Skip to main content
SpringerLink
Log in

Experimental study of the argumental transverse vibration of a beam excited through intermittent elastic contact by a harmonic axial motion

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The transverse vibration of a beam excited axially by a harmonic motion transmitted through intermittent elastic contact is experimentally studied. The beam’s configuration is clamped–(clamped–guided). It is shown that said transverse vibration can be considered essentially as the fundamental transverse mode of the beam and can occur when the frequency of the excitation is four or six times the frequency of said mode. The energy transfer between the excitation source and the beam occurs only when the beam is in certain spatial configurations. This constitutes an argumental phenomenon. Experimental results are given and compared with models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30

Similar content being viewed by others

References

  1. Béthenod, M.: Sur l’entretien du mouvement d’un pendule au moyen d’un courant alternatif de fréquence élevée par rapport à sa fréquence propre. Comptes rendus hebdomadaires de l’Académie des sciences 207(19), 847–849 (1938). (in French)

    MATH  Google Scholar 

  2. Bogolioubov, N., Mitropolski, I.: Les méthodes asymptotiques en théorie des oscillations non linéaires. Gauthiers-Villars, Paris (1962)

    MATH  Google Scholar 

  3. Burney, S., Jager, L.G.: A method of determining the regions of instability of a column by a numerical method approach. J. Sound Vib. 15(1), 75–91 (1971). https://doi.org/10.1016/0022-460X(71)90361-0

    Article  MATH  Google Scholar 

  4. Cintra, D., Argoul, P.: Attractor’s capture probability in nonlinear argumental oscillators. Commun. Nonlin. Sci. Numer. Simul. 48(Supplement C), 150–169 (2017). https://doi.org/10.1016/j.cnsns.2016.12.023

    Article  MathSciNet  Google Scholar 

  5. Cintra, D., Argoul, P.: Non-linear argumental oscillators: stability criterion and approximate implicit analytic solution. Int. J. Non-Linear Mech. 94(Supplement C), 109–124 (2017). https://doi.org/10.1016/j.ijnonlinmec.2017.03.013

    Article  Google Scholar 

  6. Cintra, D., Argoul, P.: Nonlinear argumental oscillators: a few examples of modulation via spatial position. J. Vib. Control 23(18), 2888–2911 (2017). https://doi.org/10.1177/1077546315623888

    Article  MathSciNet  Google Scholar 

  7. Cintra, D., Cumunel, G., Argoul, P.: Modeling and numerical results for the argumental transverse vibration of a beam excited through permanent or intermittent elastic contact by a harmonic axial motion. Nonlin. Dyn. 95, 495 (2019). https://doi.org/10.1007/s11071-018-4578-2

    Article  Google Scholar 

  8. Cretin, B., Vernier, D.: Quantized amplitudes in a nonlinear resonant electrical circuit. In: 2009 Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium, vols 1 and 2, vol. 1 & 2, pp. 797–800. Joint Meeting of the 23rd European Frequency and Time Forum/IEEE International Frequency Control Symposium, Besançon, France (2009). http://arxiv.org/ftp/arxiv/papers/0801/0801.1301.pdf

  9. Doubochinski, D.: Argumental oscillations. Macroscopic quantum effects. SciTech Library (2015). http://www.sciteclibrary.ru/rus/catalog/pages/15207.html

  10. Doubochinski, D., Doubochinski, J.: Amorçage argumentaire d’oscillations entretenues avec une série discrète d’amplitudes stables. E.D.F. Bulletin de la direction des études et recherches, série C mathématiques, informatique 3, 11–20 (1991). (in French)

  11. Fey, R.H.B., Mallon, N.J., Kraaij, C.S., Nijmeijer, H.: Nonlinear resonances in an axially excited beam carrying a top mass: simulations and experiments. Nonlinear Dyn. 66(3, SI), 285–302 (2011). https://doi.org/10.1007/s11071-011-9959-8

    Article  MathSciNet  Google Scholar 

  12. Huang, J., Hung, L.: Dynamic stability for a simply supported beam under periodic axial excitation. Int. J. Non-Linear Mech. 19(4), 287–301 (1984). https://doi.org/10.1016/0020-7462(84)90057-X

    Article  MATH  Google Scholar 

  13. Li, M.: Analytical study on the dynamic response of a beam with axial force subjected to generalized support excitations. J. Sound Vib. 338, 199–216 (2015). https://doi.org/10.1016/j.jsv.2014.11.004

    Article  Google Scholar 

  14. Lu, Q., To, C., Huang, K.: Dynamic stability and bifurcation of an alternating load and magnetic field excited magnetoelastic beam. J. Sound Vib. 181(5), 873–891 (1995). https://doi.org/10.1006/jsvi.1995.0175

    Article  Google Scholar 

  15. Penner, D.I., Duboshinskii, D.B., Kozakov, M.I., Vermel’, A.S., Galkin, Y.V.: Asynchronous excitation of undamped oscillations. Phys. USP. 16(1), 158–160 (1973). https://doi.org/10.1070/PU1973v016n01ABEH005156

    Article  Google Scholar 

  16. Pratiher, B., Dwivedy, S.K.: Nonlinear response of a flexible cartesian manipulator with payload and pulsating axial force. Nonlinear Dyn. 57(1), 177–195 (2009). https://doi.org/10.1007/s11071-008-9431-6

    Article  MathSciNet  MATH  Google Scholar 

  17. Shibata, A., Ohishi, S., Yabuno, H.: Passive method for controlling the nonlinear characteristics in a parametrically excited hinged-hinged beam by the addition of a linear spring. J. Sound Vib. 350, 111–122 (2015). https://doi.org/10.1016/j.jsv.2015.03.055

    Article  Google Scholar 

  18. Treilhou, J., Coutelier, J., Thocaven, J., Jacquez, C.: Payload motions detected by balloon-borne fluxgate-type magnetometers. Adv. Space Res. 26(9), 1423–1426 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Navier, UMR 8205, Ecole des Ponts, IFSTTAR, CNRS, UPE, 6 et 8, Avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455, Marne La Vallée Cedex 2, France

    Daniel Cintra & Gwendal Cumunel

  2. Laboratoire MAST-EMGCU, IFSTTAR, 77455, Marne La Vallée, Cedex 2, France

    Pierre Argoul

Authors
  1. Daniel Cintra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gwendal Cumunel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre Argoul
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Cintra.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cintra, D., Cumunel, G. & Argoul, P. Experimental study of the argumental transverse vibration of a beam excited through intermittent elastic contact by a harmonic axial motion. Nonlinear Dyn 97, 903–919 (2019). https://doi.org/10.1007/s11071-019-05017-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05017-2

Keywords

Search

Navigation