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Nonlinear free vibrations of a Timoshenko beam using multiple scales method

Ramezani, A ; Sharif University of Technology | 2004

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  1. Type of Document: Article
  2. DOI: 10.1115/esda2004-58298
  3. Publisher: American Society of Mechanical Engineers , 2004
  4. Abstract:
  5. In this paper, the large amplitude free vibration of a cantilever Timoshenko beam is considered. To this end, first Hamilton's principle is used in deriving the partial differential equation of the beam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the thick-cantilevered beam
  6. Keywords:
  7. Boundary conditions ; Vibration control ; Shear deformation ; Perturbation techniques ; Natural frequencies ; Hamiltonians ; Galerkin methods
  8. Source: Proceedings of the 7th Biennial Conference on Engineering Systems Design and Analysis - 2004, Manchester, 19 July 2004 through 22 July 2004 ; Volume 2 , 2004 , Pages 101-106 ; 0791841731 (ISBN); 9780791841730 (ISBN)
  9. URL: https://asmedigitalcollection.asme.org/ESDA/proceedings-abstract/ESDA2004/4174X/101/305547