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Nonlinear normal modes of axial-torsional vibrations of rotating thin walled composite beam

Sina, S ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. Publisher: Katholieke Universiteit Leuven , 2012
  3. Abstract:
  4. The aim of this study is to carry out the numerical computation of nonlinear normal modes for rotating pretwisted composite thin-walled beam in axial-torsional vibrations. The structural model considered here, incorporates a number of non-classical effects such as primary and secondary warping, non-uniform torsional model, rotary inertia and pretwist angle. Ignoring the axial inertia term leads to differential equation of motion in terms of angle of twist in the case of axially immovable beam ends. The governing differential equations of motion are derived using Hamilton's principle and the reduced model around the static equilibrium position is obtained using 2-mode Galerkin discretization technique. The nonlinear normal modes of the reduced model are then computed using a numerical algorithm combining shooting and pseudo-arclength continuation. Also, the method of multiple scales is used as analytical tool to solve the time domain equations and derive the equations governing the modulation of the amplitudes and phases of the vibration modes. Both fundamental and internal resonance cases are considered. Utilizing numerical methods, the nonlinear torsional behavior of rotating blade in moderately high energy levels is attainable while regular perturbation techniques are not applicable. This study can be a preliminary step in the understanding of complex dynamics of such systems in internal resonance excited by external resonant excitations
  5. Keywords:
  6. Algorithms ; Elastic waves ; Equations of motion ; Machine vibrations ; Perturbation techniques ; Structural dynamics ; Thin walled structures ; Galerkin discretization ; Governing differential equations ; Method of multiple scale ; Nonlinear normal modes ; Numerical computations ; Regular perturbation technique ; Thin-walled composite beam ; Time domain equation ; Beams and girders
  7. Source: International Conference on Noise and Vibration Engineering 2012, ISMA 2012, including USD 2012: International Conference on Uncertainty in Structure Dynamics, 17 September 2012 through 19 September 2012 ; Volume 4 , September , 2012 , Pages 2547-2556 ; 9781622768257 (ISBN)
  8. URL: https://www.isma-isaac.be/past/conf/isma2012/proceedings/papers/isma2012_0737.pdf