A refined shear deformation theory for natural frequency analysis of power law based functionally graded sandwich plate
Saloni MALVIYA, Supen Kumar SAH
Abstract. Functionally graded material is a novel composite in which the properties vary with the dimension. Numerous industrial sectors and applications, including aerospace, automotive, biomedical implants, optoelectronic devices, energy-absorbing structures, geological models, and heat exchangers, are highly interested in FGMs. The present study analyzes the natural frequencies of a functionally graded metal-ceramic (FGMC) sandwich plate that has been accomplished considering refined shear deformation theory. Since the parabolic variance in shear strain through the thickness is such that shear stresses vanish on the plate surfaces, the shear correction factor is not required. Hamilton’s principle has been utilized to derive the equation of motion to perform the free vibration analysis. Additionally, the eigen value equation for the FGMC sandwich plate is obtained via Navier’s solution. For the analysis, the three variations of sandwich plate are selected. Three various types of FGMC sandwich plate types viz. 1-1-1, 1-2-1, and 2-2-1 have been taken into consideration for conducting the free vibration study to analyze natural frequency. The material properties of each layer of the sandwich plate and the volume gradation index are obtained considering power law. Lastly, the influence of parameters such as volume fraction, length-to-width ratio, and aspect ratio on frequency parameter is investigated. It is observed that geometrical parameters volume fraction index, and thickness ratio of FGMC sandwich plate has a considerable impact on frequency parameter.
Keywords
Functionally Graded Metal-Ceramic Material, FGM Sandwich Plate, Free Vibration, Power Law, Refined Shear Deformation Theory
Published online 3/1/2025, 14 pages
Copyright © 2025 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Saloni MALVIYA, Supen Kumar SAH, A refined shear deformation theory for natural frequency analysis of power law based functionally graded sandwich plate, Materials Research Proceedings, Vol. 49, pp 494-507, 2025
DOI: https://doi.org/10.21741/9781644903438-50
The article was published as article 50 of the book Mechanical Engineering for Sustainable Development
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] J. L. Mantari, “A refined theory with stretching effect for the dynamics analysis of advanced composites on elastic foundation,” Mechanics of Materials, vol. 86, p. 31-43, Jul. 2015. https://doi.org/10.1016/j.mechmat.2015.02.010
[2] G. Jin, Z. Su, S. Shi, T. Ye, and S. Gao, “Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions,” Compos Struct, vol. 108, no. 1, p. 565-577, Feb. 2014. https://doi.org/10.1016/j.compstruct.2013.09.051
[3] S. S. Akavci, “An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation,” Compos Struct, vol. 108, no. 1, p. 667-676, Feb. 2014 . https://doi.org/10.1016/j.compstruct.2013.10.019
[4] F. Z. Zaoui, D. Ouinas, B. Achour, A. Tounsi, E. R. Latifee, and A. A. A. Al-Naghi, “A Hyperbolic Shear Deformation Theory for Natural Frequencies Study of Functionally Graded Plates on Elastic Supports,” Journal of Composites Science, vol. 6, no. 10, Oct. 2022. https://doi.org/10.3390/jcs6100285
[5] H. T. Thai and D. H. Choi, “A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation,” Compos B Eng, vol. 43, no. 5, p. 2335-2347, July 2012. https://doi.org/10.1016/j.compositesb.2011.11.062
[6] S. Kumar Sah and A. Ghosh, “Free vibration and buckling analysis of FGM plates using inverse trigonometric shear deformation theory,” Aircraft Engineering and Aerospace Technology, vol. 93, no. 2, p. 298-310, Apr. 2021. https://doi.org/10.1108/AEAT-01-2020-0001
[7] S. Kumar Sah and A. Ghosh, “Influence of porosity distribution on free vibration and buckling analysis of multi-directional functionally graded sandwich plates,” Compos Struct, vol. 279, p. 114795, Jan. 2022. https://doi.org/10.1016/j.compstruct.2021.114795
[8] A. H. Baferani, A. R. Saidi, and H. Ehteshami, “Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation,” Compos Struct, vol. 93, no. 7, p. 1842-1853, Jun. 2011. https://doi.org/10.1016/j.compstruct.2011.01.020
[9] P. Malekzadeh, “Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations,” Compos Struct, vol. 89, no. 3, p. 367-373, Jul. 2009. https://doi.org/10.1016/j.compstruct.2008.08.007
[10] R. C. Batra and J. Jin, “Natural frequencies of a functionally graded anisotropic rectangular plate,” J Sound Vib, vol. 282, no. 1-2, p. 509-516, Apr. 2005. https://doi.org/10.1016/j.jsv.2004.03.068
[11] J. L. Mantari and C. Guedes Soares, “”A novel higher-order shear deformation theory with stretching effect for functionally graded plates,” Compos B Eng, vol. 45, no. 1, p. 268-281, Feb. 2013. https://doi.org/10.1016/j.compositesb.2012.05.036
[12] A. Alibeigloo and M. Alizadeh, “Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method,” European Journal of Mechanics – A/Solids, vol. 54, p. 252-266, Nov. 2015. https://doi.org/10.1016/j.euromechsol.2015.06.011
[13] S. Kamarian, M. H. Yas, and A. Pourasghar, “Free vibration analysis of three-parameter functionally graded material sandwich plates resting on Pasternak foundations,” vol. 15, no. 3, p. 292-308, May 2013. https://doi.org/10.1177/1099636213487363
[14] Ait Atmane H, Tounsi A, Mechab I, Bedia EAA. Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory. Int J Mech Mater Des 2010 6(2):113-21. https://doi.org/10.1007/s10999-010-9110-x
[15] S. Hosseini-Hashemi, H. Rokni Damavandi Taher, H. Akhavan, and M. Omidi, “Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory,” Appl Math Model, vol. 34, no. 5, p. 1276-1291, May 2010. https://doi.org/10.1016/j.apm.2009.08.008
[16] C. P. Wu and H. Y. Li, “The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates,,” Compos Struct, vol. 92, no. 10, p. 2476-2496, Sep. 2010. https://doi.org/10.1016/j.compstruct.2010.03.001
[17] Matsunaga H. Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory. Compos Struct 2008;82(4):499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
[18] Fares ME, Elmarghany MK, Atta D. An efficient and simple refined theory for bending and vibration of functionally graded plates. Compos Struct 2009;91(3):296-305. https://doi.org/10.1016/j.compstruct.2009.05.008
[19] Neves AMA, Ferreira AJM, Carrera E, Roque CMC, Cinefra M, Jorge RMN, et al. A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos Part B Eng 2012;43(2):711-25. https://doi.org/10.1016/j.compositesb.2011.08.009
[20] Amini MH, Soleimani M, Rastgoo A. Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation. Smart Mater Struct 2009;18(8):1-9. https://doi.org/10.1088/0964-1726/18/8/085015
[21] Alipour MM, Shariyat M, Shaban M. A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations. Int J Mech Mater Des 2010;6(4):293-304 https://doi.org/10.1007/s10999-010-9134-2
