A Ritz Formulation for Vibration Analysis of Axially Functionally Graded Timoshenko-Ehrenfest Beams

Document Type : Research Paper


Trakya University, Mechanical Engineering Department, 22130, Edirne, Turkey


Dynamics of beams made of axially grading material has been analyzed in present work. Shear deformation and rotational inertia of the rectangular cross-sectional beam have been considered using Timoshenko-Ehrenfest beam model. Material properties of the beam have been assumed as a power-law function. Solution of the vibration problem of the axially functionally graded Timoshenko-Ehrenfest beam has been carried out with Ritz formulation. Present model has been validated with the previous literature works. Effects of power-law index parameter and grading material properties on the dynamics of axially functionally graded Timoshenko-Ehrenfest beam have been investigated. Transverse deflection and slope of the beam have been depicted in various cases. Present study can give useful results for designing of axially graded structural elements.


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Volume 53, Issue 1
March 2022
Pages 102-115
  • Receive Date: 16 November 2021
  • Revise Date: 05 January 2022
  • Accept Date: 05 January 2022