Investigation of the wing model dynamic stability in the airflow
Authors: Naumov A.M., Domnina O.A.
Published in issue: #10(142)/2023
DOI: 10.18698/2308-6033-2023-10-2307
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
Investigating the aircraft structure elements for compliance with dynamic stability is one of the most important ways to study their dynamic properties. The paper considers possibility of the wing model dynamic loss of stability (flutter type) in the form of a flat rod of variable geometry close to the real wing geometry in the airflow. Internal force factors manifested under the frontal aerodynamic force influence, as well as increment in the lift and aerodynamic moment arising during possible small model oscillations are taken into account from the oncoming airflow side. Due to these external forces increment, the so-called energy pumping from the airflow side occurs, and the problem becomes non-conservative. Behavior of the first three complex eigenvalues of small oscillations was numerically studied, and the critical flow velocities, at which the model could lose dynamic stability, were determined for various parameters of the external aerodynamic forces.
References
[1] Biderman V.L. Teoriya mekhanicheskikh kolebaniy [Theory of mechanical oscillations]. Moscow, 1980, Vysshaya Shkola Publ., 408 p.
[2] Strelkov S.P. Vvedenie v teoriyu kolebaniy [Introduction to the oscillation theory], Moscow, Nauka Publ., 1964, 437 p.
[3] Panovko Ya.G., Gubanova I.I. Ustoichivost i kolebaniya uprugikh system [Stability and oscillations of the elastic systems]. 4th ed., rev. Moscow, Nauka Publ., 1987, 352 p.
[4] Keldysh M.V. Vibratsiya v vozdushnom potoke kryla s podkosami [Vibration in the airflow of a wing with struts]. Trudy TsAGI, iss. 357. Moscow, 1938, 40 p.
[5] Grossman E.P., Keldysh M.V., Parkhomovskiy Ya.M. Vibratsiya kryla s ehleronom [Vibration of wing with an aileron]. Trudy TsAGI, iss. 337. Moscow, 1937, 98 p.
[6] Riz P.M. Flatter vozdushnykh vintov [Aircraft propeller flutter]. Trudy TsAGI, iss. 391. Moscow, 1938, 36 p.
[7] Fyn Ya.Ts. Vvedenie v teoriyu aerouprugosti [Introduction to the theory of aeroelasticity]. Moscow, 1959, Gos. Izd-vo Fiz-Mat Lit. Publ., 1959, 523 p.
[8] Gallay M.L. Izbrannoe [Selected works]. In 2 vol. Vol. 1. Moscow, Voenizdat Publ., 1990, 524 p.
[9] Naumov A.M., Mochilin I.K. Issledovanie dinamicheskoy poteri ustoychivosti modeli kryla v potoke vozdukha [Investigation of dynamic buckling of a wing model in air flow]. Mashinostroenie i kompyuternye tekhnologii — Mechanical Engineering and Computer Science, 2019, no. 3, pp. 15–27. https://doi.org/10.24108/0319.0001468
[10] Naumov A.M. Issledovanie vliyaniya dopolnitelnoy massy na dinamicheskuyu ustoychivost modeli kryla v potoke vozdukha [Investigation of additional mass effect on dynamic wing model stability in airflow]. Mashinostroenie i kompyuternye tekhnologii — Mechanical Engineering and Computer Science, 2019, no. 7, pp. 1–7. https://doi.org/10.24108/0719.0001506
[11] Andrievsky B.R., Kuznetsov N.V., Kudryashova E.V., Kuznetsova O.A. Krutilno-izgibnyi flatter kryla: matematicheskie modeli, issledovanie i predotvraschenie. Obzor [Elastic-flexural wing flutter: modeling, investigation and prevention. A review]. Differentsialnye uravneniya i protsessy upravleniya — Differential Equations and Control Processes, 2021, no. 4, pp.116–191.
[12] Wagner H.A. Uber die Entstehung des dynamischen Auftriebes von Tragflugeln. ZAMM, Band 5, Heft 1, 1925, S. 17–35.
[13] Theodorsen Th. General theory of aerodynamic instability and the mechanism of flutter. NASA Report No. 496, 1949.
[14] Birnbaum W. Das ebene Problem des schlagenden Flugels. ZAMM, 1924, 277 S.
[15] Naumov A.M., Tikhonova O.N. Opredelenie chastot i form svobodnykh kolebaniy predvaritelno nagruzhennogo rezinokordnogo shlanga (truboprovoda), nakhodyaschegosya v potoke gaza ili zhidkosti [Determination of frequency and modes of free oscillation of the pre-loaded hose (pipe-line) in gas or liquid stream]. Vestnik MGTU im N.E. Baumana. Ser. Mashinostroenie — Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2000, no. 3, pp. 91–102.
[16] Naumov A.M., Domnina O.A. Modalnyi analiz modeli kryla v potoke vozdukha v konservativnoy postanovke [Wing model modal analysis in the airflow in conservative formulation]. Inzhenerny zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2023, iss. 6. https://doi.org/10.18698/2308-6033-2023-6-2280
[17] Sokolov A.I. Nestatsionarnye kolebaniya i ustoichivost provisayuschikh provodov vozdushnykh liniy pri vetrovykh i gololednykh nagruzkakh. Dis. … kand. tekhn. nauk [Unsteady vibrations and stability of sagging wires of overhead lines under wind and ice loads Diss. … Cand. Sci. (Eng.)]. Moscow, BMSTU, 2012.
[18] Kazakevich M.I. Aehrodinamika mostov [Bridge aerodynamics]. Moscow, Transport Publ., 1987, 240 p.