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Nonlinear analysis of unbalanced mass of vertical conveyor: primary, subharmonic, and superharmonic response

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Abstract

In the area of mechanics and electronics, the behaviors of mechanical systems under periodic loadings have been examined by many researchers. Vertical conveyors are effective examples observing various kinds of parameters of this problem. In this study, primary, subharmonic, and superharmonic responses have been investigated with multiple scales along with numerical methods for vertical conveyors. The change in the parameters of motion, stability condition, and jump phenomena has been shown graphically by Mathematica software for comparing the results. Both analytical and numerical results obtained had good agreement.

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References

  1. Spivakovasky, A.O., Dyachkov, V.K.: Conveying Machines, vol. II. Mir, Moscow (1985)

    Google Scholar 

  2. Bayıroğlu H, .: Computational dynamic analysis of unbalanced mass of vertical conveyor elevator. In: Sixth International Conference of the Balkan Physical Union. AIP Conference Proceedings, vol. 899, p. 712 (2007)

    Google Scholar 

  3. Ganapathy, S., Parameswaran, M.A.: Transition over resonance and power requirements of an unbalanced mass driven vibratory system. Mech. Mach. Theory 21, 73–85 (1986)

    Article  Google Scholar 

  4. Rocard, Y.: General Dynamics of Vibrations, 3rd edn. Ungar, New York (1960)

    Google Scholar 

  5. Mazert, R.: Mécanique Vibratoire, C. Béranger (ed.) Paris, France (1955)

  6. Panovko, Y.G., Gubanova, I.I.: Stability and Oscillations of Elastic Systems. Consultants Bureau, New York (1965)

    Google Scholar 

  7. Götzendorfer, A.: Vibrated granular matter: transport, fluidization, and patterns. PhD, University Bayreuth (2007)

  8. Balthazar, J.M., Brasıl, R.M.L.R.F., Weber, H.I., Fenili, A., Belato, D., Felix, J.L.P., Garzelli, F.J.: A Review of New Vibration Issues Due to Non-ideal Energy Sources. CRC Press, Boca Raton (2004)

    Google Scholar 

  9. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)

    MATH  Google Scholar 

  10. Nayfeh, A.H., Chin, C.M.: Perturbation Methods with Mathematica. Dynamics Press, Virgina (1999)

    Google Scholar 

  11. Lynch, S.: Dynamical Systems with Applications Using Mathematica. Springer, Berlin (2007)

    MATH  Google Scholar 

  12. Blekhman, I.I.: Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications. World Scientific, Singapore (2000)

    Book  Google Scholar 

  13. Bayiroglu, H., Alisverisci, G.F., Unal, G.: Nonlinear response of vibrational conveyors with non-ideal vibration exciter: superharmonic and subharmonic resonance. Math. Probl. Eng. (2012). doi:10.1155/2012/717543. Article Number: 717543

    Google Scholar 

  14. Awrejcewicz, J., Lamarque, C.H.: Bifurcation and Chaos in Non-smooth Mechanical Systems. World Scientific, River Edge (2003) (electronic resource)

    Google Scholar 

  15. Alisverisci, G.F., Bayiroglu, H., Unal, G.: Nonlinear response of vibrational conveyors with non-ideal vibration exciter: primary resonance. Nonlinear Dyn. 69(4), 1611–1619 (2012). doi:10.1007/s11071-012-0372-8

    Article  Google Scholar 

  16. Bolla, M.R., Balthazar, J.M., Felix, J.L.P., Mook, D.T.: On an approximate analytical solution to a nonlinear vibrating problem, excited by a non-ideal motor. Nonlinear Dyn. 50, 841–847 (2007)

    Article  MATH  Google Scholar 

  17. Piccirillo, V., Balthazar, J.M., Pontes, B.R. Jr.: Analytical study of the nonlinear behavior of a shape memory oscillator: Part I—primary resonance and free response at low temperatures. Nonlinear Dyn. 59(4), 733–746 (2009). doi:10.1007/s11071-009-9573-1

    Article  Google Scholar 

  18. Piccirillo, V., Balthazar, J.M., Pontes, B.R. Jr.: Analytical study of the nonlinear behavior of a shape memory oscillator: Part II—resonance secondary. Nonlinear Dyn. 60(4), 513–524 (2009). doi:10.1007/s11071-009-9611-z

    Article  Google Scholar 

  19. Dantas, M.J.H., Balthazar, J.M.: A comment on a non-ideal centrifugal vibrator machine behavior with soft and hard springs. Int. J. Bifurc. Chaos 16(4), 1083–1088 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

I greatly appreciate the comments of referees.

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Authors and Affiliations

  1. Yıldız Technical University, Istanbul, Turkey

    Hüseyin Bayıroğlu

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  1. Hüseyin Bayıroğlu
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Correspondence to Hüseyin Bayıroğlu.

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Bayıroğlu, H. Nonlinear analysis of unbalanced mass of vertical conveyor: primary, subharmonic, and superharmonic response. Nonlinear Dyn 71, 93–107 (2013). https://doi.org/10.1007/s11071-012-0643-4

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  • DOI: https://doi.org/10.1007/s11071-012-0643-4

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