ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Elastic-flexural Wing Flutter: Modeling, Investigation, and Prevention. A Survey

Author(s):

Boris Rostislavich Andrievsky

Doctor of Technical Sciences, Leading Researcher, Laboratory for Control
of Complex Systems, Institute for Problems in Mechanical Engineering, RAS (IPME RAS),
Principal Researcher of the Department
of Applied Cybernetics, St. Petersburg State University,
Leading Researcher of the Baltic State Technical University "VOENMEKH" D.F. Ustinova "

boris.andrievsky@gmail.com

Nikolay Vladimirovich Kuznetsov

Doctor of Physical and Mathematical Sciences, Head of the Department
of Applied Cybernetics, St. Petersburg State University,
Head of the Laboratory of Information and Control Systems of the Institute
for Problems of Mechanical Engineering of the Russian Academy of Sciences (IPMash RAS)
Professor of the Department of Mathematical Information Technology, University of Jyvaskyla, Finland

n.v.kuznetsov@spbu.ru

Elena Vladimirivna Kudryashova

Doctor of Physical and Mathematical Sciences, Leading Researcher of the Department
of Applied Cybernetics, St. Petersburg State University

e.kudryashova@spbu.ru

Olga Aleksandrovna Kuznetsova

Doctor of Physical and Mathematical Sciences, Principal Researcher of the Department
of Applied Cybernetics, St. Petersburg State University

olga.kuznetsova@spbu.ru

Abstract:

Depending on the flight mode, the airflow can either damp aircraft oscillations, or, conversely, the oscillating structure takes energy from the incoming flow, as a result of which a rapid increase in amplitude of oscillations may occur. This dangerous phenomenon has become a significant obstacle to the development of high-speed aviation. Since the 1930s and up to the present time, the efforts of many researchers are aimed at describing the dynamics of this phenomenon, studying its properties and developing measures to prevent it. In the present paper, some existing results on elastic-flexural wing flutter are surveyed. The paper starts from various ways of modeling the elasticflexural wing flutter. The results on investigations of the elastic-flexural wing flutter phenomenon are reviewed, and several approaches of passive and active flutter suppression methods are described.

Keywords

References:

  1. Birnbaum W. Das ebene Problem des schlagenden Flugels // ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift fur Angewandte Mathematik und Mechanik. 1924. S. 277-291. (In German)
  2. Blenk H., Liebers F. Gekoppelte Biegungs- Torsions- und Biegungsschwingungen von Freitragenden und halbjreitragenden Fl ‥ ugeln // LuftfahrtForschungs. 1929. Bd. 4. S. 69-93. (In German)
  3. Blenk H., Liebers F. Gekoppelte Torsions- und Biegungsschwinguneen von Tragflugeln // Z. Flugtech. und Motorluftschif. 1925. S. 479-486. (In German)
  4. Grossman EP, Krichevsky SS, Borin AA [On the question of the loss of stability of wing structures in flight] K voprosu o potere ustoychivosti konstruktsiy kryla v polete // Proceedings of TsAGI. 1935. Vol. 202. (In Russ. )
  5. Grossman E. P. [Flutter] Flutter // Tr. TsAGI. 1937. No. 284. (In Russ. )
  6. Grossman E. P. [Vibration course of aircraft parts] Kurs vibratsiy chastey samoleta. Tutorial. M . : Oborongiz, 1940. (In Russ. )
  7. Borin A. A. [From the history of solving the flutter problem] Iz istorii resheniya problemy flattera // [From the history of aviation and cosmonautics] Iz istorii aviatsii i kosmonavtiki. 1978. Issue. Library of Astronomy and Cosmonautics, No. 32. URL: http://12apr.su/books/item/f00/s00/z0000030/st019.shtml (In Russ. )
  8. Aviation. Encyclopedia / Ed. Svishcheva G. P. Moscow: TsAGI, 1994. Great Russian Encyclopedia. 766 p. (In Russ. )
  9. Eger S. M., Matveenko A. M., Shatalov I. A. [Fundamentals of Aviation Technology: Textbook] Osnovy aviatsionnoy tekhniki: Uchebnik / Ed. I. A. Shatalov. M . : Mechanical engineering, 2003. (In Russ. )
  10. Zhang Y., Chen Y., Liu J., Meng G. Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow // Advances in Acoustics and Vibration. 2011. Vol. 2011, no. ID 926271. P. 1-10
  11. Abdelkefi A., Vasconcellos R., Nayfeh A., Hajj M. An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system // Nonlinear Dynamics. 2013. Vol. 71, no. 1-2. P. 159-173
  12. Chen C. -L., Peng C. C., Yau H. -T. High-order sliding mode controller with backstepping design for aeroelastic systems // Communications in Nonlinear Science and Numerical Simulation. 2012. Vol. 17, no. 4. P. 1813 - 1823. URL: http://www.sciencedirect.com/ science/article/pii/S1007570411005028
  13. Dowell E. A Modern Course in Aeroelasticity. Dordrecht: Kluwer, 1995
  14. GOST 20058-80. [Aircraft dynamics in atmosphere: Terms, definitions and symbols] Dinamika letatel'nykh apparatov v atmosfere: Terminy, opredeleniya i oboznacheniya Moscow: Publishing house of standards, 1981. (In Russ. )
  15. Bukov V. N. [Adaptive predictive flight control systems] Adaptivnyye prognoziruyushchiye sistemy upravleniya poletom. Moscow: Nauka, 1987. P. 230. (In Russ. )
  16. Byushgens G. S., Studnev R. V. [Dynamics of longitudinal and lateral movement] Dinamika prodol'nogo i bokovogo dvizheniya. Moscow: Mechanical Engineering, 1979. (In Russ. )
  17. Theodorsen T. General theory of aerodynamic instability and the mechanism of flutter: Tech. Rep. 496: National Advisory Committee for Aeronautics, 1935. URL: https://digital.library.unt.edu/ark: /67531/metadc53413/
  18. Theodorsen T., Garrick I. Mechanism of flutter: a theoretical and experiment investigation of the flutter problem: Tech. Rep. 685: National Advisory Committee for Aeronautics, 1940. URL: https://ntrs.nasa.gov/citations/19930091762
  19. Bisplinghoff R., Ashley H., Halfman R. Aeroelasticity. New York: Dover, 1996
  20. Edwards J., Ashley A., Breakwell J. Unsteady aerodynamic modeling for arbitrary motions // AIAA J. 1979. Vol. 17. P. 365-374
  21. Sears R. W. A systematic presentation of the theory of thin airfoils in non-uniform motion: Ph. D. thesis / California Institute of Technology. Pasadena, California, 1938
  22. Li M., Yang Y., Li M., Liao H. Direct measurement of the Sears function in turbulent flow // J. Fluid Mechanics. 2018. —June. Vol. 847. P. 768-785
  23. Baker, G. A. Jr. and Graves-Morris, P. Padé Approximants. New York: Cambridge University Press, 1996
  24. Kutta M. W. Lifting Forces in Flowing Fluids. 1902
  25. Houghton E., Carpenter P. Aerodynamics for engineering students. - 5th ed. Oxford: Butterworth-Heinemann, 2003
  26. Mohebbi F., Evans B., Sellier M. On the Kutta Condition in Compressible Flow over Isolated Airfoils // Fluids. 2019. Vol. 4, no. 2. URL: https://www.mdpi.com/2311-5521/4/2/102
  27. Mohebbi F., Sellier M. On the Kutta Condition in Potential Flow over Airfoil // Journal of Aerodynamics. 2014
  28. Queijo M. J., Wells W. R., Keskar D. A. Approximate indicial lift function for tapered, swept wings in incompressible flow. USA: NASA. Scientific and Technical Information Office, Langley Research Center, Wright State University, 1978. NASA Technical Paper 1241
  29. Jones R. T. The Unsteady Lift of a Wing of Finite Aspect Ratio: Tech. Rep. 681: National Advisory Committee for Aeronautics, 1940
  30. Liu L. P., Dowell E. H. The secondary bifurcation of an aeroelastic airfoil motion: effect of high harmonics // Nonlinear Dynamics. 2004. Vol. 37, no. 1. P. 31-49
  31. Jones R. T. Operational Treatment of the Non-Uniform Lift Theory in Airplane Dynamics // NACA Technical Note 667. NASA, 1938
  32. Lee B. H. K., Liu L., Chung K. W. Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces // J. Sound and Vibration. 2005. Vol. 281, no. 3-5. P. 699-717
  33. Liu L. P., Dowell E. H., Thomas J. P. A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces // J. Fluids and Structures. 2005. Vol. 23, no. 3. P. 351-363
  34. Peters D. A. Finite-State Airloads for Deformable Airfoils on Fixed and Rotating Wings // Proc. Symp. Aeroelasticity and Fluid/ Structure Interaction, ASME Winter Annual Meeting, Chicago, IL. 1994. —Nov
  35. Peters D. A., Karunamoorthy S., Cao W. -M. Finite state induced flow models. I - Two-dimensional thin airfoil // J. Aircraft. 1995. —Mar. Vol. 32, no. 2. P. 313-322
  36. Tang D., Conner M. D., Dowell E. H. Reduced-Order Aerodynamic Model and Its Application to a Nonlinear Aeroelastic System // J. Aircraft. 1998. Vol. 35, no. 2. P. 332-338. URL: https://doi.org/10.2514/2.2304
  37. Dowell E. H. Eigenmode analysis in unsteady aerodynamics - Reduced order models // AIAA Journal. 1996. Vol. 34, no. 8. P. 1578-1583. URL: https://doi.org/10.2514/3.13274
  38. Zhang C., Zhou Z., Zhu X., Qiao L. A Comprehensive Framework for Coupled Nonlinear Aeroelasticity and Flight Dynamics of Highly Flexible Aircrafts // Applied Sciences. 2020. Vol. 10, no. 3. URL: https://www.mdpi.com/2076-3417/10/3/949
  39. Huang R., Hu H., Zhao Y. Nonlinear Reduced-Order Modeling for Multiple-Input/Multiple-Output Aerodynamic Systems //AIAA Journal. 2014. Vol. 52, no. 6. P. 1219-1231. https://doi.org/10.2514/1.J052323 URL: https://doi.org/10 2514/1. J052323
  40. Isogai K. On the Transonic-Dip Mechanism of Flutter of a Sweptback Wing // AIAA Journal. 1979. Vol. 17, no. 7. P. 793-795
  41. Isogai K. Transonic dip mechanism of flutter of a sweptback wing. II // AIAA Journal. 1981. Vol. 19, no. 9. P. 1240-1242
  42. Dowell E., Hall K. Modeling of fluid-structure interaction // Annual Review of Fluid Mechanics. 2001. Vol. 33. P. 445-490
  43. Lomax H., Pulliam T., Zingg D. Time-Marching Methods for ODEs //Fundamentals of Computational Fluid Dynamics / Ed. by J. -J. Chattot, P. Colella, R. Glowinski et al. Berlin, Heidelberg: Springer, 2001. Ser. Scientific Computation
  44. Dowell E., Edwards J., Strganac T. Nonlinear aeroelasticity // J. Aircraft. 2003. Vol. 40, no. 5. P. 857-874
  45. Krapivko A. V. [Application of the D-partitioning method for constructing an algorithm for calculating the stability of linear systems and systems with local nonlinearities on a computer] Primeneniye metoda D-razbiyeniya dlya postroyeniya algoritma rascheta na EVM ustoychivosti lineynykh sistem i sistem s lokal'nymi nelineynostyami // [TsAGI scientific notes] Uchenye zapiski TsAGI. 1981. Vol. XII, No. 2. P. 129-136. (In Russ. )
  46. Baranov NI, Vasiliev KI, Kutin DB, Narizhny AG, Smyslov VI [Experimental study of the flutter of a controlled stabilizer with nonlinear characteristics in the control wiring for electromechanical modeling of aerodynamic forces] Eksperimental'noye issledovaniye flattera upravlyayemogo stabilizatora s nelineynymi kharakteristikami v provodke upravleniya pri elektromekhanicheskom modelirovanii aerodinamicheskikh sil // [TsAGI scientific notes] Uchenye zapiski TsAGI. 1983. Vol. XIV, No. 3. S. 94-100. (In Russ. )
  47. Lee B., LeBlanc P. Flutter Analysis of a Two-dimensional Airfoil with Cubic Non-linear Restoring Force. Aeronautical note. National Research Council Canada, 1986. URL: https://books.google.ru/books?id=Kkc7PwAACAAJ
  48. O’Neil T., Strganac T. W. Aeroelastic Response of a Rigid Wing Supported by Nonlinear Springs // J. of Aircraft. 1998. —July—Aug. Vol. 35, no. 4. P. 616-622
  49. [Computational studies of the transonic flutter of an aircraft] Raschetnyye issledovaniya transzvukovogo flattera samoleta // [TsAGI scientific notes] Uchenye zapiski TsAGI. 1989. Vol. XX, No. 6. P. 110-115. (In Russ. )
  50. Bunkov VG [Combined method for calculating aerodynamic forces on an oscillating aircraft in a supersonic flow] Kombinirovannyy metod rascheta aerodinamicheskikh sil na koleblyushchemsya letatel'nom apparate v sverkhzvukovom potoke // [TsAGI scientific notes] Uchenye zapiski TsAGI. 1984. Vol. XV, No. 3. P. 11-22. (In Russ. )
  51. Alighanbari H., Price S. J. The Post-Hopf-Bifurcation Response of an Airfoil in Incompressible Two-Dimensional Flow // Nonlinear Dynamics. 1996. Vol. 10. P. 381-400
  52. Doedel E. J., Champneys A. R., Fairgrieve T. F. et al. AUTO 97: Continuation And Bifurcation Software For Ordinary Differential Equations (with HomCont). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.9955
  53. Price S. J., Lee B. H. K., Alighanbari H. An analysis of the post instability behaviour of a two dimensional airfoil with a structural nonlinearity // J. of Aircraft. 1995. Vol. 31. P. 1395-1401
  54. Tang D., Henry J., Dowell E. Limit cycle oscillations of delta wing models in low subsonic flow // AIAA journal. 1999. Vol. 37, no. 11. P. 1355-1362
  55. Zhao L., Yang Z. Chaotic Motion of An Airfoil with Nonlinear Stiffness in Incompressible Flow // J. of Sound and Vibration. 1990. Vol. 138. P. 245-254
  56. Zhao D. -M., Zhang Q. -C. Bifurcation and chaos analysis for aeroelastic airfoil with freeplay structural nonlinearity in pitch // Chinese Physics B. 2010. Vol. 19, no. 3. P. 030518-10
  57. Zhou L., Chen Y., Chen F. Chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow // Aerospace Science and Technology. 2013. Vol. 25, no. 1. P. 138- 144. URL: http://www.sciencedirect.com/science/article/pii/S127096381200003X
  58. Chen P. C., Liu D. D., Hall K. C., Dowell E. H. Nonlinear Reduced Order Modeling of Limit Cycle Oscillations of Aircraft Wings. Final report. Scottsdale, AZ., USA: Ft. Belvoir Defense Technical Information Center, 2000. —Aug. Vol. AFRL-SR-BL-TR-00-. P. 107. Performong Organization: ZONA Technology, Inc.; In collaboration with Duke Univ., Durham, NC., USA. URL: InternetResource, handle. dtic. mil
  59. Raveh D. E. Computational-fluid-dynamics-based aeroelastic analysis and structural design optimization - a researcher’s perspective // Computer Methods in Applied Mechanics and Engineering. 2005. Vol. 194, no. 30. P. 3453-3471. Structural and Design Optimization
  60. Krist S., Biedron R., Rumsey C. CFL3D User’s Manual Version 5. 0: Tech. rep. Hampton, VA: NASA Langley Research Center, 1997. —Sep
  61. Cho H., Venturi D., Karniadakis G. Karhunen-Loeve expansion for multi-correlated stochastic processes // Probabilistic Engineering Mechanics. 2013. Vol. 34. P. 157-167
  62. Bendiksen O. Role of Shock Dynamics in Transonic Flutter // Proc. AIAA Dynamics Specialists Conference, Dallas, TX. No. AIAA-92-2121-CP. 1992. —Jan. 1
  63. Sapatnekar S. S. Overcoming Variations in Nanometer-Scale Technologies // IEEE J. Emerging and Selected Topics in Circuits and Systems. 2011. Vol. 1, no. 1. P. 5-18
  64. Hall K., Thomas J., Dowell E. Reduced-Order Modeling of Unsteady Small Disturbance Flows Using a Frequency-Domain Proper Orthogonal Decomposition Technique // Proc. 37th Aerospace Sciences Meeting and Exhibit. No. AIAA 99-0655. 1999. —Jan
  65. Dowell E. Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system // J. Sound and Vibration. 1982. Vol. 85. P. 333-344
  66. Thomas J., Dowell E., Hall K. Nonlinear Inviscid Aerodynamic Effects on Transonic Divergence, Flutter, and Limit-Cycle Oscillations // AIAA Journal. 2002. —April. Vol. 40, no. 4. P. 638-646
  67. Thomas J., Dowell E., Hall K., Denegri C. Modeling Limit Cycle Oscillation Behavior of the F-16 Fighter Using a Harmonic Balance Approach // Proc. 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference. Palm Springs, California, USA: 2004. —19 - 22 April
  68. Sheta E., Harrand V., Thompson D., Strganac T. Computational and experimental investigation of limit cycle oscillations of nonlinear aeroelastic systems // J. Aircraft. 2002. Vol. 39, no. 1. P. 133-141
  69. Dowell E., Thomas J., Hall K. Transonic limit cycle oscillation analysis using reduced order aerodynamic models // J. Fluids and Structures. 2004. Vol. 19, no. 1. P. 17-27
  70. Silva W. Identification of nonlinear aeroelastic systems based on the Volterra theory: Progress and opportunities // Nonlinear Dynamics. 2005. Vol. 39, no. 1-2. P. 25-62
  71. Beran P., Lucia D. A reduced order cyclic method for computation of limit cycles // Nonlinear Dynamics. 2005. Vol. 39, no. 1-2. P. 143-158
  72. Guo H., Chen Y. Supercritical and subcritical Hopf bifurcation and limit cycle oscillations of an airfoil with cubic nonlinearity in supersonic/hypersonic flow // Nonlinear Dyn. 2012. Vol. 67. P. 2637-2649
  73. Lee B., Price S., Wong Y. Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos // Progress in Aerospace Sciences. 1999. Vol. 35, no. 3. P. 205 - 334. URL: http://www.sciencedirect.com/ science/article/pii/S0376042198000153
  74. Patil M., Hodges D., Cesnik C. Nonlinear aeroelastic analysis of complete aircraft in subsonic flow // Journal of Aircraft. 2000. Vol. 37, no. 5. P. 753-760
  75. Goland M. The Flutter of a Uniform Cantilever Wing // J. Applied Mechanics. 1945. Vol. 12, no. 4. P. A197-A208
  76. Walker W. P. Unsteady Aerodynamics of Deformable Thin Airfoils. Master’s thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 2009. —August 5
  77. Walker W. P., Patil M. J. Unsteady Aerodynamics of Deformable Thin Airfoils // J. Aircraft. 2014. Vol. 51, no. 6
  78. Garrick I. Propulsion of a Flapping and Oscillating Airfoil: Tech. Rep. 567: National Advisory Committee for Aeronautics (NACA), 1936
  79. Theodorsen T., Garrick I. Flutter Calculations in Three Degrees of Freedom: Tech. Rep. 741: National Advisory Committee for Aeronautics, 1942. URL: https://ntrs.nasa.gov/search.jsp?R=19930090938
  80. Peters D. A., Hsieh M. -C. A., Torrero A. A state-space airloads theory for flexible airfoils // Annual Forum Proc. - AHS International. Vol. III. Phoenix, AZ, US: 2006. —May 9-11. P. 1806-1823
  81. Peters D. Two-dimensional incompressible unsteady airfoil theory - An overview // J. Fluids and Structures. 2008. Vol. 24, no. 3. P. 295-312
  82. Bigoni D., Noselli G. Experimental evidence of flutter and divergence instabilities induced by dry friction // J. Mechanics and Physics of Solids. 2011. Vol. 59, no. 10. P. 2208-2226
  83. Kuznetsov A. A., Matrosov A. A. [Conditions for the occurrence of wing flutter of the An-124-100 aircraft] Usloviya vozniknoveniya flattera kryla samoleta An-124-100 // [Young researcher of the Don] Molodoy issledovatel' Dona. 2016. Vol. XX, No. 1. P. 110-115. (In Russ. )
  84. Tauchert T. R. Large Plate Deflections, von K’arm’an Theory, Statical Problems // Encyclopedia of Thermal Stresses / Ed. by R. B. Hetnarski. Dordrecht: Springer Netherlands, 2014. P. 2697-2704. URL: https://doi.org/10.1007/978-94-007-2739-7_177
  85. Ghassemi A., Hassani M., Oveissi S. Comparison of nonlinear Von Karman and Cosserat theories in very large deformation of skew plates // Int. J. Adv. Struct. Eng. 2018. Vol. 10. P. 73-84
  86. Gordnier R. Computation of limit-cycle oscillations of a delta wing // J. Aircraft. 2003. Vol. 40, no. 6. P. 1206-1208
  87. Asjes D. C. Nonlinear analysis of a two- and three-degree-of-freedom aeroelastic system with rotational stiffness free-play: Ph. D. thesis / Iowa State University. 2015
  88. Prananta B. B., Kok J., Spekreijse S. et al. Simulation of limit cycle oscillation of fighter aircraft at moderate angle of attack // Int. Forum Aeroelasticity and Structural Dynamics, Amsterdam, The Netherlands. 2003. —4-6 June
  89. Attar P., Dowell E., Tang D. A theoretical and experimental investigation of the effects of a steady angle of attack on the nonlinear flutter of a delta wing plate model // J. Fluids and Structures. 2003. Vol. 17, no. 2. P. 243-259
  90. Bae J. -S., Inman D., Lee I. Effects of structural nonlinearity on subsonic aeroelastic characteristics of an aircraft wing with control surface // J. Fluids and Structures. 2004. Vol. 19, no. 6. P. 747-763
  91. Eversman W., Pitt D. M. Hybrid doublet lattice/doublet point method for lifting surfaces in subsonic flow // J. Aircraft. 1991. —Sep. Vol. 28, no. 9. P. 572-578
  92. Liu J., Chen F., Chen Y. Bifurcation analysis of aeroelastic systems with hysteresis by incremental harmonic balance method // Applied Mathematics and Computation. 2012. Vol. 219, no. 5. P. 2398-2411. URL: http://www.sciencedirect.com /science/ article/pii/ S0096300312008272
  93. Raghothama A., Narayanan S. Non-linear dynamics of a two-dimensional airfoil by incremental harmonic balance method //J. Sound Vibration. 1999. Vol. 226, no. 3. P. 493- 517. URL: http://www.sciencedirect.com/science/article/pii/S0022460X99922605
  94. Chen Y., Liu J., Meng G. Incremental harmonic balance method for nonlinear flutter of an airfoil with uncertain-but-bounded parameters // Applied Mathematical Modelling. 2012. Vol. 36, no. 2. P. 657 - 667. URL: http://www.sciencedirect.com/science/ article/pii/ S0307904X11003969
  95. Zhang W., Wang B., Ye Z., Quan J. Efficient Method for Limit Cycle Flutter Analysis Based on Nonlinear Aerodynamic Reduced-Order Models // AIAA Journal. 2012. —May. Vol. 50, no. 5. P. 1019-1028
  96. Dietz G., Schewe G., Mai H. Experiments on heave/pitch limit-cycle oscillations of a supercritical airfoil close to the transonic dip // J. Fluids and Structures. 2004. Vol. 19, no. 1. P. 1-16
  97. Farmer M., Hanson P. Comparison of Supercritical and Conventional Wing Flutter Characteristics // Proc. 17th Structures, Structural Dynamics, and Materials Conf., King of Prussia, U. S. A. 1976. —05 - 07 May
  98. Dimitriadis G. Continuation of higher-order harmonic balance solutions for nonlinear aeroelastic systems // J. Aircraft. 2008. Vol. 45, no. 2. P. 523-537
  99. Bykov A. V., Smyslov V. I. [On the use of experimental data in the calculation of the flutter of unmanned maneuverable aircraft] Ob ispol'zovanii eksperimental'nykh dannykh v raschete na flatter bespilotnykh manevrennykh letatel'nykh apparatov // [TsAGI scientific notes] Uchenye zapiski TsAGI. 2008. Vol. XXXIX, No. 4. P. 91-100. (In Russ. )
  100. Vedeneev V. V. Panel flutter at low supersonic speeds // J. Fluids and Structures. 2012. Vol. 29. P. 79-96
  101. Kulikov A. N. [Nonlinear panel flutter. Resonances of natural frequencies - one of the possible reasons for the hard excitation of oscillations] Nelineynyy panel'nyy flatter. Rezonansy sobstvennykh chastot - odna iz vozmozhnykh prichin zhestkogo vozbuzhdeniya kolebaniy // Vestn. Nizhny Novgorod University named after N. I. Lobachevsky. General and applied mechanics. 2011. No. 4 (2). P. 193-194. (In Russ. )
  102. Bykov A. V. [Means of computational and experimental studies of aeroelastic stability of highly maneuverable missiles] Sredstva raschetno-eksperimental'nykh issledovaniy aerouprugoy ustoychivosti vysokomanevrennykh raket // Bulletin of the Moscow Aviation Institute. 2012. T. 19, No. 1. P. 65-74. (In Russ. )
  103. Zhang S. -J., Wen G. -L., Peng F., Liu Z. -Q. Analysis of limit cycle oscillations of a typical airfoil section with freeplay // Acta Mechanica Sinica. 2013. Vol. 29, no. 4. P. 583-592
  104. Narizhny A. G., Smyslov V. I., Sychev S. I. [Investigation of aeroelastic stability of a cruciform aircraft] Issledovaniye aerouprugoy ustoychivosti letatel'nogo apparata krestoobraznoy skhemy // Uchenye zapiski TsAGI. 2013. T. XLIV, No. 6. P. 116-134
  105. Winter M., Breitsamter C. Reduced-Order Modeling of Unsteady Aerodynamic Loads Using Radial Basis Function Neural Networks // Proc. Deutscher Luft- und Raumfahrtkongress (DLRK). 2014. —Sep. P. 1-10. Doc. ID: 340013
  106. Reimer L., Boucke A., Ballmann J., Behr M. Computational Analysis of High Reynolds Number Aero-Structural Dynamics (HIRENASD) Experiments // Proc. Int. Forum on Aeroelasticity and Structural Dynamics (IFASD 2009), Stockholm, Sweden. 2009. Art. # IFASD-2009-130
  107. Winter M., Breitsamter C. Nonlinear reduced-order modeling of unsteady aerodynamic loads based on dynamic local linear neuro-fuzzy models // Proc. Int. Forum on Aeroelasticity and Structural Dynamics 2015, Saint Petersburg, Russia. 2015. —June 28 - July 02. P. 1-20. Art. # IFASD-2015-82
  108. Cavallaro R., Bombardieri R., Demasi L., Iannelli A. PrandtlPlane Joined Wing: Body freedom flutter, limit cycle oscillation and freeplay studies // J. Fluids and Structures. 2015. Vol. 59. P. 57 - 84. URL: http://www.sciencedirect.com/science/ article/pii/S0889974615002157
  109. Cavallaro R., Bombardieri R., Silvani S. et al. Aeroelasticity of the PrandtlPlane: Body Freedom Flutter, Freeplay, and Limit Cycle Oscillation // Variational Analysis and Aerospace Engineering / Ed. by A. Frediani, B. Mohammadi, O. Pironneau, V. Cipolla. Springer Int. Publishing, 2016. Springer Optimization and Its Applications. P. 65-94
  110. Tian W., Yang Z., Gu Y., Wang X. Analysis of nonlinear aeroelastic characteristics of a trapezoidal wing in hypersonic flow // Nonlinear Dynamics. 2017. —Apr. P. 1205-1232
  111. Leissa A. The historical bases of the Rayleigh and Ritz methods // J. Sound and Vibration. 2005. Vol. 287, no. 4. P. 961 - 978. URL: http://www.sciencedirect.com/science/ article/pii/S0022460X05000362
  112. Cao X., Taylor N. A fundamental study of the aeroelastic behaviors of vehicles in hypersonic range // Proc. 16th AIAA/DLR/DGLR Int. Space Planes and Hypersonic Systems and Technologies Conf. 2009. URL: https://arc.aiaa.org/doi/abs/10.2514/6.2009-7398
  113. Niu Y., Wang Z., Wang D., Liu B. Modified Homotopy Analysis Method for Nonlinear Aeroelastic Behavior of Two Degree-of-Freedom Airfoils // Int. J. Structural Stability and Dynamics. 2016. Vol. 16, no. 9
  114. Bartels R. E., Funk C. J., Scott R. C. Limit-Cycle Oscillation of the Subsonic Ultra-Green Aircraft Research Truss-Braced Wing Aeroelastic Model // J. Aircraft. 2017. Vol. 54, no. 5. P. 1605-1613
  115. Denegri Jr. C. Limit cycle oscillation flight test results of a fighter with external stores // J. Aircraft. 2000. Vol. 37, no. 5. P. 761-769
  116. Nabiullin EN [Method for calculating unsteady aerodynamic loads on a thin wing of finite aspect ratio, performing elastic harmonic oscillations in a subsonic flow] Metod rascheta nestatsionarnykh aerodinamicheskikh nagruzok na tonkoye krylo konechnogo udlineniya, sovershayushcheye uprugiye garmonicheskiye kolebaniya v dozvukovom potoke // Uchenye zapiski TsAGI. 1972. Vol. III, No. 6. P. 94-100. (In Russ. )
  117. Nabiullin EN, Rybakov AA [On the determination of generalized aerodynamic forces based on flutter in a subsonic flow at low Strouhal numbers] Ob opredelenii obobshchennykh aerodinamicheskikh sil v raschete na flatter v dozvukovom potoke pri malykh chislakh Strukhalya // Uchenye zapiski TsAGI. 1974. T. V, No. 5. P. 111-113. (In Russ. )
  118. Bunkov VG [The complete problem of eigenvalues of matrices in calculations for flutter] Polnaya problema sobstvennykh znacheniy matrits v raschetakh na flatter // Uchenye zapiski TsAGI. 1975. Vol. VI, No. 2. P. 82-92. (In Russ. )
  119. Baranov NI, Komapov AI, Makhlin IM, Ponomarev Yu. V., Strelkov SP [On the influence of wing attachment stiffness on the stability of aeroelastic vibrations] O vliyanii zhestkosti krepleniya kryla na ustoychivost' aerouprugikh kolebaniy // Uchenye zapiski TsAGI. 1975. Vol. VI, No. 6. P. 82-88. (In Russ. )
  120. Bulychev GA [Some criteria and formulas for the analysis of flexural-torsional flutter] Nekotoryye kriterii i formuly dlya analiza izgibno-krutil'nogo flattera // Uchenye zapiski TsAGI. 1984. T. XV, No. 3. P. 143-150. (In Russ. )
  121. Bulychev GA [On the possibility of analyzing various forms of flutter on one dynamic model] O vozmozhnosti analiza razlichnykh form flattera na odnoy dinamicheskoy modeli // Uchenye zapiski TsAGI. 1986. T. XVII, No. 3. P. 126-132. (In Russ. )
  122. Ishmuratov FZ, Kuzmina SI, Mosunov VA [Computational studies of transonic flutter] Raschetnyye issledovaniya transzvukovogo flattera // Uchenye zapiski TsAGI. 1999. T. XX, No. 3-4. P. 151-163. (In Russ. )
  123. Atassi H. Unsteady Two-Dimensional Thin Airfoil Theory // Unsteady Aerodyanmics and Aeroacoustics, AME 90934. Aerospace and Mechanical Engineering, University of Notre Dame. Teaching Notes. P. 1-23. URL: https://www3.nd.edu/~atassi/Teaching/Unsteady \_Aero\_AME\_90934\_f2010/Notes/uthin111101. pdf
  124. Kuzmin VP, Kuzmina SI, Mosunov VA [Determination of aerodynamic forces acting in a supersonic flow on oscillating bearing surfaces located in different planes] Opredeleniye aerodinamicheskikh sil, deystvuyushchikh v sverkhzvukovom potoke na koleblyushchiyesya nesushchiye poverkhnosti, raspolozhennyye v raznykh ploskostyakh // Uchenye zapiski TsAGI. 2000. Vol. XXXI, No. 1-2. P. 92-110
  125. Lyschinsky V. V., Rybakov A. A. [Application of similarity transformations in parametric studies of flutter] Primeneniye preobrazovaniy podobiya pri parametricheskikh issledovaniyakh flattera // Uchenye zapiski TsAGI. 2009. Vol. XL, No. 4. P. 71-77
  126. Tang D., Dowell E. Effects of angle of attack on nonlinear flutter of a delta wing // AIAA journal. 2001. Vol. 39, no. 1. P. 15-21
  127. Bunton R. W., Jr. C. M. D. Limit Cycle Oscillation Characteristics of Fighter Aircraft // J. Aircraft. 2000. —Sep. Vol. 37, no. 5. P. 916-918
  128. Chuban V. D. [Method for calculating the flutter of the T-shaped tail, taking into account the influence of the angle of attack and the angle of installation of the stabilizer on the critical parameters of the flutter] Metod rascheta flattera T-obraznogo opereniya, uchityvayushchiy vliyaniye ugla ataki i ugla ustanovki stabilizatora na kriticheskiye parametry flattera // Uchenye zapiski TsAGI. 2004. Vol. XXXV, No. 3-4. P. 90-99. (In Russ. )
  129. Lyschinsky V. V., Mosunov V. A., Rybakov A. A. [Method for solving multiparameter problems of aeroelasticity based on the theory of similarity] Metod resheniya mnogoparametricheskikh zadach aerouprugosti na osnove teorii podobiya // Uchenye zapiski TsAGI. 2011. Vol. XLII, No. 4. P. 84-92. (In Russ. )
  130. Bykov A. V., Smyslov V. I. [The problem of flutter of a maneuverable aircraft taking into account its oscillations in two planes] Zadacha o flattere manevrennogo letatel'nogo apparata s uchetom yego kolebaniy v dvukh ploskostyakh // Uchenye zapiski TsAGI. 2011. Vol. XLII, No. 3. P. 92-100. (In Russ. )
  131. Ovchinnikov V. V., Popov V. M., Filimonov S. V. [Application of the extended hypothesis of harmony for calculating the flutter characteristics of an aircraft] Primeneniye rasshirennoy gipotezy garmonichnosti dlya rascheta flatternykh kharakteristik samoleta // Scientific Bulletin of MSTU GA. 2013. Vol. XLIV, No. 9 (195). P. 93-100. (In Russ. )
  132. Strganac T., Ko J., Thompson D., Kurdila A. Identification and control of limit cycle oscillations in aeroelastic systems // Proc. 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit. 1999. AIAA Paper No. 99-1463
  133. Ko J., Strganac T., Kurdila A. Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Nonlinearity // Nonlinear Dynamics. 1999. —March. Vol. 18, no. 3. P. 289-301
  134. Gilliatt H., Straganac T., Kurdilla A. An investigation of internal resonance in aeroelastic systems // Nonlinear Dynamics. 2003. Vol. 31. P. 1-22
  135. Leonov G., Kuznetsov N. Hidden attractors in dynamical systems: From hidden oscillations in hilbert-kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in chua circuits // Intern. J. Bifurcation and Chaos. 2013. Vol. 23, no. 1
  136. Kuznetsov N., Leonov G. Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors // IFAC Proceedings Volumes. 2014. Vol. 47. P. 5445-5454. (survey lecture, 19th IFAC World Congress)
  137. Kuznetsov N., Lobachev M., Yuldashev M. et al. The birth of the global stability theory and the theory of hidden oscillations // 2020 European Control Conference Proceedings. 2020. P. 769-774
  138. Leonov G. A., Kuznetsov N. V., Vagaitsev V. I. Hidden attractor in smooth Chua systems // Physica D. 2012. Vol. 241, no. 18. P. 1482-1486
  139. V. O. Bragin, V. I. Vagaitsev, N. V. Kuznetsov, G. A. Leonov, Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua’s Circuits, Journal of Computer and Systems Sciences International, 50(4), 2011, pp. 511-543 (doi:10. 1134/S106423071104006X)
  140. Leonov G. A., Kuznetsov N. V., Vagaitsev V. I. Localization of hidden Chua’s attractors // Physics Letters A. 2011. Vol. 375, no. 23. P. 2230-2233
  141. Kuznetsov N. Theory of hidden oscillations and stability of control systems // Journal of Computer and Systems Sciences International. 2020. Vol. 59, no. 5. P. 647-668
  142. Leonov G., Kuznetsov N., Yuldashev M., Yuldashev R. Hold-in, pullin, and lock-in ranges of PLL circuits: rigorous mathematical definitions and limitations of classical theory // IEEE Trans. Circuits Syst. I. 2015. Vol. 62, no. 10. P. 2454-2464
  143. Dudkowski D., Jafari S., Kapitaniak T. et al. Hidden attractors in dynamical systems // Physics Reports. 2016. Vol. 637. P. 1 - 50. URL: http://www.sciencedirect.com/science/ article/pii/S0370157316300928
  144. Kiseleva M., Kuznetsov N., Leonov G. Hidden and self-excited attractors in electromechanical systems with and without equilibria // IFACPapersOnLine. 2016. —01. Vol. 49
  145. Kuznetsov N., Kuznetsova O., Leonov G., Vagaitsev V. Hidden attractor in Chua’s circuits // Proc. 8th Int. Conf. Informatics in Control, Automation and Robotics (ICINCO 2011). Vol. 1. 2011. —01. P. 279-283
  146. Singh J., Lochan K., Kuznetsov N., Roy B. Coexistence of single- and multi-scroll chaotic orbits in a single-link flexible joint robot manipulator with stable spiral and index-4 spiral repellor types of equilibria //Nonlinear Dynamics. 2017. —10. Vol. 90. P. 1-23
  147. Glyzin SD, Kolesov A. Yu., Rozov N. Kh. [On a mechanism of rigid excitation of oscillations in nonlinear flutter systems] Ob odnom mekhanizme zhestkogo vozbuzhdeniya kolebaniy v nelineynykh flatternykh sistemakh // [Model. and analysis of inform. Systems] Model. i analiz inform. sistem. 2014. Vol. 21, No. 1. P. 32-44. (In Russ. )
  148. Morgunov S. V. [Frequency approach to the analysis of flutter and its use in computational and experimental studies] Chastotnyy podkhod k analizu flattera i yego ispol'zovaniye pri raschetno-eksperimental'nykh issledovaniyakh// Uchenye zapiski TsAGI. 2014. T. XLV, No. 1. P. 113-118. (In Russ. )
  149. Dulina N. G. [Investigation of the influence of the parameters of the configuration of the wing with engines on the value of the critical flutter speed] Issledovaniye vliyaniya parametrov komponovki kryla s dvigatelyami na velichinu kriticheskoy skorosti flattera // Uchenye zapiski TsAGI. 1979. Vol. X, No. 6. P. 90-98. (In Russ. )
  150. Bichiou Y., Hajj M., Nayfeh A. Effectiveness of a nonlinear energy sink in the control of an aeroelastic system // Nonlinear Dynamics. 2016. Vol. 86, no. 4. P. 2161-2177
  151. Habib G., Kerschen G. Passive flutter suppression using a nonlinear tuned vibration absorber // Proc. 33rd IMAC Conference and Exposition on Structural Dynamics. Vol. 1 of Conf. Proc. Society for Experimental Mechanics Series. 2016. —2-5 Feb. P. 133-144
  152. Denegri J., C. M., Sharma V., Northington J. F-16 limit-cycle oscillation analysis using nonlinear damping // J. Aircraft. 2016. Vol. 53, no. 1. P. 243-250
  153. Edwards J. Unsteady Aerodynamic Modeling and Active Aeroelastic Control. Department of Aeronautics and Astronautics, Stanford University., 1977. URL: https://books.google.ru/books?id=dNYDAAAAIAAJ
  154. Ko J., Strganac T., Junkins J. et al. Structured Model Reference Adaptive Control for a Wing Section with Structural Nonlinearity // J. Vibration and Control. 2002. —July. Vol. 8, no. 5. P. 553-573
  155. Li D., Guo S., Xiang J. Aeroelastic Dynamic Response and Control of an Airfoil Section with Control Surface Nonlinearities // J. Sound and Vibration. 2010. —Oct. Vol. 329, no. 22. P. 4756-4771
  156. Piovanelli F., Paoletti P., Innocenti G. Enhanced nonlinear model and control design for a flexible wing // European Control Conference (ECC 2016). Aalborg, Denmark: EUCA, 2016. —June 29 - July 1. P. 80-85
  157. Wei X., Mottershead J. E. Robust passivity-based continuous sliding-mode control for under-actuated nonlinear wing sections // Aerospace Science and Technology. 2017. Vol. 60. P. 9 - 19
  158. Fazelzadeh S., Azadi M., Azadi E. Suppression of nonlinear aeroelastic vibration of a wing/store under gust effects using an adaptive-robust controller // J. Vibration and Control. 2017. Vol. 23, no. 7. P. 1206-1217
  159. Andrievsky B., Kudryashova E., Kuznetsov N. et al. Simple adaptive control for airfoil flutter suppression // Mathematics in Engineering, Science and Aerospace. 2018. Vol. 9, no. 1. P. 5-20
  160. Andrievsky B., Kudryashova E., Kuznetsov N. et al. Hidden nonlinear oscillations in aircraft stabilization system with restrictions at the actuator control // AIP Conference Proceedings. Vol. 2046. 2018
  161. Andrievsky B., Kuznetsov N., Kuznetsova O. Hidden Nonlinear Oscillations in Controlled Aircraft with Saturated Inputs // Proc. 2018 15th International Conference on Control, Automation, Robotics and Vision, ICARCV 2018. 2018. P. 704-709
  162. Andrievsky B., Kudryashova E., Kuznetsov N. et al. Hidden oscillations in an active flutter suppression system and flight of a manned aircraft // Mathematics in Engineering, Science and Aerospace. 2019. Vol. 10, no. 3. P. 357-371
  163. Leonov G. A., Kuznetsov N. V. On the Keldysh problem of flutter suppression // AIP Conference Proceedings. 2018. Vol. 1959, no. 1. P. 020002. URL: https://aip.scitation.org/doi/pdf/10.1063/1.5034578
  164. Keldysh M. V. [On dampers with a nonlinear characteristic] O dempferakh s nelineynoy kharakteristikoy // Proceedings of TsAGI. 1944. Vol. 557. P. 26-37. (In Russ. )
  165. Sutherland A. A Demonstration of Pitch-Plunge Flutter Suppression using LQG Control // Proc. 27th Congress of the International Council of the Aeronautical Sciences (ICAS 2010), Nice, France. 2010
  166. Sutherland A. A Small Scale Pitch-Plunge Flutter Model for Active Flutter Control Research // Proc. 26th Congress of the International Council of the Aeronautical Sciences (ICAS 2008), Anchorage, Alaska. 2008
  167. Rodden W. P., Stahl B. A strip method for prediction of damping in subsonic wind tunnel andflight flutter tests. // J. Aircraft. 1969. Vol. 6, no. 1. P. 9-17. URL: https://doi.org/10.2514/3.43994
  168. Kiseleva M., Kondratyeva N., Kuznetsov N. et al. Hidden periodic oscillations in drilling system driven by induction motor // IFAC Proceedings Volumes. 2014. Vol. 47, no. 19. P. 5872-5877
  169. Leonov G. A., Kuznetsov N. V., Mokaev T. N. Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion // The European Physical Journal Special Topics. 2015. Vol. 224, no. 8. P. 1421-1458
  170. Tantaroudas N. D., Da Ronch A., Gai G., Badcock K. J. An Adaptive Aeroelastic Control Approach using Non Linear Reduced Order Models // Proc. 14th AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, GA, 16-20 June 2014. 2014. P. 1-21. AIAA 2014-2590
  171. Wang Y., Wynn A., Palacios R. Robust Aeroelastic Control of Very Flexible Wings using Intrisic Models // Proc. 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Boston, Massachusetts. 2013. —08-11 Apr. AIAA 2013-1485
  172. Yucelen T., Calise A. J. Derivative-Free Model Reference Adaptive Control of a Generic Transport Model // Proc. AIAA Guidance, Navigation, and Control Conference, Toronto, Ontario, Canada. AIAA, 2010. —August 02-05. P. 1-17
  173. Da Ronch A., Badcock K. J., Wang Y. et al. Nonlinear Model Reduction for Flexible Aircraft Control Design // Proc. AIAA Atmospheric Flight Mechanics Conference, Minneapolis, MN. 2012. —13-16 August. AIAA Paper 2012-4404
  174. Strganac T., Ko J., Thompson D., Kurdila A. Identification and control of limit cycle oscillations in aeroelastic systems // Journal of Guidance, Control, and Dynamics. 2000. Vol. 23, no. 6. P. 1127-1133
  175. Petrov B. N., Rutkovsky V. Yu., Krutova I. N., Zemlyakov S. D. [Principles of construction and design of self-adjusting control systems] Printsipy postroyeniya i proyektirovaniya samonastraivayushchikhsya sistem upravleniya. Moscow: Mashinostroyeniye, 1972. (In Russ. )
  176. Landau Y. D. Adaptive control: The model reference approach. New York: Marcel Dekker, 1979
  177. Khalil H. K. Nonlinear Systems. New York: Macmillan, 1992
  178. Fradkov A. L. Synthesis of an adaptive system for linear plant stabilization // Autom. Remote Control. 1974. Vol. 35, no. 12. P. 1960-1966
  179. Andrievskii B. R., Fradkov A. L. Method of Passification in Adaptive Control, Estimation, and Synchronization // Autom. Remote Control. 2006. Vol. 67, no. 11. P. 1699-1731
  180. Andrievskii B., Selivanov A. New Results on the Application of the Passification Method. A Survey // Automation and Remote Control. 2018. Vol. 79, no. 6. P. 957-995
  181. Andrievsky B., Selivanov A. Historical Overview of the Passification Method and its Applications to Nonlinear and Adaptive Control Problems // Proc. European Control Conference 2020, ECC 2020. 2020. P. 791-794

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