Advanced Search

Journal Navigation

Journal Home

Subscriptions

Archive

Contact Us

Table of Contents

Sign In to gain access to subscriptions and/or personal tools.
Journal of Vibration and Control
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
1077546309103262v1
15/11/1627    most recent
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by Al-Qaisia, A.A.
Right arrow Articles by Hamdan, M.N.
Social Bookmarking
Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?

Nonlinear Frequency Veering in a Beam Resting on an Elastic Foundation

A.A. Al-Qaisia

Department of Mechanical Engineering, Faculty of Engineering and Technology, University of Jordan, Amman 11942, Jordan , alqaisia{at}ju.edu.jo

M.N. Hamdan

Department of Mechanical Engineering, Faculty of Engineering and Technology, University of Jordan, Amman 11942, Jordan

In this work we present an investigation into nonlinear frequency veering of an elastic Euler— Bernoulli beam resting on a Winkler elastic foundation subjected to a static lateral load and hinged—hinged, with a torsional spring at one end. The beam is assumed to have an initial quarter-sine shape rise owing to a constant differential edge settlement. The beam static deflection is obtained by using a combined numerical—analytical procedure that accounts for the induced nonlinear axial force to mid-plane stretching. The harmonic balance method is used to solve for the nonlinear natural frequency of the associated nonlinear temporal problem obtained using the assumed mode method. The results are presented in the form of characteristic curves which show variation of the nonlinear natural frequency of the three modes of a selected range of system parameters. These results indicate that, depending on the system parameters, the nonlinear natural frequency of various modes can exhibit complicated behaviors not found using linear analysis.

Key Words: Nonlinear frequency veering • edge settlement • elastic foundation • static deflection.

This version was published on November 1, 2009

Journal of Vibration and Control, Vol. 15, No. 11, 1627-1647 (2009)
DOI: 10.1177/1077546309103262
Add to CiteULike CiteULike   Add to Complore Complore   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati   Add to Twitter Twitter    What's this?