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Non-linear vibration analysis of laminated composite plates resting on non-linear elastic foundations

Pirbodaghi, T ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jfranklin.2010.12.002
  3. Publisher: 2011
  4. Abstract:
  5. In this study, the homotopy analysis method (HAM) is used to obtain an approximate analytical solution for geometrically non-linear vibrations of thin laminated composite plates resting on non-linear elastic foundations. Geometric non-linearity is considered using von Karman's straindisplacement relations. Then, the effects of the initial deflection, ply properties, aspect ratio of the plate and foundation parameters on the non-linear free vibration is studied. Comparison between the obtained results and those available in the literature demonstrates the potential of HAM for the analysis of such vibration problems, whose governing differential equations include the quadratic and cubic non-linear terms. This study shows that only a first-order approximation of the HAM leads to highly accurate solutions for this type of non-linear problems
  6. Keywords:
  7. Approximate analytical solutions ; First-order approximations ; Geometric non-linearity ; Governing differential equations ; Homotopy analysis methods ; Initial deflection ; Laminated composite plates ; Non-linear ; Non-linear free vibration ; Non-linear vibrations ; Nonlinear problems ; Strain-displacement relation ; Vibration problem ; Von Karman ; Aspect ratio ; Differential equations ; Laminated composites ; Laminating ; Plates (structural components) ; Vibration analysis
  8. Source: Journal of the Franklin Institute ; Volume 348, Issue 2 , March , 2011 , Pages 353-368 ; 00160032 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0016003210002735