Effect of Material Composition on Free Vibration of Bidirectional Functionally Graded Beam via a Quasi-3D Theory
Keywords:
free vibration; bidirectional functionally graded beam; quasi- 3D theory; aspect ratio.Abstract
In this paper, the influence of material composition on free vibration of bidirectional functionally graded beam using a quasi-3D theory is investigated. The material properties are assumed to be graded in both the thickness and longitudinal directions by power gradation laws and four different distribution patterns are considered. Equations of motion based on a quasi-3D model that contains undetermined integral forms and involves few unknowns to derive, are obtained from Hamilton's principle. The problem is solved using the Navier solution for a simply supported beam. The accuracy of the present solution is demonstrated by comparing it with some results available in the literature and a good agreement is showed. Effects on the fundamental frequencies are examined and highlighted.doi: https://doi.org/10.55787/jtams.2026.1.AI00038
References
M. KOIZUMI (1993) The concept of FGM. Ceramic Transactions, Functionally Gradient Materials 34 3-10.
M. KOIZUMI (1997) FGM activities in Japan. Composites Part B: Engineering 28(1-2) 1-4.
C. LÜ , C. LIM, W. CHEN (2009) Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory. International Journal of Solids and Structures 46 1176-118.
M. RAHAEIFARD, M. KAHROBAIYAN, M. AHMADIAN (2009) Sensitivity Analysis of Atomic Force Microscope Cantilever Made of Functionally Graded Materials. In: Proceedings of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, San Diego, California, USA, August 30 –September 2, 2009.
B. ZHANG, Y. HE, D. LIU, Z. GAN, Y. HE, L. SHEN (2014) Size-dependent functionally graded beam model based on an improved third-order shear deformation theory. European Journal of Mechanics A/Solids 47 211-230.
M. ŞIMŞEK (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Engineering and Design 240 697–705.
M. BOURADA, A. KACI, M.S.A. HOUARI, A. TOUNSI (2015) A new simple shear and normal deformations theory for functionally graded beams. Steel Composite Structures 18 409-423.
H.T. THAI, T.P. VO (2012) Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences 62 57-66.
R.B. BOUIADJRA, A. BACHIRI, S. BENYOUCEF, B. FAHSI, F. BERNARD (2020) An investigation of the thermodynamic effect on the response of FG beam on elastic foundation. Structural Engineering and Mechanics 76(1) 115-127.
A. BACHIRI, M. BOURADA, A. MAHMOUDI, S. BENYOUCEF, A. TOUNSI (2018) Thermodynamic effect on the bending response of elastic foundation FG plate by using a novel four variable refined plate theory. Journal of Thermal Stresses 41(8) 1042-1062.
I. BENABERRAHMANE, S. BENYOUCEF, M. SEKKAL, M. MEKERBI, R.B. BOUIADJRA, M.M. SELIM, A. TOUNSI, M. HUSSAIN (2021) Investigating of free vibration behavior of bidirectional FG beams resting on variable elastic foundation. Geomechanics and Engineering 25(5) 383-394.
A.G. ARANI, SH. NIKNEJAD, A. MIHANKHAH, I. SAFARI (2022) Dynamic Stability Analysis of Bi-Directional Functionally Graded Beam with Various Shear Deformation Theories Under Harmonic Excitation and Thermal Environment. Journal of Solid Mechanics 14(3) 272-290.
T.T. TRAN, D.K. NGUYEN (2018) Free vibration of two-directional FGM beams using a higher-order Timoshenko beam element. Vietnam Journal of Science and Technology 56(3) 380-396.
Y. LU, X. CHEN (2020) Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams. Shock and Vibration 1-13.
J. WU, L. CHEN, R. WU, X. CHEN (2021) Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam. Shock and Vibration 1-13.
A.A. DAIKH, M.O. BELARBI, A. KHECHAI, L. LI, S. KHATIR, A.A. ABDELRAHMAN, M.A. ELTAHER (2023) Bending of Bi-directional inhomogeneous nanoplates using microstructure-dependent higher-order shear deformation theory. Engineering Structures 291 1-21.
S.N. BALIREDDY, J. PITCHAIMANI (2022) Stability and dynamic behaviour of bidirectional functionally graded beam subjected to variable axial load. Materials Today Communications 32 104043.
A. KARAMANLI, T.P. VO (2021) Bending, vibration, buckling analysis of bidirectional FG porous microbeams with a variable material length scale parameter. Applied Mathematical Modelling 91 723-748.
T.T. TRUONG, T. NGUYEN-THOI, J. LEE (2019) Isogeometric size optimization of bi-directional functionally graded beams under static loads. Composite structures 227 111259.
A. KARAMANLI, M. AYDOGDU (2019) Size dependent flapwise vibration analysis of rotating two-directional functionally graded sandwich porous microbeams based on a transverse shear and normal deformation theory. International Journal of Mechanical Sciences 159 165-181.
M. ŞIMŞEK (2015) Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions. Composite Structures 133 968-978
Q.H. PHAM, V.K. TRAN, P.C. NGUYEN (2022) Hygro-thermal vibration of bidirectional functionally graded porous curved beams on variable elastic foundation using generalized finite element method. Case Studies in Thermal Engineering 40 1-20.
A. KARAMANLI (2017) Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory. Composite Structures 174 70-86.
L.C. TRINH, T.P. VO, H.T. THAI, T.K. NGUYEN (2018) Size-dependent vibration of bi-directional functionally graded microbeams with arbitrary boundary conditions. Composites Part B: Engineering 134 225-245.
A. KARAMANLI, T.P. VO (2018) Size dependent bending analysis of two directional functionally graded microbeams via a quasi-3D theory and finite element method. Composites Part B: Engineering 144 171-183.
A. SAIMI, I. BENSAID, ¨O. CIVALEK (2023) A study on the crack presence effect on dynamical behaviour of bi-directional compositionally imperfect material graded micro beams. Composite structures 316 117032.
