IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/080705.html
   My bibliography  Save this article

Autoparametric vibrations of a nonlinear system with pendulum

Author

Listed:
  • J. Warminski
  • K. Kecik

Abstract

Vibrations of a nonlinear oscillator with an attached pendulum,excited by movement of its point of suspension, have been analysedin the paper. The derived differential equations of motion showthat the system is strongly nonlinear and the motions of bothsubsystems, the pendulum and the oscillator, are strongly coupledby inertial terms, leading to the so-called autoparametricvibrations. It has been found that the motion of the oscillator,forced by an external harmonic force, has been dynamicallyeliminated by the pendulum oscillations. Influence of a nonlinearspring on the vibration absorption near the mainparametric resonance region has been carried out analytically,whereas the transition from regular to chaotic vibrations has beenpresented by using numerical methods. A transmission force on thefoundation for regular and chaotic vibrations is presented aswell.

Suggested Citation

  • J. Warminski & K. Kecik, 2006. "Autoparametric vibrations of a nonlinear system with pendulum," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-19, May.
    • Handle: RePEc:hin:jnlmpe:080705
    DOI: 10.1155/MPE/2006/80705
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2006/080705.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2006/080705.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/MPE/2006/80705?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vasile Marinca & Nicolae Herisanu, 2020. "Optimal Auxiliary Functions Method for a Pendulum Wrapping on Two Cylinders," Mathematics, MDPI, vol. 8(8), pages 1-18, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jnlmpe:080705. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.