analytical methods for studying wave processes. Kiev: Nauk. dumka, 2001. 452 p.
- Gladky A.V., Skopetsky V.V. On numerical modeling and optimization of unidirectional wave processes in inhomogeneous media. Kibernetika i sistemnyj analiz. 2010. N 5. P. 177–186.
- Gubarev V.F. Rational approximation of systems with distributed parameters. Kibernetika i sistemnyj analiz. 2008. N 2. P. 99–115.
- Trofimchuk A.N. Seismic resistance of structures, taking into account their interaction with the soil base [in Russian]. Kiev: UIIOSR, 2004. 72 p.
- Paїdoussis M.P. (Ed.). Slender structures and axial flow. Ser. Fluid-Structure Interactions, Vol. 1. Elsevier, 1988. 573 p.
- Paїdoussis M.P. (Ed.). Slender structures and axial flow. Ser. Fluid-Structure Interactions, Vol. 2. Elsevier, 2003. P. 573–1585.
- Sharhaty A.I. Nonlinear and hysteretic twisting effects in ocean cable laying. Trans. ASME: J. Energy Resource Hehnal. 1983. Vol. 105, A 3. P. 341–345.
- The future of wind: RAZOR. URL: https://www.youtube.com/watch?v=B_vg-EM3-18.
- The Vortex Bladeless wind turbine. URL: https://www.herox.com/blog/354-the-vortex -bladeless-wind-turbine .
- Good vibes: Bladeless turbines could bring wind power into your home: renewable energy. URL: https://digismak.com/good-vibes-bladeless-turbines-could-bring-wind-power-into-your-home-renewable-energy/.
- Sprigss D., Messiter A., Anderson W. Paradox in the membrane flutter problem - explanations using singular perturbation methods. Raketnaya tekhnika i kosmonavtika. 1969. Vol. 7, N 9. P. 52–59.
- Kachurin V.K. Flexible threads with small arrows [in Russian]. Moscow: Gostekhizdat, 1956. 224 p.
- Kaliukh Iu.I. Specific features of using the linearization method for the analysis of low-frequency oscillations of a towed system. International Applied Mechanics. 2021. Vol. 57, N 1. P. 103–110.
- Saltanov N.V. Flexible threads in streams [in Russian]. Kiev: Nauk. thought, 1974. 140 p.
- Kalyukh Iu.I., Lebid O.G. Constructing the adaptive algorithms for solving multi-wave problems. Kibernetyka ta systemnyi analiz. 2021. Vol. 57, N 6. P. 106–117.
- Kaliukh I., Trofymchuk O., Lebid O. Numerical solution of two-point static problems for distributed extended systems by means of the Nelder–Mead method. Cybernetics and Systems Analysis. 2019. Vol. 55, N 4. P. 616–624. https://doi.org/10.1007/s10559-019-00170-3.
