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Free Vibration Analysis of FGM Beams With Different Boundary Conditions Using RKPM Meshless Method

[+] Author Affiliations
R. Saljooghi, M. T. Ahmadian

Sharif University of Technology, Tehran, Iran

Paper No. DETC2011-47640, pp. 1187-1191; 5 pages
doi:10.1115/DETC2011-47640
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5478-5
  • Copyright © 2011 by ASME

abstract

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.

Copyright © 2011 by ASME

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