Skip to main content
SpringerLink
Log in

Dynamics of a parallelepiped on a horizontal vibrating plane

  • Nonlinear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We consider the dynamics of a rigid parallelepiped on a horizontally vibrating rigid support plane and the possibility to control its oscillations. We assume that there is no slipping of the parallelepiped’s base along the plane. We find such excitation parameters for which the parallelepiped breaks off from the plane and performs oscillations, resting upon alternating support edges. In case of harmonic oscillations of the plane, we find possible modes of forced oscillations. We study the problem of reducing the amplitude of oscillations for the parallelepiped with a mathematical pendulum. We show results as frequency and phase responses.

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

Similar content being viewed by others

References

  1. Housner, J., The Behavior or Inverted Pendulum Structures During Earthquakes, Bullet. Seismologic. Soc. Am., 1963, vol. 53, no. 2, pp. 403–417.

    Google Scholar 

  2. Pena, F., Prieto, F., Lourenco, P.B., et al., On the Dynamics of Rocking Motions of Single Rigid-Block Structures, Earthquake Eng. Struct. Dynam., 2007, vol. 36, pp. 2383–2399.

    Article  Google Scholar 

  3. Prieto, F. and Lourenco, P.B., On the Rocking Behavior of Rigid Object, Meccanica, 2005, vol. 40, pp. 121–133.

    Article  MATH  MathSciNet  Google Scholar 

  4. Andreaus, U. and Casini, P., On the Rocking-uplifting Motion of a Rigid Block in Free and Forced Motion: Influence of Sliding and Bouncing, Acta Mechanica, 1999, vol. 138, pp. 219–241.

    Article  MATH  Google Scholar 

  5. Hogan, S.G., On the Dynamics of Rigid Block Motion under Harmonic Forcing, Earthquake Eng. Tenth World Conf., Bulkema, Rotterdam, 1992, ISNB 90 5410 060 5, pp. 3973–3977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. V. Karapetyan

  2. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia

    M. A. Munitsyna

Authors
  1. A. V. Karapetyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Munitsyna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Karapetyan.

Additional information

Original Russian Text © A.V. Karapetyan, M.A. Munitsyna, 2015, published in Avtomatika i Telemekhanika, 2015, No. 3, pp. 32–43.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karapetyan, A.V., Munitsyna, M.A. Dynamics of a parallelepiped on a horizontal vibrating plane. Autom Remote Control 76, 394–404 (2015). https://doi.org/10.1134/S0005117915030042

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117915030042

Keywords

Search

Navigation