Free vibration analysis of functionally graded beams using a higher-order shear deformation theory

Free vibration analysis of functionally graded beams using a higher-order shear deformation theory

Zaoui F. ZohraHanifi H. A. Lemya Younsi Abderahman Meradjah Mustapha Tounsi Abdelouahed Ouinas Djame 

Laboratory of numerical and experimental modeling of the mechanical phenomena, Mechanical Engineering Department, Faculty of sciences and Technology / Ibn Badis University, Mostaganem 27000, Algeria

Laboratoire de Ressources Hydriques et Environnement, Civil Engineering Department, Faculty of Technology/ University of Moulay Tahar, Saïda 20000, Algeria

Material and Hydrology Laboratory, Civil Engineering Department, Faculty of sciences and Technology/ University of Sidi Bel Abbes 22000, Algeria

Material and Hydrology Laboratory, Civil Engineering Department, Faculty of sciences and Technology/ University of Sidi Bel Abbes 22000, Algeria

Material and Hydrology Laboratory, Civil Engineering Department, Faculty of sciences and Technology/ University of Sidi Bel Abbes 22000, Algeria

Laboratory of numerical and experimental modeling of the mechanical phenomena, Mechanical Engineering Department, Faculty of sciences and Technology / Ibn Badis University, Mostaganem 27000, Algeria

Corresponding Author Email: 
fatima.zaoui@univ-mosta.dz
Page: 
7-12
|
DOI: 
https://doi.org/10.18280/mmep.040102
Received: 
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Accepted: 
|
Published: 
31 March 2017
| Citation

OPEN ACCESS

Abstract: 

This paper presents an analytical solution to the free vibration analysis of functionally graded beams by using a refined hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of beams is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. Equations of motion are derived from Hamilton’s principle and Navier-type analytical solutions for simply supported beams are compared with the existing solutions to verify the validity of the developed theory. Numerical results are obtained to investigate the effects of the power-law index and sideto-thickness ratio on the natural frequencies. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of FG beams.

Keywords: 

Analytical Modeling, Beam, Functionally Graded Material, Natural Frequencies, Free Vibration

1. Introduction
2. Theoretical Formulations
3. Analytical Solutions
4. Numerical Results and Discussion
5. Conclusions
Acknowledgement
Nomenclature
  References

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