Localized and Non-Localized Nonlinear Normal Modes in a Multi-Span Beam With Geometric Nonlinearities

[+] Author and Article Information
J. Aubrecht, A. F. Vakakis

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana—Champaign, Urbana, IL 61801

J. Vib. Acoust 118(4), 533-542 (Oct 01, 1996) (10 pages) doi:10.1115/1.2888332 History: Received November 01, 1993; Revised January 01, 1995; Online February 26, 2008


The nonlinear normal modes of a geometrically nonlinear multi-span beam consisting of n segments, coupled by means of torsional stiffeners are examined. Assuming that the stiffeners possess large torsional stiffness, the beam displacements are decomposed into static and flexible components. It is shown that the static components are much smaller in magnitude than the flexible ones. A Galerkin approximation is subsequently employed to discretize the problem, whereby the computation of the nonlinear normal modes of the multi-span beam is reduced to the study of the periodic solutions of a set of weakly coupled, weakly nonlinear ordinary differential equations. Numerous stable and unstable, localized and non-localized nonlinear normal modes of the multi-span beam are detected. Assemblies consisting of n = 2, 3, and 4 beam segments are examined, and are found to possess stable, strongly localized nonlinear normal modes. These are free synchronous oscillations during which only one segment of the assembly vibrates with finite amplitude. As the number of periodic segments increases, the structure of the nonlinear normal modes becomes increasingly more complicated. In the multi-span beams examined, nonlinear mode localization is generated through two distinct mechanisms: through Pitchfork or Saddle-node mode bifurcations, or as the limit of a continuous mode branch when a coupling parameter tends to zero.

Copyright © 1996 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.






Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In