[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.12989/scs.2015.19.2.369

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

Atmane, Hassen Ait (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bernard, Fabrice (Laboratoire de Genie Civil et Genie Mecanique INSA de Rennes)
Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)

Publication Information

Steel and Composite Structures / v.19, no.2, 2015 , pp. 369-384 More about this Journal

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.

Keywords

FG beam; shear deformation theory; vibration; porosity;

Citations & Related Records

Times Cited By KSCI : 14 (Citation Analysis)

Reference
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4	(2015) Wind & structures A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams / 27 (4) , 269
2	(2015) Structural engineering and mechanics : An international journal An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models / 69 (2) , 231
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2	(2019) Geomechanics & engineering Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections / 17 (2) , 175
3	(2015) Materials research express Strain gradient based dynamic response analysis of heterogeneous cylindrical microshells with porosities under a moving load / 6 (3) , 035029
5	(2015) Structural engineering and mechanics : An international journal Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT / 69 (5) , 511
6	(2019) Steel & Composite structures : an international journal Free vibration of imperfect sigmoid and power law functionally graded beams / 30 (6) , 603
3	(2015) Smart structures and systems Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers / 23 (3) , 215
2	(2015) Mechanics of composite materials Assessing the Effects of Porosity on the Bending, Buckling, and Vibrations of Functionally Graded Beams Resting on an Elastic Foundation by Using a New Refined Quasi-3D Theory / 55 (2) , 219
5	(2015) European physical journal Plus Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency / 134 (5) , 214
3	(2015) Coupled systems mechanics Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities / 8 (3) , 247
2	(2015) Structural monitoring and maintenance Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities / 6 (2) , 147
1	(2019) Steel & Composite structures : an international journal Static stability analysis of axially functionally graded tapered micro columns with different boundary conditions / 33 (1) , 133
4	(2015) Computers & concrete Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT / 24 (4) , 347
5	(2015) Earthquakes and structures Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory / 17 (5) , 447
24	(2019) Arabian journal of geosciences Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation / 12 (24) , 809
5	(2015) Steel & Composite structures : an international journal Wave dispersion properties in imperfect sigmoid plates using various HSDTs / 33 (5) , 699
2	(2015) Advances in nano research Nonlocal strain gradient effects on forced vibrations of porous FG cylindrical nanoshells / 8 (2) , 149
1	(2020) Structural monitoring and maintenance A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads / 7 (1) , 27
1	(2020) Steel & Composite structures : an international journal Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory / 35 (1) , 147
3	(2015) Steel & Composite structures : an international journal Transversely isotropic thin circular plate with multi-dual-phase lag heat transfer / 35 (3) , 343
4	(2015) Steel & Composite structures : an international journal Nonlocal nonlinear dynamic behavior of composite piezo-magnetic beams using a refined higher-order beam theory / 35 (4) , 545
4	(2020) Steel & Composite structures : an international journal Post-buckling of higher-order stiffened metal foam curved shells with porosity distributions and geometrical imperfection / 35 (4) , 567
6	(2015) Computers & concrete Assessment of transient vibrations of graphene oxide reinforced plates under pulse loads using finite strip method / 25 (6) , 575
2	(2015) Structural monitoring and maintenance Dynamic response of size-dependent porous functionally graded beams under thermal and moving load using a numerical approach / 7 (2) , 69
3	(2015) Structural engineering and mechanics : An international journal Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method / 76 (3) , 413
2	(2020) Structural monitoring and maintenance Numerical investigation on scale-dependent vibrations of porous foam plates under dynamic loads / 7 (2) , 85
2	(2020) Smart structures and systems Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model / 26 (2) , 253
6	(2015) Structural engineering and mechanics : An international journal Porosity effects on post-buckling behavior of geometrically imperfect metal foam doubly-curved shells with stiffeners / 75 (6) , 701
2	(2015) European physical journal Plus A compressive study for porous FG curved nanobeam under various boundary conditions via a nonlocal strain gradient theory / 136 (2) , 248
3	(2015) Advances in nano research Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory / 10 (3) , 281
1	(2015) Steel & Composite structures : an international journal Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory / 39 (1) , 95
1	(2015) Geomechanics & engineering Analyzing dynamic response of nonlocal strain gradient porous beams under moving load and thermal environment / 26 (1) , 89
2	(2021) Steel & Composite structures : an international journal Investigating dynamic response of nonlocal functionally graded porous piezoelectric plates in thermal environment / 40 (2) , 243
6	(2021) Steel & Composite structures : an international journal Numerical forced vibration analysis of compositionally gradient porous cylindrical microshells under moving load and thermal environment / 40 (6) , 893