Yuri V. Mikhlin

MikhlinYuri V. Mikhlin,

DSc, Professor.

 NTU KhPI, 2 Kyrpychova Str., Department of Applied Mathematics, educational building U-2, app. 404

 +38057 707-67-94

  muv@kpi.kharkov.ua, Yuri_Mikhlin@mail.ru

 Scientific interests in Mechanics and Applied Mathematics.

Born 21.09.1947 in Dnepropetrovsk.

• 1988 Doctor of Science (Physics & Mathematics) from Moscow Institute for Problems in Mechanics, Russian Academy of Sciences. Thesis “Normal vibrations of the nonlinear finite-dimensional systems”
• 1974 PhD (Physics & Mathematics) from Dnepropetrovsk State University
• 1970 Graduated from the Mechanics & Mathematics Faculty of the Dnepropetrovsk State University summa cum laude in Dynamics and Strength of Machine Tools


  • 1995 – at present: National Technical University “Kharkiv Polytechnic Institute” (Professor at the Applied Mathematics Department).
  • 1989-1995: Dnepropetrovsk State University (Professor).
  • 1976-1989: Dnepropetrovsk Civil Engineering Institute (Docent in Mathematics, Researcher in Mechanics).
  • 1970-1976: Dnepropetrovsk Automation in Metallurgy Institute (Engineer and Researcher in Mechanics and Control).


Nonlinear vibrations, Asymptotic methods in applied mathematics, Nonlinear oscillations and stability of motion, Ordinary differential equations, Application of the group theory in ODE, Differential geometry, Complex variable functions, Variational calculus, Mathematical modeling and other courses


About 48 years of experience in Nonlinear Dynamics and Applied Mathematics.
The main scientific results in: Theory of nonlinear normal vibration modes; Analysis of the nonlinear vibrations stability; Asymptotic methods; Nonlinear Dynamics of elastic systems.
Current research focuses on: Nonlinear normal mode theory; Resonance dynamics of dissipative systems; Nonlinear dynamics of the systems with limited power supply, Nonlinear dynamics of elastic systems, Vibro-absorption problems; Transient and localization problems, Nonlinear waves et al.
Supervisor for one Dr. Sci. Thesis and five PhD theses.


  • Memberships in Editorial Board in journals “Nonlinear Dynamics”, “Mathematical Problems in Engineering” and “Proceedings of the Institution of Mechanical Engineers, Part C:  Journal of Mechanical Engineering Science”.
  • Organizer and Chairman of the Sci. Committees of the International Conferences on Nonlinear Dynamics at the National Technical University “Kharkiv Polytechnic Institute” (2004, 2007, 2010, 2013 and 2016) with participation of scientists from Australia, Brazil, Canada, Germany, Italy, Japan, Korea, Poland, Portuguese, Russia, Serbia, Ukraine, UK, USA, and other countries.
  • Organizer and Chair of Mini-symposia in framework of ENOC (European Nonlinear Oscillations Conferences) in S-Petersberg, 2008, Roma, 2011, Vienna, 2014, Budapest, 2017. Memberships in Scientific Committees of Int. conferences in Belgium, Canada, France, Greece, Italy, Poland, Ukraine, UK et al.
  • Memberships in AMS, GAMM, EUROMECH.
  • Visits to: Mathematical Institute, Beograd, Serbia, 2017, Technion, Haifa, Israel, 2015, University UNESP-Rio Claro, SP, Brazil, 2012; Glasgow University, UK, 2008; Aberdeen University, UK, 2008; Michigan University at Ann Arbor, USA, 2005;  ENTPE, Lion, France, 2003;  Modena University, Italy, 2001;  Technical University, Vienna, Austria, 2000 et al.
  • Participation at the Int. conferences in Austria, Belgium, France, Germany, Greece, Israel, Italy, Netherlands, Russia, UK et al. Organizer of Mini-Symposiums at the European Nonlinear Oscillation Conferences (Sankt-Petersberg, 2008; Rome, 2011)

Number of publications: more than 240 papers in refereed journals and communications to scientific meetings. Number of books: 7 (with co-authors)

Guest Editor of Special Issues in Journal of Sound and Vibration (2009), Mathematical Problems in Engineering (2010), Proceedings of the Institution of Mechanical Engineers. Journal of Mechanical Engineering Science (2016), Int. Journal of Nonlinear Mechanics (2017).

H-index=19 by Google Scholar Citation.


  1. Yuri V Mikhlin, Matthew P Cartmell and Jerzy Warminski. Special Issue on Nonlinear Dynamics. Proceedings of the Institution of Mechanical Engineers, Journal of Mechanical Engineering Science, 230(1), 2016. 3–4.
  2. «Nonlinear Dynamics of Elastic Systems. Volume 2. Applications», Moscow-Izhevsk: IKI, 2015, 700 p. (К.V. Аvramov, Yu.V. Mikhlin)
  3. «Nonlinear Dynamics of Elastic Systems. Volume 1. Models, Methods, Phenomena» (Second Edition), Moscow-Izhevsk: IKI, 2015, 716 p. (К.V. Аvramov, Yu.V. Mikhlin)
  4. K.Y. Plaksiy, Yu.V. Mikhlin. Dynamics of nonlinear dissipative systems in the vicinity of resonance. Journal of Sound and Vibration, 334, 2015, 319-337.
  5. K.Y. Plaksiy, Yu.V. Mikhlin. Resonance behavior of the limited power-supply systemc oupled with the nonlinear absorber, Mathematics in Engineering, Science and Aerospace, 6 (3), 2015, 475-495.
  6. K.V. Avramov, Yu.V. Mikhlin. Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems. Applied Mechanics Review, 65(2), 2013 (20 pages).
  7. N.V. Perepelkin, Yu.V.  Mikhlin,  C. Pierre. Non-linear normal forced vibration modes in systems with internal resonance. Int. Journal of Non-Linear Mechanics, 57, 2013, 102–115.
  8. Yuri V. Mikhlin. Two formulations of nonlinear normal vibration modes and their applications. IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design, Aberdeen, UK, 2010 (eds. M.Wiercigroch, G. Rega). Springer, 2013, 31-45.
  9. A.A. Klimenko, Y.V. Mikhlin, J. Awrejcewicz. Nonlinear normal modes in pendulum systems.  Nonlinear Dynamics, 70 (1), 2012, 797-813.
  10. Yu.V. Mikhlin, N.V. Perepelkin, A.A. Klimenko and E. Harutyunyan. Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems. Journal of Physics: Conference Series, 382, 2012, Conference 1.
  11. Y.V. Mikhlin, N.V. Perepelkin. Nonlinear normal modes and their applications in mechanical systems. Proc. of the Institution of Mechanical Engineers, Part C: J. of Mechanical Engineering Science, 2011, 225 (10), 2369-2384.
  12. «Nonlinear Dynamics of Elastic Systems. Volume 1. Models, Methods, Phenomena», Moscow-Izhevsk: Regular and Chaotic Dynamics», 2010, 704 p. (К.V. Аvramov, Yu.V. Mikhlin).
  13. Yu.V. Mikhlin, K.V. Avramov. Nonlinear normal modes for vibrating mechanical systems. Review of Theoretical Developments. Applied Mechanics Review, 63 (6), 2010 (21 pages)
  14. Yu.V. Mikhlin, S.G. Mitrokhin. Nonlinear oscillatory processes in vehicles. Int. Applied Mechanics, 11, 2010, 115-123
  15. I.D. Breslavsky, K.V. Avramov, Yu.V. Mikhlin, R. Kochurov. Nonlinear modes of snap-through motions of shallow arch. J. of Sound and Vibrations, 311, 2008, P. 297-313
  16. Kozmin, Yu. Mikhlin, C. Pierre. Transient in a two-DOF nonlinear system. Nonlinear Dynamics, 51 (1-2), 2008, 141-154
  17. K.Avramov, Yu.Mikhlin, E.Kurilov. Asymptotic analysis of nonlinear dynamics of simply supported cylindrical shells. Nonlinear Dynamics, 47, 2007, 331-352
  18. K.Avramov, Yu.Mikhlin. Snap-through truss as absorber of forced oscillations. Journal of Sound and Vibration, 290, 2006, 705-722
  19. Yu.V. Mikhlin, G.V. Manucharyan. Determination of the chaos onset in mechanical systems with several equilibrium positions. Meccanica, 2006, 41, 253-267.
  20. Yu.Mikhlin, S.Reshetnikova. Dynamical interaction of an elastic system and essentially nonlinear absorber. Journal of Sound and Vibration, 283, 2005, 91-120
  21. V. Avramov and Yu. V. Mikhlin. Snap-through truss as a vibration absorber. Journal of Vibration and Control, 10, 2004, 291-308.
  22. Yu.Mikhlin, T.Shmatko and G.Manucharyan. Lyapunov definition and stability of regular or chaotic vibration modes. Computers and Structures, 82, 2004, 2733-2742
  23. G.V. Manucharyan and Yu. V. Mikhlin. Construction of homo- and heteroclinic trajectories in nonlinear systems. Applied Mathematics and Mechanics (PMM), V. 68, N 6, 2004, 958-968 (in Russian).
  24. Yu. Mikhlin and G. Manucharyan. Construction of homoclinic and heteroclinic trajectories in mechanical systems with several equilibrium positions. Chaos, Solitons & Fractals, 16, 2003, 299-309
  25. Yu. Mikhlin, B. Morgunov. Normal vibrations in near-conservative self-excited viscoelastic nonlinear systems. Nonlinear Dynamics 25, 2001, 33-48
  26. Yu.V. Mikhlin and A.M.Volok. Solitary transversal waves and vibro-impact motions in infinite chains and rods. Int. J. of Solids and Structure, N12, 1999, 3403-3420.
  27. Yu.V. Mikhlin, A.F. Vakakis and G. Salenger. Direct and inverse problems encountered in vibro-impact oscillations of a discrete system. J. of Sound and Vibration, 216(2), 1998, 227-250.
  28. Yu.V. Mikhlin and A.L. Zhupiev. An application of the Ince algebraization to the stability of non-linear normal vibration modes. Int. J. of Nonlinear Mechanics, 1997, 32(1), 493-509.
  29. «Normal Modes and Localization in Nonlinear Systems, New York, издательство Wiley, 1996, 552 p. (A.Vakakis, L.Manevitch, Yu.Mikhlin, V.Pilipchuk, A.Zevin)
  30. Yu.V. Mikhlin. Normal vibrations of a general class of conservative oscillators. Nonlinear Dynamics, 1996, 11(1) ,1-16.
  31. Yu.V. Mikhlin. Matching of local expansions in the theory of non-linear vibrations. J. of Sound and Vibration, 1995, 182(4), 577-588.
  32. «Method of Normal Vibrations for Essentially Nonlinear Systems», Moscow, Nauka, 1989, 216 p. (L.I. Manevitch, Yu.V. Mikhlin, V.N. Pilipchuk)
  33. Yu.V. Mikhlin. Resonance modes of near-conservative nonlinear systems, Applied Mathematics and Mechanics (PMM USSR) 1974, 425-429 (in Russian).
  34. A.L. Zhupiev and Yu.V. Mikhlin. Stability and bifurcations of normal modes of nonlinear systems, Applied Mathematics and Mechanics (PMM USSR), 45 (3), 450-455, 1981 (in Russian).
  35. L.I. Manevitch and Yu.V. Mikhlin. On periodic solutions close to rectilinear vibration modes, Applied Mathematics and Mechanics (PMM USSR) 1972, 988-994 (in Russian).