IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/7314280.html
   My bibliography  Save this article

Flexural Free Vibrations of Multistep Nonuniform Beams

Author

Listed:
  • Guojin Tan
  • Wensheng Wang
  • Yubo Jiao

Abstract

This paper presents an exact approach to investigate the flexural free vibrations of multistep nonuniform beams. Firstly, one-step beam with moment of inertia and mass per unit length varying as and was studied. By using appropriate transformations, the differential equation for flexural free vibration of one-step beam with variable cross section is reduced to a four-order differential equation with constant coefficients. According to different types of roots for the characteristic equation of four-order differential equation with constant coefficients, two kinds of modal shape functions are obtained, and the general solutions for flexural free vibration of one-step beam with variable cross section are presented. An exact approach to solve the natural frequencies and modal shapes of multistep beam with variable cross section is presented by using transfer matrix method, the exact general solutions of one-step beam, and iterative method. Numerical examples reveal that the calculated frequencies and modal shapes are in good agreement with the finite element method (FEM), which demonstrates the solutions of present method are exact ones.

Suggested Citation

  • Guojin Tan & Wensheng Wang & Yubo Jiao, 2016. "Flexural Free Vibrations of Multistep Nonuniform Beams," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-12, November.
    • Handle: RePEc:hin:jnlmpe:7314280
    DOI: 10.1155/2016/7314280
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2016/7314280.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2016/7314280.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/7314280?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
    ---><---

    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:7314280. 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.