Free geometrically nonlinear oscillations of perfect and imperfect laminates with curved fibres by the shooting method

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• 作者：Hamed Akhavan ; Pedro Ribeiro
• 关键词：Free vibration ; Nonlinear dynamics ; Bifurcation ; Curvilinear fibres
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：81
• 期：1-2
• 页码：949-965
• 全文大小：1,625 KB
• 参考文献：1.Ribeiro, P., Akhavan, H., Teter, A., Warminski, J.: A review on the mechanical behaviour of curvilinear fibre composite laminated panels. J. Compos. Mater. 48(22), 2761-777 (2014). doi:10.-177/-021998313502066-/span> View Article
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  4.Akhavan, H., Ribeiro, P., de Moura, M.F.S.F.: Large deflection and stresses in variable stiffness composite laminates with curvilinear fibres. Int. J. Mech. Sci. 73, 14-6 (2013)View Article
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  7.Akhavan, H., Ribeiro, P., De Moura, M.: Composite laminates with linearly varying fiber angles under static and dynamic loads. In: 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2013)
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• 作者单位：Hamed Akhavan (1)
  Pedro Ribeiro (1)
  
  1. DEMec, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

Large-amplitude free vibrations of composite laminated plates with curvilinear fibres are studied. The fibre angle in a ply changes linearly in relation to one Cartesian coordinate. The plates are rectangular with geometric imperfections (out-of-planarity). The edges of the laminates are clamped, except in comparison studies, where simply supported conditions are applied. The displacement field is modelled by a third-order shear deformation theory, and the equations of motion (full model), in the time-domain, are obtained using a \(p\)-version finite element method. When possible, the model is statically condensed neglecting in-plane inertias but still taking into account the in-plane displacements. The condensed model is transformed to modal coordinates in order to have a model with fewer degrees of freedom (reduced model). Backbone curves are found by the shooting method, using Runge–Kutta–Fehlberg method modified with Cash–Karp method to control the error with adaptive stepsize. Backbone curves of composite laminates with different curvilinear fibre angles are plotted and compared. In addition to the fundamental backbone curve, the method is able to find bifurcations leading to other branches, as shown in some examples. Oscillations of some points are studied in detail using phase-plane plots and Fourier spectra of deflection. Finally, the effects of geometrical imperfection on the backbone curves are analysed.