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Nonlinear free vibrations of thin-walled beams in torsion

Sina, S. A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1007/s00707-012-0688-y
  3. Publisher: 2012
  4. Abstract:
  5. Nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warpings are investigated. The coupled nonlinear torsional-axial equations of motion are considered. Ignoring the axial inertia term leads to a differential equation of motion in terms of angle of twist. Two sets of torsional boundary conditions, that is, clamped-clamped and clamped-free boundary conditions are considered. The governing partial differential equation of motion is discretized and transformed into a set of ordinary differential equations of motion using Galerkin's method. Then, the method of multiple scales is used to solve the time domain equations and derive the equations governing the modulation of the amplitudes and phases of the vibration modes. The obtained results are compared with the available results in the literature that are obtained from boundary element and finite elementmethods,which reveals an excellent agreement between different solution methodologies. Finally, the internal resonance and the stability of coupled and uncoupled nonlinear modes are investigated. This study can be a preliminary step in the understanding of complex dynamics of such systems in internal resonance excited by external resonant excitations
  6. Keywords:
  7. Axial inertia ; Boundary elements ; Complex dynamics ; Galerkin's method ; Internal resonance ; Method of multiple scale ; Non-linear free vibration ; Nonlinear mode ; Resonant excitation ; Solution methodology ; Thin-walled beam ; Time domain equation ; Torsional vibration ; Vibration modes ; Warpings ; Equations of motion ; Galerkin methods ; Ordinary differential equations ; Partial differential equations ; Thin walled structures ; Boundary conditions
  8. Source: Acta Mechanica ; Volume 223, Issue 10 , 2012 , Pages 2135-2151 ; 00015970 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00707-012-0688-y