A Refined Theory for Bending Vibratory Analysis of Thick Functionally GradedBeams

A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded-Beams

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
  
© 2021 by IJETT Journal
Volume-69 Issue-4
Year of Publication : 2021
Authors : Zakaria Ibnorachid, Lhoucine Boutahar, Khalid El bikri
DOI :  10.14445/22315381/IJETT-V69I4P209

Citation 

MLA Style: Zakaria Ibnorachid, Lhoucine Boutahar, Khalid El bikri  "A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded-Beams" International Journal of Engineering Trends and Technology 69.4(2021):57-66. 

APA Style:Zakaria Ibnorachid, Lhoucine Boutahar, Khalid El bikri. A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded-Beams  International Journal of Engineering Trends and Technology, 69(4),57-66.

Abstract
A refined beam-theory taking a count the thickness-stretching is presented in this research for bending vibratory behavior analysis of thick FG-beams. In this theory, the number of unknowns is reduced to four instead of five in the other theories. Transverse displacement is expressed through a hyperbolic function and subdivided into bending, shear, and thickness-stretching components. The number of unknowns is so reduced, which involves a decrease of the governing equations number. The boundary conditions at the top and bottom FG-beam faces are satisfied without any shear correction factor. Effective characteristics of FG-beam material change continuously in the thickness direction according to a distribution law depending on the constituents volume proportion. Equations of motion are obtained from Hamilton`s principle and are solved by assuming the Navier’s solution type, for the case of a Simply Supported FG-beam, transversely loaded. Numerical results obtained are exposed and analyzed in detail to verify the validity of the current theory and to prove the influence of the material composition, geometry, shear, and normal deformation on the frequency response and stresses.

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Keywords
Refined beam-theory, Functionally Graded Beam, Thickness stretching.