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Free vibration analysis of FGM beams with different boundary conditions using RKPM meshless method

Saljooghi, R ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1115/DETC2011-47640
  3. Abstract:
  4. This paper presents free vibration analysis of functionally graded material (FGM) beams with different boundary conditions, using RKPM (Reproducing Kernel Particle Method), which is a meshless method. System of equations of motion is derived by using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of beam are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is applied to obtain eigenvalue equation of vibration and natural frequencies are obtained. It should be noted that for special cases where the beam is uniform, natural frequencies match nicely with theoretical prediction
  5. Keywords:
  6. Different boundary condition ; Eigenvalue equations ; Euler Bernoulli beam theory ; Free-vibration analysis ; Lagrange's method ; Material property ; Mesh-less methods ; Power-law ; Reproducing kernel particle method ; System of equations ; Theoretical prediction ; Thickness direction ; Design ; Eigenvalues and eigenfunctions ; Equations of motion ; Functionally graded materials ; Lagrange multipliers ; Natural frequencies ; Structural analysis ; Vibration analysis ; Boundary conditions
  7. Source: Proceedings of the ASME Design Engineering Technical Conference, 28 August 2011 through 31 August 2011 ; Volume 1, Issue PARTS A AND B , August , 2011 , Pages 1187-1191 ; 9780791854785 (ISBN)
  8. URL: http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1639319