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Dynamic analysis of a functionally graded simply supported Euler-Bernoulli beam subjected to a moving oscillator

Rajabi, K ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1007/s00707-012-0769-y
  3. Publisher: 2013
  4. Abstract:
  5. The dynamic behavior of a functionally graded (FG) simply supported Euler-Bernoulli beam subjected to a moving oscillator has been investigated in this paper. The Young's modulus and the mass density of the FG beam vary continuously in the thickness direction according to the power-law model. The system of equations of motion is derived by using Hamilton's principle. By employing Petrov-Galerkin method, the system of fourth-order partial differential equations of motion has been reduced to a system of second-order ordinary differential equations. The resulting equations are solved using Runge-Kutta numerical scheme. In this study, the effect of the various parameters such as power-law exponent index and velocity of the moving oscillator on the dynamic responses of the FG beam is discussed in detail. To validate the present formulation, the mid-point displacement of the beam is compared with that of the existing literature, and also a comparison study is performed for free vibration of an FG beam. Good agreement is observed. The results indicated that the above-mentioned parameters have a significant role in the analysis
  6. Keywords:
  7. Comparison study ; Dynamic behaviors ; Euler Bernoulli beams ; Fourth order partial differential equations ; Free vibration ; Functionally graded ; Hamilton's principle ; Mass densities ; Moving oscillators ; Numerical scheme ; Petrov-Galerkin methods ; Power law exponent ; Power law model ; Second-order ordinary differential equations ; Simply supported ; System of equations ; Thickness direction ; Young's Modulus ; Dynamic analysis ; Dynamic response ; Equations of motion ; Galerkin methods ; Ordinary differential equations ; Partial differential equations ; Runge Kutta methods ; Oscillators (mechanical)
  8. Source: Acta Mechanica ; Volume 224, Issue 2 , 2013 , Pages 425-446 ; 00015970 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00707-012-0769-y