#11 Department of Nonlinear Mechanics and Mathematical Modeling

Head of Department

Corresponding Member of the National Academy of Sciences of Ukraine, Doctor of Technical Sciences, Professor

Kostiantyn V. Avramov

E-mail: kvavramov@gmail.com

Deputy Head of Department


Doctor of Technical Sciences, Principal Scientist

Maryna V. Chernobryvko

full-time personnel:

Oleg F. Polischuk – Candidate of Technical Sciences, Senior Scientific Researcher
Boris V. Uspensky – Candidate of Technical Sciences, Senior Research Scientist
Iryna V. Biblik – Principal Engineer-Researcher
Ivan S. Tertyshnyi – Engineer

Yurii G. Stoyan – Chief Researcher, Corresponding Member of the National Academy of Sciences of Ukraine
Tetiana Ye. Romanova – Doctor of Technical Sciences, Principal Scientist, Professor
Mykola I. Gil – Doctor of Technical Sciences, Principal Scientist
Oleksandr V. Pankratov – Doctor of Technical Sciences, Principal Scientist
Volodymyr M. Patsuk – Candidate of Technical Sciences, Senior Scientific Researcher
Georgii M. Yaskov – Doctor of Technical Sciences, Senior Scientific Researcher


The department was created in 1972 by the Doctor of Technical Sciences, Professor Oleksandr Ye. Bozhko, provided with highly skilled personnel.

The results of the fundamental and applied research of the department are reflected in 17 monographs, more than 730 articles, as well as in 255 patents for inventions. The developments are implemented in power machine building, engine construction, aviation and space industries.

Main scientific trends of research

  • Nonlinear dynamics of constructions and machines
  • Nonlinear dynamics of thin-walled structures
  • Dynamics and durability of rocket carrier elements
  • Acoustics and aerodynamics of rocket carriers
  • Dynamic strength of nodes and components of armored vehicles
  • Experimental analysis of dynamic strength of machine elements
  • Fatigue testing of machine nodes
  • Dynamics and strength of turbomachines
  • Non-stationary mechanical processes
  • Mechanics of Nanoconstructions
  • Dynamics of structures with damages

Directions of fundamental research

  • Estimation of reliability of power equipment at fatigue damage of its elements
  • Analysis and improvement of dynamic strength properties of promising power machines elements and rocket-space technology under the influence of loads of different physical nature
  • Development of methods of materials surface treatment for increasing the reliability of power equipment elements
  • Dynamic strength of elements of aerospace and armored vehicles under the influence of mechanical loads
  • Development of means for reducing the vibrational tensile strength of the titanium alloy blades with erosion damage to extend the life of the turbines of 3000 rpm. power units BBER-1000
  • Development of mathematical models and methods of nonlinear torsional oscillations analysis of nodes of armored vehicles diesel engines

Areas of applied research

  • Development of the method for estimating acoustic loads at the start of RKN
  • Verification of the working capacity and mechanical state of the fastening systems БE during transportation on the basis of computer simulation of technological and operational influences
  • Investigation of the causes of the destruction of packets of blades regulating the degree of the rotor of high pressure turbines K-100-90 st. No. 6 DTEK Dobrotvirska TPP
  • Increase of energy efficiency and dynamic strength of diesel mini-power station for agriculture on the basis of the latest intelligent information-control technologies
  • Analysis of vibration stresses in the working blades of the compressor GTE with allowance for temperature, centrifugal forces and excitability of oscillations by non-stationary aerodynamic forces, and also taking into account various types of damping of oscillations

Publications 2015-2017

  • 1. Avramov K. Bifurcations behavior of bending vibrations of beams with two breathing cracks / K.Avramov, T.Raimberdiyev // Engineering Fracture Mechanics. – 2017. – V. 178. – P. 22-38.
  • 2. AvramovK.V.Dynamic instability of shallow shells in three-dimensional incompressible inviscid potential flow / K.V. Avramov, S.V. Papazov, I. D. Breslavsky // Journal of Sound and Vibration. – 2017. – V. 394. P. 593-611,https://doi.org/10.1016/j.jsv.2017.01.048.
  • 4. UspenskyB. Numerical Analysis of Nonlinear Modes of Piecewise Linear Systems Torsional Vibrations / B. Uspensky, K. Avramov // Meccanica. – V. 52. – P. 3743-3757,https://doi.org/10.1007/s11012-017-0677-2.
  • 5. Uspenskii B.V. Nonlinear normal modes of essentially nonlinear piecewise systems under periodic excitation / B.V. Uspenskii, K.V. Avramov // Journal of Mathematical Sciences. – 2017. – V. 226, No.2. – P. 104-113, https://hal.archives-ouvertes.fr/hal-01580816.
  • 6. Dynamic instability of parabolic shells in supersonic gas stream /K.Avramov, M.V Chernobryvko, O.Kazachenko, T.J.Batutina// Meccanica. – 2016.– V.51, №4. – Р. 939-950, https://doi.org/10.1007/s11012-015-0247-4.
  • 7. Avramov K.V.Bifurcation behavior of steady vibrations of cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow / K.V. Avramov//J. of Vibration and Control. –2016. – V.22, №5. – Р. 1198-1216, https://doi.org/10.1177/1077546314534716.
  • 8. Nonlinear longitudinal oscillations of fuel in rockets feed lines with gas-liquid damper /K.V.Avramov, S.Filipkovsky, A.M.Tonkonogenko, D.V.Klimenko//ActaAstronautica.–2016. – V.120. – Р. 20-29, https://doi.org/10.1016/j.actaastro.2015.11.028.
  • 9. Kruszka L.The resistance of structural elements to impact and shock-wave load /L.Kruszka, I.Vorobiov, N.Ovcharova//Key Engineering Materials. –2016.– V. 715. – P. 216-221,https://doi.org/10.4028/www.scientific.net/KEM.715.216.
  • 10. Dynamics of thin-walled elements of rocket engine under impact loads /M.Chernobryvko, K.Avramov, L.Kruszka, A.Tonkonogenko//Key Engineering Materials. –2016. – V. 715. – P. 237-242,https://doi.org/10.4028/www.scientific.net/KEM.715.237.
  • 11. Dynamic instability of ring-stiffened conical thin-walled rocket fairing in supersonic gas stream /M.V.Chernobryvko, K.V.Avramov, V.N.Romanenko, T.J.Batutina, U.S.Suleimenov//Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. –2016. – V.230, №1. – Р. 55-68,https://doi.org/10.1177/0954406215592171.
  • 12. Influence of periodic excitation on self-sustained vibrations of one disk rotors in arbitrary length journals bearings /K.Avramov, M.Shulzhenko, O.Borysiuk, C.Pierre //International Journal of Non-Linear Mechanics. –2015. – V.77, №12. – Р.274-280,https://doi.org/10.1016/j.ijnonlinmec.2015.08.011.
  • 13. Kruszka L.Sensitivity of high strain rate of structural elements in relation to dynamics properties of material /L.Kruszka, I.S.Vorobiov, N.I.Ovcharova//EPJ Web of Conferences. –2015. – V.94. – 3 р., https://doi.org/10.1051/epjconf/20159404045.
  • 14. Chernobryvko M.Deformation of compound shells under action of internal shock wave loading /M.Chernobryvko, L.Kruszka, K.Avramov //EPJ Web of Conferences. –2015. – V.94. – 4 р., https://doi.org/10.1051/epjconf/20159404046.
  • 15. Avramov K.V.Saturation of Almost Periodic and Chaotic Aeroelastic Oscillations of Plates Under a Resonant Multimode Force /K.V.Avramov, E.A.Strel’nikova//International Applied Mechanics. –2015. – V.51, №3. – Р.342-349, https://doi.org/10.1007/s10778-015-0694-6.