Home / Regular Issue / JST Vol. 29 (3) Jul. 2021 / JST-2475-2021

 

Analytical and Numerical Investigation of Free Vibration Behavior for Sandwich Plate with Functionally Graded Porous Metal Core

Emad Kadum Njim, Sadeq H. Bakhy and Muhannad Al-Waily

Pertanika Journal of Science & Technology, Volume 29, Issue 3, July 2021

DOI: https://doi.org/10.47836/pjst.29.3.39

Keywords: Free vibration, frequency, functionally graded, porous, sandwich plate

Published on: 31 July 2021

The current work presents a free vibration analysis of a simply supported rectangular functionally graded sandwich plate using a new analytical model. The core of the sandwich plate is made up of porous metal, and the top and bottom faces are made up of homogenous materials. The core metal properties are assumed to be porosity dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The contribution of this paper is to evaluate the performance of functionally graded porous materials (FGPMs) as it is used for many biomedical applications, particularly in tissue engineering. Theoretical formulations are based on the classical plate theory to find the free vibration characteristics of the imperfect FGM sandwich plate and include different parameters. Parameters included are graded distributions of porosity, power-law index, core metal type, and aspect ratios. A numerical investigation using finite element analysis (FEA) and the modal analysis was conducted with the assistance of the commercial ANSYS-2020-R2 software to validate the analytical solution. To detect the various parameters influencing the fundamental frequencies of sandwich plate comprehensive numerical results are presented in dimensionless tabular and graphical forms. The results reveal that the frequency parameter of the sandwich plate increases with the increase of the porosity parameter and number of the constraints in the boundary conditions. Furthermore, the increase in the number of layers leads to an increase in the accuracy of the results for the same FGM core thickness. An accepted agreement can be observed between the proposed analytical solution and numerical results with a maximum error discrepancy of 8%.

  • Al-Waily, M., Al-Shammari, M. A., & Jweeg, M. J. (2020). An analytical investigation of thermal buckling behavior of composite plates reinforced by carbon nano-particles. Engineering Journal, 24(3),11-21. https://doi.org/10.4186/ej.2020.24.3.11

  • Ambartsumyan, S. A., Ashton, J. E. (Ed), & Cheron, T. (Trans). (1970). Theory of Anisotropic Plates: Strength, Stability, and Vibration (Progress in Materials Science Series, Vol. 2). Technomic Publishing Company

  • Anderson, T. (2003). A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere. Composite Structures, 60(3), 265-274. https://doi.org/10.1016/S0263-8223(03)00013-8

  • Baferani, A. H., Saidi, A. R., & Ehteshami, H. (2011). Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation. Composite Structures, 93(7), 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020

  • Bonnheim, N., Ansari, F., Regis, M., Bracco, P., & Pruitt, L. (2019). Effect of carbon fiber type on monotonic and fatigue properties of orthopedic grade PEEK. Journal of the mechanical behavior of biomedical materials, 90, 484-492. https://doi.org/10.1016/j.jmbbm.2018.10.033

  • Burlayenko, V. N., & Sadowski, T. (2020). Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements. Meccanica, 55(4), 815-832. https://doi.org/10.1007/s11012-019-01001-7

  • Chakraverty, S., & Pradhan, K. K. (2014). Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions. Aerospace Science and Technology, 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005

  • Chi, S., & Chung, Y. (2006). Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis. International Journal of Solids and Structures, 43(13), 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011

  • Coskun, S., Kim, J., & Toutanji, H. (2019). Bending, free vibration, and buckling analysis of functionally graded porous micro-plates using a general third-order plate theory. Journal of Composites Science, 3(1), Article 15. https://doi.org/10.3390/jcs3010015

  • Cui, J., Zhou, T., Ye, R., Gaidai, O., Li, Z., & Tao, S. (2019). Three-dimensional vibration analysis of a functionally graded sandwich rectangular plate resting on an elastic foundation using a semi-analytical method. Materials, 12(20), Article 3401. https://doi.org/10.3390/ma12203401

  • Dang, Y. H., Li, Y. H., Chen, D., & Yang, J. (2018). Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion. Composites Part B: Engineering, 145, 1-13. https://doi.org/10.1016/j.compositesb.2018.03.009

  • Goel, M. D., Matsagar, V. A., Marburg, S., & Gupta, A. K. (2013). Comparative performance of stiffened sandwich foam panels under impulsive loading. Journal of performance of constructed facilities, 27(5), 540-549. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000340

  • Hadji, L., Atmane, H. A., Tounsi, A., Mechab, I., & Bedia, E. A. (2011). Free vibration of functionally graded sandwich plates using four-variable refined plate theory. Applied Mathematics and Mechanics, 32, 925-942. https://doi.org/10.1007/s10483-011-1470-9

  • Hayat, S., & Meriem, S. (2019). Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminium (Al) and Alumina (Al2O3) embedded in an elastic medium. Frattura ed Integrità Strutturale, 13(50), 286-299. https://doi.org/10.3221/IGF-ESIS.50.24

  • Kapuria, S., Bhattacharyya, M., & Kumar, A. N. (2008). Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation. Composite Structures, 82(3), 390-402. https://doi.org/10.1016/j.compstruct.2007.01.019

  • Kiani, Y., & Eslami, M. R. (2012). Thermal buckling and post-buckling response of imperfect temperature-dependent sandwich FGM plates resting on elastic foundation. Archive of Applied Mechanics, 82, 891-905. https://doi.org/10.1007/s00419-011-0599-8

  • Kiani, Y., Bagherizadeh, E., & Eslami, M. R. (2011). Thermal and mechanical buckling of sandwich plates with FGM face sheets resting on the Pasternak elastic foundation. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 226(1), 32-41. https://doi.org/10.1177/0954406211413657

  • Kim, J., Żur, K. K., & Reddy, J. N. (2019). Bending, free vibration and buckling of modified couples stress-based functionally graded porous micro-plates. Composite Structures, 209, 879-888. https://doi.org/10.1016/j.compstruct.2018.11.023

  • Kumar, V., Singh, S. J., Saran, V. H., & Harsha, S. P. (2021). Vibration characteristics of porous FGM plate with variable thickness resting on Pasternak’s foundation. European Journal of Mechanics-A/Solids, 85, Article 104124. https://doi.org/10.1016/j.euromechsol.2020.104124

  • Lashkari, M. J., & Rahmani, O. (2016). Bending behavior of sandwich structures with flexible functionally graded core based on high-order sandwich panel theory. Meccanica, 51(5), 1093-1112. https://doi.org/10.1007/s11012-015-0263-4

  • Latifi, M., Farhatnia, F., & Kadkhodaei, M. (2013). Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion. European Journal of Mechanics - A/Solids, 41, 16-27. https://doi.org/10.1016/j.euromechsol.2013.01.008

  • Leissa, A. W. (1969). Vibration of plates (Vol. 160). Scientific and Technical Information Division, National Aeronautics and Space Administration.

  • Liu, Y., Hu, Y., Liu, T., Ding, J. L., & Zhong, W. H. (2015). Mechanical behavior of high density polyethylene and its carbon nanocomposites under quasi-static and dynamic compressive and tensile loadings. Polymer Testing, 41, 106-116. https://doi.org/10.1016/j.polymertesting.2014.11.003

  • Meiche, N. E., Tounsi, A., Ziane, N., Mechab, I., & Bedia, E. A. (2011). A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. International Journal of Mechanical Sciences, 53(10), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004

  • Merdaci, S. (2019). Free vibration analysis of composite material plates case of a typical functionally graded FG plates ceramic/metal with porosities. Nano Hybrids and Composites, 25, 69-83. https://doi.org/10.4028/www.scientific.net/NHC.25.69

  • Meziane, M. A. A., Abdelaziz, H. H., & Tounsi, A. (2014). An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions. Journal of Sandwich Structures and Materials, 16(3), 293-318. https://doi.org/10.1177/1099636214526852

  • Muc, A., & Flis, J. (2021). Flutter characteristics and free vibrations of rectangular functionally graded porous plates. Composite Structures, 261, 113301. https://doi.org/10.1016/j.compstruct.2020.113301

  • Najim, A. S., & Adwaa, M. (2014). Studying mechanical properties specially fatigue behavior of (polyether ether ketone)/glass fiber composites in aerospace applications. In Applied Mechanics and Materials (Vol. 666, pp. 8-16). Trans Tech Publications Ltd. https://doi.org/10.4028/www.scientific.net/AMM.666.8

  • Natarajan, S., & Manickam, G. (2012). Bending and vibration of functionally graded material sandwich plates using an accurate theory. Finite Elements in Analysis and Design, 57, 32-42. https://doi.org/10.1016/j.finel.2012.03.006

  • Neves, A. M. A., Ferreira, A. J. M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R. M. N., & Soares, C. M. M. (2013). Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Composites Part B: Engineering, 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089

  • Nguyen, N. V., Nguyen, H. X., Lee, S., & Xuan, H. N. (2018). Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates. Advances in Engineering Software, 126, 110-126. https://doi.org/10.1016/j.advengsoft.2018.11.005

  • Rao, S. S. (2004). The finite element method in engineering. Elsevier.

  • Reddy, J. N. (1993). An introduction to the finite element method. McGraw-Hill, Inc.

  • Rezaei, A. S., & Said, A. R. (2015). Exact solution for free vibration of thick rectangular plates made of porous materials. Composite Structures, 134, 1051-1060. https://doi.org/10.1016/j.compstruct.2015.08.125

  • Sadiq, S. E., Jweeg, M. J., & Bakhy, S. H. (2020). The effects of honeycomb parameters on transient response of an aircraft sandwich panel structure. In IOP Conference Series: Materials Science and Engineering (Vol. 928, No. 2, p. 022126). IOP Publishing.

  • Singh, S. A., & Harsha, S. P. (2020). Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov’s method: A semi-analytical approach. Thin-Walled Structures, 150, Article 106668. https://doi.org/10.1016/j.tws.2020.106668

  • Thai, H. T., Nguyen, T. K., Vo, T. P., & Lee, J. (2013). Analysis of functionally graded sandwich plates using a new first-order shear deformation theory. European Journal of Mechanics-A/Solids, 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008

  • Tossapanon, P., & Wattanasakulpong, N. (2020). Flexural vibration analysis of functionally graded sandwich plates resting on elastic foundation with arbitrary boundary conditions: Chebyshev collocation technique. Journal of Sandwich Structures and Materials, 22(2), 156-189. https://doi.org/10.1177/1099636217736003

  • Wadee, M. A. (2001). Shear Deformable Beams and Plates: Relationships with Classical Solutions-CM Wang, JN Reddy and KH Lee, Elsevier, 2000, pp. 312,@ $69.30, ISBN 0080437842. Engineering Structures, 7(23), 873-874.

  • Wang, Y. Q., & Zu, J. W. (2017). Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment. Aerospace Science and Technology, (69), 550-562. https://doi.org/10.1016/j.ast.2017.07.023

  • Wattanasakulpong, N., & Chaikittiratana, A. (2015). Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method. Meccanica, 50(5), 1331-1342. https://doi.org/10.1007/s11012-014-0094-8

  • Wattanasakulponga, N., & Ungbhakorn, V. (2014). Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology, 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002

  • Zhang, X. Y., Fang, G., Leeflang, S., Zadpoor, A. A., & Zhou, J. (2019). Topological design, permeability and mechanical behavior of additively manufactured functionally graded porous metallic biomaterials. Acta Biomaterialia, 84, 437-452. https://doi.org/10.1016/j.actbio.2018.12.013

  • Zhang, Y., & Wang, J. (2017). Fabrication of functionally graded porous polymer structures using thermal bonding lamination techniques. Procedia Manufacturing, 10, 866-875. https://doi.org/10.1016/j.promfg.2017.07.073

  • Zhao, J., Wang, Q., Deng, X., Choe, K., Zhong, R., & Shuai, C. (2019). Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions. Composites Part B: Engineering, 168, 106-120. https://doi.org/10.1016/j.compositesb.2018.12.044

ISSN 0128-7680

e-ISSN 2231-8526

Article ID

JST-2475-2021

Download Full Article PDF

Share this article

Recent Articles