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YURI MIKHLIN

KONSTANTIN AVRAMOV

SVETLANA RESHETNIKOVA

GAYANE MANUCHARYAN

YEVGENIY KURYLOV

 

Yuri Vladimirovich MIKHLIN, Professor             Top

Books:

1.     The Method of Normal Oscillations for Essentially Nonlinear systems. Moscow: Nauka, 1989, (in Russian; L.I.Manevich, Yu.V.Mikhlin, V.N.Pilipchuk), ISBN 5-02-014011-2.

2.     Normal Modes and Localization in Nonlinear Systems. NY: Wiley, 1996 (A.F.Vakakis, L.I.Manevich, Yu.V.Mikhlin, V.N. Pilipchuk, A.A.Zevin), ISBN 0-471-13319-1.

3.     Nonlinear Dynamics of Shells with Fluid-Structure Interaction. Ed. Institute of Thermomechanics AS CR Prague, 2002 (F. Pellicano, Y. Mikhlin and I. Zolotarev), ISBN 80-85918-76-5.

Some selected publications:

1.     Yu.V.Mikhlin and K.V.Avramov. Analysis of nonlinear normal modes in cylindrical shells. In "Nonlinear Dynamics of Shells with fluid-structure interaction. NATO CLG Grant Report Proceedings (Ed. By F.Pellicano, Yu.Mikhlin, I.Zolotarev). Prague, 33-44, 2002.

2.     Yu.V.Mikhlin and G.V.Manucharyan. Construction of homoclinic and heteroclinic trajectories in mechanical systems with several equilibrium positions. Chaos, Solitons & Fractals 16, 2003, 299-309. pdf-file

3.     Yu.V.Mikhlin and B.I.Morgunov. Normal vibrations in near-conservative self-excited viscoelastic nonlinear systems. Nonlinear Dynamics 25, 2001, 33-48. pdf-file

4.     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 37, 2000, 3403-3420. pdf-file

5.     Yu.V.Mikhlin. Analytical construction of homoclinic orbits of two- and three-dimensional dynamical systems, J. of Sound and Vibration 230(5), 2000, 971-983.

6.     Yu.V.Mikhlin. Stability of regular or chaotic post-buckling vibrations of elastic shells. In "Nonlinear Dynamics of Shells and Plates". ASME International Mechanical Engineering Congress and Exposition. Orlando, 2000, 95-103.

7.     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.

8.     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 32(1), 1997, 493-509. pdf-file

9.     Yu.V.Mikhlin. Normal vibrations of a general class of conservative oscillators. Nonlinear Dynamics 11(1),1996,1-16. pdf-file

10. I.V.Andrianov, Yu.V.Mikhlin, S.Tokarzevski. Two-point Pade' approximants and their applications to in solving mechanical problems. Mechanika Teoretyczna i Stosovana (J. of Theor. and Appl. Mech.), Warsawa, Poland, 35(3), 1997, 577-606.

11. Yu.V.Mikhlin. Normal vibrations of a general class of conservative oscillators. Nonlinear Dynamics, 11(1), 1996, 1-16.

12. Yu.V.Mikhlin. Matching of local expansions in the theory of non-linear vibrations. J. of Sound and Vibration 182(4), 1995, 577-588. pdf-file

13. L.I.Manevich, Yu.V.Mikhlin. Normal vibrations of nonlinear finite-dimensional systems. Advances in Mechanics 12(3), 1989, 3-38 (in Russian).

14. Yu.V.Mikhlin. Resonance modes of near-concervative nonlinear systems. J. Appl. Math. and Mech. (PMM) 38(3), 1974, 425-429.

15. L.I.Manevich, Yu.V.Mikhlin. On periodic solution close to rectilinear vibration modes. J. Appl. Math. and Mech. (PMM) 36(6), 1972, 988-994 (with co-author).

Submitted publications:

1.     K.V.Avramov and Yu.V.Mikhlin. Snap-through truss as a vibration absorber. Vibration and Control (in press).

2.     Yu.V.Mikhlin and S.N.Reshetnikova. Analysis of dynamical interaction of elastic system and essentially nonlinear absorber by using the nonlinear normal vibration modes (in Russian). Applied Mechanics, Kiev.

3.     Yu.V.Mikhlin and S.N.Reshetnikova. Analysis of interaction of elastic spring and essentially nonlinear oscillator under the shock impact (in Russian). In: Notices of the Dnepropetrovsk University. Mechanics, 2003 (in press).

 

 

Konstantin Vitalievich AVRAMOV, Dr., Senior Researcher          Top

SOME SELECTED PUBLICATIONS:

  1. Avramov K. V. Nonlinear beam oscillations excited by lateral force at combination resonance// Journal of Sound and Vibration.-2002. V. 257(2). P. 337-359.pdf-file
  2. Avramov K. V. Bifurcations of parametric oscillations of beams with three equilibrium// Acta Mechanica. - 2003. V. 164. P. 115- 138.pdf-file
  3. K. V. Avramov, Yu. V. Mikhlin. Forced oscillations of a system, containing a snap-through truss, close to its equilibrium position. Nonlinear Dynamics 35, 2004, 361-379. pdf-file
  4. K. V. Avramov. Analysis of periodic-doubling bifurcation in impact oscillator by using of amplitude surface method. Mechanics of solid 3, 2004, 30-37. pdf-file
  5. K. V. Avramov, Yu. V. Mikhlin. Snap-through truss as a vibration absorber. Journal of Vibration and Control, 10, 2004, 291-308. pdf-file
  6. K. V. Avramov, Yu. V. Mikhlin. Snap - through truss as an absorber of forced oscillations. Journal of Sound and Vibration (in press).pdf-file
  7. F. Pellicano, K. V. Avramov. Linear and Nonlinear Dynamics of a circular cylindrical shell connected to a rigid disk. Communications in Nonlinear Science and Numerical Simulations (in press).
  8. K. V. Avramov, J. Awrejcewicz, Frictional auto-oscillations under the action of almost periodic excitations. Meccanica (in press).
  9. K. V. Avramov. Bifurcation analysis of a vibropercussion system by the method of amplitude surfaces. International Applied Mechanics,- Plenum Publishing Corporation, 2002.-Vol. 38, No.9.- P. 1151-1156.pdf-file
  10. K. V. Avramov. Bifurcations at combination resonance and quasiperiodic vibrations of flexible beams. International Applied Mechanics,- Plenum Publishing Corporation, 2003.- Vol. 39, No.8.- P. 976- 982.pdf-file
  11. Avramov K. V., Mikhlin Yu. V. Analysis of nonlinear normal modes in cylindrical shells// Nonlinear Dynamics of shells with fluid- structure interaction.- 2002, Institute of Thermo mechanics, Prague, editors F. Pellicano, Ð. 33-45.

 

Svetlana Nikolaevna RESHETNIKOVA               Top

SOME SELECTED PUBLICATIONS:

  1. Yuri V. Mikhlin and S.N.Reshetnikova. Dynamical interaction of an elastic system and essentially nonlinear absorber. Mathematical Problems in Engineering, 2005 (in press).
  2. Yu.V.Mikhlin and S.N.Reshetnikova. Analysis of dynamical interaction of elastic system and essentially nonlinear absorber by using the nonlinear normal vibration modes. International Applied Mechanics, N2, 2005 (in Russian).
  3. Yu.V.Mikhlin and S.N.Reshetnikova. Dynamical interaction of an elastic system and essentially nonlinear absorber. J. of Sound and Vibration, 2005, 283, 91-120. pdf-file
  4. Yu.V.Mikhlin and S.N.Reshetnikova. Analysis of interaction of elastic spring and essentially nonlinear oscillator under the shock impact. In: Notices of the Dnepropetrovsk University. Mechanics, V. 7 (2), 2003, 120-128 (in Russian).

 

Gayane V. MANUCHARYAN                Top

PUBLICATIONS:

  1. Manucharyan G.V., Mikhlin Yu.V. The construction of homo- and heteroclinic orbits in non-linear systems, J. of Applied Mathematics and Mechanics 69, p.39-48 (2005).
  2. Mikhlin Yu.V., Shmatko T.V., Manucharyan G.V. Lyapunov definition and stability of regular or chaotic vibration modes in systems with several equilibrium positions // Computers & Structures. - 2004. - 82. - 2733-2742.pdf-file
  3. Mikhlin Yu.V., Manucharyan G.V. Construction of homoclinic and heteroclinic trajectories in mechanical systems with several equilibrium positions, J. of Chaos, Solitons and Fractals 16, p.299-309 (2003).
  4. Manucharyan G.V. Mutual instability of phase trajectories and chaos beginning in dynamical systems, Proc. of the 7th Conference on Dynamical Systems. Theory and Applications, Lodz, p.361-366 (2003).
  5. Manucharyan G.V. Construction of homoclinic trajectories in forced and parametrically excited nonlinear systems, the Book of Conference Proceedings of the conference "MathTools-2003", Saint-Petersburg (2003).
  6. Mikhlin Yu.V., Manucharyan G.V.and Savenkova S.N. Analysis of homoclinic trajectories in mechanical systems with several equilibrium positions, Proc. of the 6th Conference on Dynamical Systems. Theory and Applications, Lodz, p.309-316 (2001).

 

Yevgeniy A. KURYLOV                     Top

PUBLICATIONS:

  1. Kurylov, Ye.A. 2003. Nonlinear normal modes in 2-DOF dynamical systems. Applied mathematics and informatics. Proc. of the Student Int. Conf., Lvov, 17-18 April, 2003.
  2. Kurylov, Ye.A. 2004. Aeroelastic stability and nonlinear normal modes of cylindrical shells in supersonic flow. Notices of the NTU “KhPI”  №20, 2004, p. 29-38.
  3. Kurylov, Ye.A. 2005. Analysis of nonlinear normal modes in cylindrical shells with imperfections. Notices of the NTU “KhPI” (in press).
  4. Mikhlin, Yu.V., Avramov, K.V.& Kurylov Ye.A. 2005. Nonlinear dynamics of simply supported cylindrical shells, Part I: Nonlinear normal vibration modes analysis. Int. Journal of Solids and Structures (is presented).
  5. Mikhlin, Yu.V., Avramov, K.V.& Kurylov Ye.A. 2005. Nonlinear normal modes and forced vibrations of simply supported cylindrical shells. Proc. Of Shell Structures: Theory and Applications, Gdansk-Jurata, 12-14 October 2005.

 

 

 

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Last Modified: November 2005
Questions and comments contact: gayane@kpi.kharkov.ua