Meccanica

, Volume 38, Issue 6, pp 613–621

An Overview on Non-Ideal Vibrations

  • José Manoel Balthazar
  • Dean T. Mook
  • Hans Ingo Weber
  • Reyolando M.L.R.F. Brasil
  • A. Fenili
  • D. Belato
  • J.L.P. Felix
Article

Abstract

We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power.

Limited power supply Non-ideal vibrations Sommerfeld effect 

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References

  1. 1.
    Sommerfeld, A., 'Beiträge zum dynamischen ausbau der festigkeitslehe', Physikal Zeitschr 3 (1902) 266 and 286.Google Scholar
  2. 2.
    Kononenko, V.O., Vibrating Systems with a Limited Power Supply (in Russian: 1959), English translation, Illife Books, 1969.Google Scholar
  3. 3.
    Bleckman, I.I., 'Self-Synchronization of certain vibratory devices', Eng. Trans. 16 (1953).Google Scholar
  4. 4.
    Evan-Iwanowski, R.M., Resonance Oscillators in Mechanical Systems, Elsevier, 1976.Google Scholar
  5. 5.
    Dimentberg M.F., Statistical Dynamics of Nonlinear and Time Varying Systems, John Wiley and Sons, 1988.Google Scholar
  6. 6.
    Dimentberg, M.F., McGovern, L., Norton, R.L., Chapdelaine, J. and Harrison, R., 'Dynamics of an unbalanced shaft interacting with a limited power supply', Nonlinear Dyn. 13 (1997) 171-187.Google Scholar
  7. 7.
    Nayfeh, A.H. and Mook, D.T., Nonlinear Oscillations, John Wiley and Sons, 1979.Google Scholar
  8. 8.
    Balthazar, J.M., Mook, D.T., Weber, H.I., Fenili, A., Belato, D., de Mattos, M.C. and Wieczorek, S., 'On vibrating systems with a limited power supply and their applications to engineering sciences', in: Honig, C.S. (ed), 49th Brazilian Seminar of Mathematical Analysis, State University of Campinas, Campinas, SP, Brazil, Short Course, March 5–9, 1999, pp. 137-277.Google Scholar
  9. 9.
    Balthazar, J.M., Mook, D.T., Brasil, R.M.L.R.F., Weber, H.I., Fenili, A., Belato, D. and Felix, J.L.P., 'Recent results on vibrating problems with limited power supply', in: Awrejcewicz, J., Brabski, J. and Nowakowski, J. (eds), Sixth Conference on Dynamical Systems Theory and Applications, Lodz, Poland, December, 10–12, 2001, pp. 27-50.Google Scholar
  10. 10.
    Yamanaka, H. and Murakami, S., 'Optimum designs of operating curves for rotating shaft systems with limited power supplier', in: Chung, H. (ed.), Current Topics in Structural Mechanics, PVP, 179 ASME NY, 1989, pp. 181-185.Google Scholar
  11. 11.
    Balthazar, J.M., Cheshankov, B.I., Rushev, D.T., Barbanti, L. and Weber, H.I., 'Remarks on the passage through resonance of a vibrating system, with two degree of freedom', J. Sound Vib. 239(5) (2001) 1075-1085.Google Scholar
  12. 12.
    Christ, H., 'Stationärer und Instatioärer Betrieb Eines Federnd Gelagerten, Unwuchtigen Motors', Dissertation Universität Karlsruhe, 1966.Google Scholar
  13. 13.
    Wauer, J. and Bürle, P., 'Dynamics of a flexible slider-crank mechanism driven by a non-ideal source of energy', Nonlinear Dyn. 13 (1997) 221-242.Google Scholar
  14. 14.
    Wauer, J. and Suherman, S., 'Vibration suppression of rotating shafts passing through resonances by switching shaft stiffness', J. Vib. Acoust. 120 (1997) 170-180.Google Scholar
  15. 15.
    Suherman, S., 'Transient Analysis and Vibrating Suppression of a Cracked Rotating Shaft with a Ideal and a Non-Ideal Motor Passing Through a Critical Speed, PhD Thesis, Virginia Polytechnic Institute and State University, 1996.Google Scholar
  16. 16.
    Iwatsubo, T., Kanki, H. and Kawai, R., 'Vibration of asymmetric rotor through critical speed with limited power supply', J. Mech. Eng. Sci. 14(3) (1972) 184-194.Google Scholar
  17. 17.
    Suzuki, S.H., 'Dynamic behavior of a beam subject to a force of time-dependent frequency', J. Sound Vib. 57 (1978) 59-64.Google Scholar
  18. 18.
    Suzuki, S.H., 'Dynamic behavior of a beam subject to a force of time-dependent frequency (continued), J. Sound Vib. 60(3) (1978) 417-422.Google Scholar
  19. 19.
    Balthazar, J.M., Rente, M.L., Mook, D.T. and Weber, H.I., 'Some observations on numerical simulations of a non-ideal dynamical system', in: Balthazar, J.M., Mook, D.T. and Rosario, J.M. (eds), Nonlinear Dynamics, Chaos, Control and Their Applications to Engineering Sciences, Vol. 1, 1997, pp. 97-104.Google Scholar
  20. 20.
    Balthazar, J.M., Mook, D.T., Weber, H.I. and Mattos M.C., 'Some remarks on the behaviour of non-ideal dynamical systems', in: Balthazar, J.M., Mook, D.T. and Rosario, J.M. (eds), Nonlinear Dynamics, Chaos, Control and Their Applications to Engineering Sciences, Vol. 1, 1997, pp. 88-96.Google Scholar
  21. 21.
    De Mattos, M.C., Balthazar, J.M., Wieczork, S. and Mook, D.T., 'An experimental study of vibrations of non-ideal systems', in: Proceedings of DETC'97, ASME Design Engineering Technical Conference, September 14–17, Sacramento, California, USA, CD-ROM, 1997, pp. 10.Google Scholar
  22. 22.
    De Mattos, M.C., Balthazar, J.M., 'On the dynamics of an armature controlled dc motor mounted on an elastically table', in: Proceedings of 15th Brazilian Congress of Mechanical Engineering, November 22–16, Águas de Lindóia, São Paulo, Brazil, 1999, pp. 10.Google Scholar
  23. 23.
    Brasil, R.M.F.L. and Balthazar J.M., 'Nonlinear oscillations of a portal frame structure excited by a non-ideal motor', in: Chernousko, A.L. and Fradkov, A.I. (eds), Control of Oscillations and Chaos, Vol. 2, 2000, pp. 275-278.Google Scholar
  24. 24.
    Palacios, J.F., Balthazar, J.M. and Brasil, R.M.L.R.F., 'On Non-ideal dynamics of nonlinear portal frame analysis using averaging method', in: Espindola, J.J., Lopes, E.O.M. and Bazan, F.S.V. (eds), Proceedings of the Ninth International Symposium on Dynamic Problems of Mechanics, Florianópolis, SC, Brazil, 5–9 March 2001, pp. 341-346.Google Scholar
  25. 25.
    Fenili, A., 'On Slewing Structure: Modeling and Dynamical Analysis', PhD Thesis, State University of Campinas, SP, Brazil, 2000 (in Portuguese).Google Scholar
  26. 26.
    Fenili, A., Balthazar, J.M., Weber, H.I. and Mook, D.T., 'Nonlinear analysis of the motion of a flexible, rotating, cantilever beam', (2002) (submitted).Google Scholar
  27. 27.
    Fenili, A., Balthazar, J.M., Weber, H.I. and Mook, D.T., 'On the comparison between two mathematical models for flexible slewing structures-linear and nonlinear curvature', in: Balthazar, J.M., Gonçalves, P.B., Brasil, R.M.F.L.R.F., Caldas I.L. and Rizatto, F.B. (eds), Nonlinear Dynamics, Chaos and Their Applications to Engineering Sciences, 4: Recent Developments in Nonlinear Phenomena, 2001, pp. 372-382.Google Scholar
  28. 28.
    Fenili, A., Balthazar, J.M., Mook, D.T. and Weber, H.I., 'Application of the center manifold reduction to the slewing flexible non-ideal model', J. Brazil. Soc. Mech. Sci. (2002) (in press).Google Scholar
  29. 29.
    Fenili, A., Balthazar, J.M. and Mook, D.T., 'Some remarks about the experimental analysis of slewing flexible structures and mathematical modeling', in: Espindola, J.J., Lopes, E.O.M. and Bazan, F.S.V. (eds), Proceedings of the Ninth International Symposium on Dynamic Problems of Mechanics, Florianópolis, SC, Brazil, 5–9 March 2001, pp. 341-346.Google Scholar
  30. 30.
    Fenili, A., Balthazar, J.M. and Mook, D.T., 'A brief note on experimental identification of dc-motor parameters', Sci. Eng. J. 10(1) (2001) 105-108.Google Scholar
  31. 31.
    Pontes, B.R., De Oliveira, V.A. and Balthazar, J.M., 'On friction-driven vibrations in a mass block-belt-motor with limited power supply', J. Sound Vib. 234(4) (2000) 713-723.Google Scholar
  32. 32.
    Pontes, B.R., De Oliveira, V.A. and Balthazar, J.M, 'On the dynamic response of a mechanical system with dry friction and limited power supply', in: Balthazar, J.M., Gonçalves P.B., Brasil, R.M.F.L.R.F., Caldas I.L. and Rizatto, F.B. (eds), Nonlinear Dynamics, Chaos and Their Applications to Engineering Sciences, 4: Recent Developments in Nonlinear Phenomena, 2001, pp. 355-371.Google Scholar
  33. 33.
    Alifov, A. and Frolov, K.V., 'Investigation of self-excited oscillations with friction, under conditions of parametric excitation and limited power of energy source', Mekhanika Tvedogo Tela 15(4) (1977) 25-33.Google Scholar
  34. 34.
    Warminski, J., Balthazar, J.M. and Brasil, R.M.L.R.F., 'Vibrations of non-ideal parametrically and self-excited model', J. Sound Vib. 234(4) (2001) 713-723.Google Scholar
  35. 35.
    De Souza, S.L.T., Caldas, I.L., Balthazar, J.M. and Brasil, R.M.L.R.F., 'Analysis of regular and irregular dynamics of a non-ideal gear rattling problem', J. Brazil. Soc. Mech. Sci. (2002) 111-114.Google Scholar
  36. 36.
    Krasnopol'skaya, T.S. and Shevts, A.Y., 'Chaotic interactions in a pendulum energy source system', Prikladnaya Mekhanika 26(5) (1990) 90-96.Google Scholar
  37. 37.
    Belato, D., 'Nonlinear Analysis of Non-Ideals Holonomic Dynamical Systems', PhD Thesis, Faculdade de Engenharia Mecânica, UNICAMP, Campinas, São Paulo, Brazil, 2002 (in Portuguese).Google Scholar
  38. 38.
    Belato, D., Weber, H.I., Balthazar, J.M. and Mook, D.T., 'Chaotic vibrations of a non-ideal electromechanical system', Int. J. Solids Struct. 38 (2001) 669-1706.Google Scholar
  39. 39.
    Palacios, J.F., Balthazar, J.M. and Brasil, R.M.L.R.F., 'Some comments on a control technique by using internal resonance and saturation phenomenon: applications to a simple machine foundation', in: VII Pan American Congress of Applied Mechanics, Chile, Telmuco, 2002, pp. 141-144.Google Scholar
  40. 40.
    Brasil, R.M.L.R.F., Garzeri, F.J. and Balthazar, J.M., 'An experimental study of the nonlinear dynamics of a portal frame foundation for a non-ideal motor', in: Proceedings of DETC'01 ASME 2001 Design Engineering Technical Conference and Computers and Information in Engineering Conference, Pittsburgh, Pennsylvania, September 9–12, CD ROM, 2001.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • José Manoel Balthazar
    • 1
    • 2
  • Dean T. Mook
    • 3
  • Hans Ingo Weber
    • 4
  • Reyolando M.L.R.F. Brasil
    • 5
  • A. Fenili
    • 6
  • D. Belato
    • 6
  • J.L.P. Felix
    • 6
  1. 1.State University of São Paulo at Rio ClaroRio Claro, SP
  2. 2.State University of CampinasBrazil
  3. 3.Virginia TechBlacksburgUSA
  4. 4.Catholic UniversityGávea, RJBrazil
  5. 5.Polytechnic SchoolUniversity of São PauloBrazil
  6. 6.School of Mechanical EngineeringUNICAMPCampinas, SPBrazil

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