Analytical Investigation of Free Vibrations in Functionally Graded Material Beams with Different Property Distributions
DOI:
https://doi.org/10.63746/njtd.v22i3.3530Keywords:
vibratory analysis, beams, property gradients, eigenfrequencies, Functionally Graded Materials (FGM)Abstract
This study focuses on the analysis of the vibrational behavior of functionally graded material (FGM) beams, characterized by continuously varying mechanical properties along their thickness. Emphasis is placed on understanding the free vibrations of these structures and determining their eigenfrequencies using the Euler-Bernoulli beam model. The study considers several boundary conditions to evaluate the influence of material property variations on the beam’s dynamics. Three types of distributions are considered to describe the evolution of material properties: the power-law distribution (P-FGM), the exponential distribution (E-FGM), and the sigmoid distribution (S-FGM). This approach allows for a better understanding of the effect of each gradient type on the vibrational performance of the FGM beams and optimizes their design for various engineering applications. The principle of virtual work is applied to establish the equation of motion, and an eigenvalue problem is solved to determine the solutions. The comparison of numerical results with those found in the literature validates the proposed model, confirming its accuracy for the case of an E-FGM beam. Numerous studies are conducted to analyze the impact of the material property distributions on eigenfrequencies, considering various vibration modes and different boundary conditions.
References
Ghorbanpour Arani, A. A., Niknejad, S., & Abbasian Arani, A. A. (2021). Dynamic response of Bi-directional functionally graded materials (BDFGMs) beams rested on visco-pasternak foundation under periodic axial force. Journal of Solid Mechanics, 13(3), 269-285.
Bagheri, H., Kiani, Y., & Eslami, M. R. (2023). Geometrically nonlinear response of FGM beams on elastic foundation subjected to thermal shock. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 47(1), 187-201.
Belarbi, M. O., Khechai, A., Houari, M. S. A., Bessaim, A., Hirane, H., & Garg, A. (2024). Free vibration behavior of sandwich FGM beams: parametric and uncertainty analysis. Journal of Vibration Engineering & Technologies, 12(Suppl 1), 883-905.
Chi, S. H., & Chung, Y. L. (2006). Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis. International Journal of Solids and Structures, 43(13), 3657-3674.
Chikh, A. (2019). Analysis of static behavior of a P-FGM Beam. Journal of Materials and Engineering Structures «JMES», 6(4), 513-524.
Das, P., Benslimane, A., Islam, M. A., Mondal, D., & Nazim, M. S. (2024). A thermo-mechanically loaded rotating FGM cylindrical pressure vessels under parabolic changing properties: An analytical and numerical analysis. Heliyon, 10(4), e25969.
Delale, F., & Erdogan, F. (1983). The crack problem for a nonhomogeneous plane, J. Appl. Mech.50(3),609-614.
Wei, D., Liu, Y., & Xiang, Z. (2012). An analytical method for free vibration analysis of functionally graded beams with edge cracks. Journal of Sound and Vibration, 331(7), 1686-1700.
Elhannani, A., Refassi, K., Elmeiche, A., & Bouamama, M. (2019). Vibration analysis of functionally graded tapered rotor shaft system. Mechanics and Mechanical Engineering, 23(1), 241-245.
Elmeiche, A., Bouamama, M., Elhannani, A., Belaziz, A., & Hammoudi, A. (2022). dynamic modeling of functionally graded beams undergoing mobile mass. Materials Physics & Mechanics, 48(1), 91-105
Esen, I. (2019). Dynamic response of functional graded Timoshenko beams in a thermal environment subjected to an accelerating load. European Journal of Mechanics-A/Solids, 78, 103841.
Gayen, D. (2024). Thermo-elastic buckling and free vibration behavior of functionally graded beams with various materials gradation laws. International Journal on Interactive Design and Manufacturing (IJIDeM), 1-20. https://doi.org/10.1007/s12008-024-02141-1.
Ghorbanpour Arani, A., & Niknejad, S. (2020). Dynamic stability analysis of Euler-Bernoulli and Timoshenko beams composed of bi-directional functionally graded materials. AUT Journal of Mechanical Engineering, 4(2), 201-214.
Hadji, L., Daouadji, T. H., & Bedia, E. A. (2016). Dynamic behavior of FGM beam using a new first shear deformation theory. Earthquakes and Structures, 10(2), 451-461.
Jabbar, N. A., Hussain, I. Y., Abdullah, O. I., & Mohammed, M. N. (2024). Finite element analysis of the thermal and thermo-mechanical coupling problems in the dry friction clutches using functionally graded material. Curved and Layered Structures, 11(1), 20240001.
Karabulut, ?., Karakoc, H., Bilgin, M., Canpolat, H., Krolczyk, G. M., & Sar?kaya, M. (2023). A comparative study on mechanical and ballistic performance of functionally graded Al6061 composites reinforced with B4C, SiC, and Al2O3. Journal of Materials Research and Technology, 23, 5050-5065.
Liu, Z., Nie, M., Yue, T., Jiang, P., Li, X., & Zhang, Z. (2024). Directed energy deposition of functional gradient material to enhance mechanical properties of heterogeneous stainless steels. Optics & Laser Technology, 179, 111326.
Ma, Z., Liu, W., Li, W., Liu, H., Song, J., Liu, Y., ... & Zhang, Y. (2024). Additive manufacturing of functional gradient materials: A review of research progress and challenges. Journal of Alloys and Compounds, 971, 172642.
Mechab. (2011). Study of composite structures using high order theories under thermomechanical loading. Doctoral Thesis, Djilali Liabes University, Sidi Bel Abbes.
Mesbah, A., Belabed, Z., Amara, K., Tounsi, A., Bousahla, A. A., & Bourada, F. (2023). Formulation and evaluation a finite element model for free vibration and buckling behaviours of functionally graded porous (FGP) beams.Structural Engineering and Mechanics,86(3),291-309.
Mishra, A. K., Yadav, K., & Kumar, A. (2023). Selective laser melting of functionally graded material: Current trends and future prospects. In Advances in Additive Manufacturing (pp. 281-297). Elsevier.
Priyanka, R., Twinkle, C. M., & Pitchaimani, J. (2022). Stability and dynamic behavior of porous FGM beam: influence of graded porosity, graphene platelets, and axially varying loads. Engineering with Computers, 38(Suppl 5), 4347-4366.
Quang, V. D., Khoa, N. D., & Duc, N. D. (2021). The effect of structural characteristics and external conditions on the dynamic behavior of shear deformable FGM porous plates in thermal environment. Journal of Mechanical Science and Technology, 35(8), 3323-3329.
Su, X., Hu, T., Zhang, W., Kang, H., Cong, Y., & Yuan, Q. (2024). Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions. Applied Mathematics and Mechanics, 45(6), 983-1000.
Tüfekci, M., Dear, J. P., & Salles, L. (2024). Forced vibration analysis of beams with frictional clamps. Applied Mathematical Modelling, 128, 450-469.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Nigerian Journal of Technological Development
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
In accordance with the Copyright Act of 1976, which became effective January 1, 1978, the following statement signed by each author must accompany the manuscript submitted: "I, the undersigned author, transfer all copyright ownership of the manuscript referenced above to the Nigerian Journal of Technological Development, in the event the work is published. I warrant that the article is original, does not infringe upon any copyright or other proprietary right of any third party, is not under consideration by another journal, and has not been published previously. I have reviewed and approve the submitted version of the manuscript and agree to its publication in the Nigerian Journal of Technological Development." A copyright transfer form should be downloaded from the NJTD Website ( http://njtd.com.ng/index.php/njtd). Author(s) will be consulted, whenever possible, regarding republication of material. All authors must have access to the data presented and the authors and sponsor (if applicable) must agree to share original data with the editor if requested.
