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Nonlinear Torsional Vibrations of Thin Walled Beam with Semi-Analytic Methods

Sina, Ali | 2014

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47000 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Haddadpour, Hassan
  7. Abstract:
  8. Thin Walled Beams are widely used in engineering applications with the minimum weight design criteria, ranging from civil to aerospace and many other industrial fields. The weight reduction of the beam leads to importance of the dynamic behavior of the structure. Frequently used thin walled beams have low torsional stiffness and their torsional deformations may be of such magnitudes that it is not adequate to treat the angles of cross section rotation as small. When the vibration amplitudes are moderate or large, the geometric nonlinearity must be included and some new phenomena which do not exist in linear torsional dynamic come into play. Unfortunately, the equations of motion of nonlinear systems are very complicated and there are no exact or analytical solutions, in most cases. Approximate solutions such as perturbation methods can be used to investigate the global and qualitative behavior of the nonlinear systems. In this thesis, nonlinear torsional vibrations of thin walled beams will be investigated. The method of multiple scales will be implemented as solution method and different nonlinear phenomena will be studied. The obtained results are compared with the available results in the literature that are obtained from boundary element and finite element methods which reveals an excellent agreement between different solution methodologies. The outcomes of this study show that beam nonlinear torsional dynamics and the related phenomena could influence the linear torsional dynamic of beams under axial load (e.g. rotating beams). On the other hand, free and forced torsional vibrations of beam have been investigated. nonlinear torsional modes, corresponding frequencies and their stability in different torsional boundary conditions have been investigated. It has been demonstrated that in the case of beam with two ends clamped boundary conditions, three-to-one internal resonance will be appeared. Finally, forced torsional vibrations of beam with the excitation in the form of primary resonance of first and second mode have been investigated. Fixed points of the nonlinear system and their stability have also been studied
  9. Keywords:
  10. Thin Walled Beam ; Nonlinear Vibration ; Torsional Vibration ; Perturbation Method ; Trapezoidal Effect ; Nonlinear Modes ; Three-to-one Internal Resonance ; Primary Resonance

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