A computational shear displacement model for vibrational analysis of functionally graded beams with porosities

被引:177
作者
Atmane, Hassen Ait [1 ,2 ]
Tounsi, Abdelouahed [1 ,3 ]
Bernard, Fabrice [4 ]
Mahmoud, S. R. [5 ,6 ]
机构
[1] Univ Djillali Liabes Sidi Bel Abbes, Dept Civil Engn, Fac Technol, Mat & Hydrol Lab, Sidi Bel Abbes, Algeria
[2] Univ Hassiba Ben Bouali Chlef, Fac Genie Civil & Architecture, Chlef, Algeria
[3] Univ Djillali Liabes Sidi Bel Abbes, Lab Struct & Mat Avances Genie Civil & Travaux Pu, Fac Technol, Dept Genie Civil, Sidi Bel Abbes, Algeria
[4] INSA Rennes, Lab Genie Civil & Genie Mecan, Rennes, France
[5] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia
[6] Univ Sohag, Dept Math, Fac Sci, Sohag, Egypt
关键词
FG beam; shear deformation theory; vibration; porosity; HIGHER-ORDER SHEAR; THERMOMECHANICAL BENDING RESPONSE; NEUTRAL SURFACE POSITION; DEFORMATION-THEORY; BUCKLING PROPERTIES; CYLINDRICAL-SHELLS; CARBON NANOTUBES; WAVE-PROPAGATION; SANDWICH PLATES; STATIC ANALYSIS;
D O I
10.12989/scs.2015.19.2.369
中图分类号
TU [建筑科学];
学科分类号
0813 ;
摘要
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.
引用
收藏
页码:369 / 384
页数:16
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