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Nonlinear free vibration of nanobeams with surface effects considerations

Fallah, A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1115/DETC2011-48373
  3. Publisher: 2011
  4. Abstract:
  5. In this paper, simple analytical expressions are presented for geometrically non-linear vibration analysis of thin nanobeams with both simply supported and clamped boundary conditions. Gurtin-Murdoch surface elasticity together with Euler-Bernoulli beam theory is used to obtain the governing equations of motions of the nanobeam with surface effects consideration. The governing nonlinear partial differential equation is reduced to a single nonlinear ordinary differential equation using Galerkin technique. He's variational approach is employed to obtain analytical solution for the resulted nonlinear governing equation. The effects of different parameters such as vibration amplitude, boundary conditions, and beam dimensions on the natural frequencies of nanobeams are investigated and results are presented for future studies
  6. Keywords:
  7. Analytical expressions ; Euler Bernoulli beam theory ; Galerkin technique ; Governing equations ; Governing equations of motion ; Non-linear free vibration ; Non-linear vibrations ; Nonlinear ordinary differential equation ; Nonlinear partial differential equations ; Simply supported ; Surface effect ; Surface elasticities ; Variational approaches ; Vibration amplitude ; Boundary conditions ; Design ; Elasticity ; Equations of motion ; Nanowires ; Ordinary differential equations ; Partial differential equations ; Stress analysis ; Nonlinear equations
  8. Source: Proceedings of the ASME Design Engineering Technical Conference, 28 August 2011 through 31 August 2011 ; Volume 7 , August , 2011 , Pages 191-196 ; 9780791854846 (ISBN)
  9. URL: http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1641194