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Dynamic Instability of Cantilever Beams With Open Cross-Section

[+] Author Affiliations
Júlio C. Coaquira, Paulo B. Gonçalves

Pontifical Catholic University, Rio de Janeiro, Brazil

Eulher C. Carvalho

Federal Institute of Education, Science and Technology of Goiás, Jataí, Brazil

Paper No. IMECE2016-65674, pp. V04BT05A012; 6 pages
doi:10.1115/IMECE2016-65674
From:
  • ASME 2016 International Mechanical Engineering Congress and Exposition
  • Volume 4B: Dynamics, Vibration, and Control
  • Phoenix, Arizona, USA, November 11–17, 2016
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5055-8
  • Copyright © 2016 by ASME

abstract

Structural elements with thin-walled open cross-sections are common in metal and composite structures. These thin-walled beams have generally a good flexural strength with respect to the axis of greatest inertia, but a low flexural stiffness in relation to the second principal axis and a low torsional stiffness. These elements generally have an instability, which leads to a flexural-flexural-torsional coupling. The same applies to the vibration modes. Many of these structures work in a nonlinear regime, and a nonlinear formulation that takes into account large displacements and the flexural-flexural-torsional coupling is required. In this work a nonlinear beam theory that takes into account large displacements, warping and shortening effects, as well as flexural-flexural-torsional coupling is adopted. The governing nonlinear equations of motion are discretized in space using the Galerkin method and the discretized equations of motion are solved by the Runge-Kutta method. Special attention is given to the nonlinear oscillations of beams with low torsional stiffness and its influence on the bifurcations and instabilities of the structure, a problem not tackled in the previous literature on this subject. Time responses, phase portraits and bifurcation diagrams are used to unveil the complex dynamic.

Copyright © 2016 by ASME

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