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Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation

Fallah, A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1016/j.euromechsol.2011.01.005
  3. Publisher: 2011
  4. Abstract:
  5. In this study, simple analytical expressions are presented for large amplitude free vibration and post-buckling analysis of functionally graded beams rest on nonlinear elastic foundation subjected to axial force. Euler-Bernoulli assumptions together with Von Karman's strain-displacement relation are employed to derive the governing partial differential equation of motion. Furthermore, the elastic foundation contains shearing layer and cubic nonlinearity. He's variational method is employed to obtain the approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of this method. Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the effect of vibration amplitude, elastic coefficients of foundation, axial force, and material inhomogenity are presented for future references
  6. Keywords:
  7. Analytical expressions ; Axial forces ; Buckling loads ; Closed form solutions ; Cubic nonlinearities ; Effect of vibration ; Elastic coefficient ; Elastic foundation ; Euler-Bernoulli ; Functionally graded beams ; Governing equations ; Large amplitude free vibration ; New results ; Non-linear free vibration ; Non-linear vibrations ; Nonlinear elastic foundation ; Post-buckling analysis ; Strain-displacement relation ; Variational methods ; Von Karman ; Axial flow ; Buckling ; Control nonlinearities ; Equations of motion ; Foundations ; Nonlinear analysis ; Nonlinear equations ; Partial differential equations ; Plates (structural components) ; Vibration analysis
  8. Source: European Journal of Mechanics, A/Solids ; Volume 30, Issue 4 , July , 2011 , Pages 571-583 ; 09977538 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0997753811000155