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Analysis of large amplitude free vibrations of unsymmetrically laminated composite beams on a nonlinear elastic foundation

Jafari Talookolaei, R. A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1007/s00707-010-0439-x
  3. Publisher: 2011
  4. Abstract:
  5. The large amplitude free vibration of an unsymmetrically laminated composite beam (LCB) on a nonlinear elastic foundation subjected to axial load has been studied. The equation of motion for the axial and transverse deformations of a geometrically nonlinear LCB is derived. Using the Ritz method, the governing equation is reduced to a time-dependent Duffing equation with quadratic and cubic nonlinearities. The homotopy analysis method (HAM) is used to obtain exact expressions for the dynamic response of the LCB. This study shows that the third-order approximation of the HAM leads to highly accurate solutions that are valid for a wide range of vibration amplitudes. The effects of different parameters on the ratio of nonlinear to linear natural frequency of beams and the post-buckling load-deflection relationship are studied
  6. Keywords:
  7. Cubic nonlinearities ; Duffing equations ; Geometrically nonlinear ; Governing equations ; Homotopy analysis methods ; Laminated composite beam ; Large amplitude free vibration ; Load-deflection relationships ; Nonlinear elastic foundation ; Postbuckling ; Ritz methods ; Third-order ; Time-dependent ; Transverse deformation ; Vibration amplitude ; Buckling ; Composite beams and girders ; Control nonlinearities ; Dynamic response ; Equations of motion ; Laminated composites ; Laminating ; Nonlinear equations ; Vibration analysis
  8. Source: Acta Mechanica ; Volume 219, Issue 1-2 , January , 2011 , Pages 65-75 ; 00015970 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00707-010-0439-x