Dynamic analysis of a functionally graded simply supported Euler–Bernoulli beam subjected to a moving oscillator
 K. Rajabi,
 M. H. Kargarnovin,
 M. Gharini
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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 powerlaw model. The system of equations of motion is derived by using Hamilton’s principle. By employing Petrov–Galerkin method, the system of fourthorder partial differential equations of motion has been reduced to a system of secondorder ordinary differential equations. The resulting equations are solved using Runge–Kutta numerical scheme. In this study, the effect of the various parameters such as powerlaw 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 midpoint 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 abovementioned parameters have a significant role in the analysis.
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 Title
 Dynamic analysis of a functionally graded simply supported Euler–Bernoulli beam subjected to a moving oscillator
 Journal

Acta Mechanica
Volume 224, Issue 2 , pp 425446
 Cover Date
 20130201
 DOI
 10.1007/s007070120769y
 Print ISSN
 00015970
 Online ISSN
 16196937
 Publisher
 Springer Vienna
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 Authors

 K. Rajabi ^{(1)}
 M. H. Kargarnovin ^{(1)}
 M. Gharini ^{(1)}
 Author Affiliations

 1. School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran