Wing model modal analysis in the airflow in conservative formulation
Authors: Naumov A.M., Domnina O.A.
Published in issue: #6(138)/2023
DOI: 10.18698/2308-6033-2023-6-2280
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
Modal analysis of the elastic system dynamic properties is one of the most important types of research. The paper investigates eigen frequencies and oscillation modes of a wing model in the form of a flat rod of variable geometry, close to the real wing geometry in the air flow with zero angle of attack. Influence of the oncoming airflow is considered due to the internal force factors appearing under the frontal aerodynamic force action from the flow side. Aerodynamic forces and moments increment arising from the model small oscillations are not taken into account, i.e. the energy is not being “pumpe” at small oscillations from the airflow side, and the problem is solved in the conservative formulation. First three frequencies of natural oscillations and their corresponding forms are numerically determined; it is shown that all of them are purely bending. Dependence of the first three frequencies behavior on the oncoming flow speed was studied.
References
[1] Dimentberg F.M., Kolesnikov K.S., ed. Vibratsii v tekhnike: Spravochnik. V 6 tomakh. Tom 3. Kolebaniya mashin, konstruktsiy i ikh elementov [Vibrations in technology: Reference book. In 6 vols. Vol. 3. Vibrations of machines, structures and their elements], Moscow, Mashinostroenie Publ., 1980, 544 p.
[2] Rukin Yu.B., Lopatin A.Yu., Shershneva Yu.A. Issledovanie sobstvennykh kolebaniy modeli kryla samoleta metodom konechnykh elementov [Investigation of natural vibrations of the wing model aircraft finite element method]. Informatsionnye tekhnologii v stroitelnykh, sotsialnykh i ekonomicheskikh sistemakh — Information technologies in construction, social and economy systems, 2020, no. 1 (19), pp. 152–154.
[3] Menzulskiy S.Yu., Bura R.V. Opredelenie modalnykh kharakteristik i raschetnye issledovaniya po obespecheniyu bezopasnosti letatelnogo apparata ot flattera [Determination of modal characteristics and calculated analysis of ensuring the aircraft flutter safety]. Inzhenernyi zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovation, 2018, iss. 12. https://doi.org/10.18698/2308-6033-2018-12-1833
[4] Garifullin M.F., Borodina Yu.N., Slitinskaia A.Yu. Korrektsiya parametrov matematicheskoy modeli kryla bolshogo udlineniya po rezultatam eksperimentalnykh issledovaniy form i chastot sobstvennykh kolebaniy [Correction of the mathematical model parameters of a large aspect ratio wing based on the results of experimental studies of the eigenforms and eigenfrequencies]. In: Modeli i metody aerodinamiki. Materialy Vosemnadtsatoy mezhdunarodnoy shkoly-seminara [Models and methods of aerodynamics. Materials of the Eighteenth International School-Seminar]. Moscow, TsAGI Publ., 2018, 59 p.
[5] Demirtas A.M., Bayraktar M. Free vibration of an aircraft wing by considering as a cantilever beam. Selcuk University Journal of Engineering Sciences, 2019, vol. 7, no. 1, pp. 12–21.
[6] Banerjee J.R. Modal analysis of sailplane and transport aircraft wings using the dynamic stiffness method. Journal of Physics: Conference Series, 2016, ser. 721, art. no. 012005. https://doi.org/10.1088/1742-6596/721/1/012005
[7] Bezuyevskiy A.V. Vliyaniye bolshikh deformatsiy konstruktsii kryla na yego modalnye kharakteristiki [Influence of large deformations of the wing structure on its modal characteristics]. In: Trudy 55-y nauchnoy konferentsii MFTI. Aeromekhanika i letatelnaya tekhnika [Proceedings of the 55th MIPT Scientific Conference. Aeromechanics and Aircraft Technology]. Moscow, MFTI Publ., 2012, pp. 51–53.
[8] Pavlov V.A. Mekhanika kryla samoleta. Katastroficheskie kolebaniya. Otkrytie: monografiya [Aircraft wing mechanics. catastrophic oscillations. Discovery: monography]. Kazan, KNITU-KAI Publ., 2017, 200 p.
[9] Naumov A.M., Tikhonova O.N. Opredeleniye 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. 91–101.
[10] Ponomarev S.D., Biderman V.L., Likharev K.K., et al. Raschety na prochnost v mashinostroenii: v 3 tomakh. Tom 3 Inertsionnye nagruzki [Strength calculations in mechanical engineering. In 3 vols. Vol. 3. Inertial loads]. S.D. Ponomarev, ed. Moscow, Mashgiz Publ., 1959, 1118 p.