Buy article PDF
The purchased file will be sent to you
via email after the payment is completed.
US$ 35
|
Steel and Composite Structures Volume 19, Number 2, August 2015 , pages 369-385 DOI: https://doi.org/10.12989/scs.2015.19.2.369 |
|
|
|
A computational shear displacement model for vibrational analysis of functionally graded beams with porosities |
||
Hassen Ait Atmane, Abdelouahed Tounsi, Fabrice Bernard and S.R. Mahmoud
|
||
| Abstract | ||
| This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton\'s principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams. | ||
| Key Words | ||
| FG beam; shear deformation theory; vibration; porosity | ||
| Address | ||
| (1) Hassen Ait Atmane, Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (2) Hassen Ait Atmane: Faculté de Génie Civil et D\'Architecture, Université Hassiba Ben Bouali Chlef, Algérie; (3) Abdelouahed Tounsi: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algeria; (4) Fabrice Bernard: Laboratoire de Génie Civil et Génie Mécanique INSA de Rennes, France; (5) S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia; (6) S.R. Mahmoud: Mathematics Department, Faculty of Science, University of Sohag, Egypt. | ||