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Sharma, Sumit Kumar, Ahlawat, Neha. (1405). Vibration Analysis of FGM Annular Plate with Linearly Varying Thickness for Several Boundary Conditions. هنرهای کاربردی, 13(2), 475-494. doi: 10.22075/macs.2025.37061.1812
Sumit Kumar Sharma; Neha Ahlawat. "Vibration Analysis of FGM Annular Plate with Linearly Varying Thickness for Several Boundary Conditions". هنرهای کاربردی, 13, 2, 1405, 475-494. doi: 10.22075/macs.2025.37061.1812
Sharma, Sumit Kumar, Ahlawat, Neha. (1405). 'Vibration Analysis of FGM Annular Plate with Linearly Varying Thickness for Several Boundary Conditions', هنرهای کاربردی, 13(2), pp. 475-494. doi: 10.22075/macs.2025.37061.1812
Sharma, Sumit Kumar, Ahlawat, Neha. Vibration Analysis of FGM Annular Plate with Linearly Varying Thickness for Several Boundary Conditions. هنرهای کاربردی, 1405; 13(2): 475-494. doi: 10.22075/macs.2025.37061.1812

Vibration Analysis of FGM Annular Plate with Linearly Varying Thickness for Several Boundary Conditions

Mechanics of Advanced Composite Structures
دوره 13، شماره 2 - شماره پیاپی 28، بهمن 2026، صفحه 475-494    اصل مقاله (1.6 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22075/macs.2025.37061.1812
نویسندگان
Sumit Kumar Sharma؛ Neha Ahlawat*
Department of Mathematics, Jaypee Institute of Information Technology, Noida-201303, India
تاریخ دریافت: 15 اسفند 1403،  تاریخ بازنگری: 11 شهریور 1404،  تاریخ پذیرش: 04 آذر 1404 
چکیده
The present article depicts the influence of linear thickness variation on the free axisymmetric vibration of functionally graded material annular plates. For this, three different types of boundary conditions have been taken into consideration. An ordinary differential equation of fourth order has been formulated using classical plate theory and Hamilton's principle. The differential transform method has been developed for the numerical solution of such a differential equation along with three boundary conditions. The obtained numerical results are reported and then analyzed by varying the various parameters, like volume fraction index of plate materials, radius ratio, and taper parameter. The comparative study has also been made to validate the obtained numerical results as well as the technique. It has been observed that natural frequencies drop as the volume fraction index rises. The frequency parameter usually increases with a smaller radius ratio. A decrease in the natural frequency value has been seen when the plate thickness increases. Moreover, the 3-D mode shapes for all the plates are also presented.
کلیدواژه‌ها
FGM؛ Variable thickness؛ Annular plate؛ Axisymmetric vibration؛ DTM
مراجع
  1. Kermani, I.D., Ghayour, M. and Mirdamadi, H.R., 2012. Free vibration analysis of multidirectional functionally graded circular and annular plates. Journal of Mechanical science and Technology, 26(11), pp.3399-3410. DOI: 10.1007/s12206-012-0860-2.
  2. Asemi, K., Salehi, M. and Akhlaghi, M., 2014. Three dimensional biaxial buckling analysis of functionally graded annular sector plate fully or partially supported on Winkler elastic foundation. Aerospace Science and Technology, 39, pp.426-441. HYPERLINK https://doi.org/10.1016/j.ast.2014.04.011. DOI: 10.1016/j.ast.2014.04.011.
  3. Asemi, K., Salehi, M. and Akhlaghi, M., 2015. Three dimensional graded finite element elasticity shear buckling analysis of FGM annular sector plates. Aerospace Science and Technology, 43, pp. 1-13. DOI: 10.1016/j.ast.2015.02.009.
  4. Wang, Q., Shi, D., Liang, Q. and Shi, X., 2016. A unified solution for vibration analysis of functionally graded circular, annular and sector plates with general boundary conditions. Composites Part B: Engineering, 88, pp.264-294. HYPERLINK https://doi.org/10.1016/j.compositesb.2015.10.043 DOI: 10.1016/j.compositesb.2015.10.043.
  5. Lal, R. and Ahlawat, N., 2017. Buckling and vibrations of two-directional functionally graded circular plates subjected to hydrostatic in-plane force. Journal of Vibration and Control, 23(13), pp.2111-2127. doi:10.1177/1077546315611328.
  6. Żur, K.K., 2018. Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green's function method. Composites Part B: Engineering, 144, pp.37-55. DOI: 10.1016/j.compositesb.2018.02.019.
  7. Civalek, Ö. and Baltacıoğlu, A.K., 2018. Vibration of carbon nanotube reinforced composite (CNTRC) annular sector plates by discrete singular convolution method. Composite Structures, 203, pp.458-465. DOI: 10.1016/j.compstruct.2018.07.037
  8. Zhang, N., Khan, T., Guo, H., Shi, S., Zhong, W. and Zhang, W., 2019. Functionally graded materials: an overview of stability, buckling, and free vibration analysis. Advances in Materials Science and Engineering, 2019(1), p.1354150. HYPERLINK https://doi.org/10.1155/2019/1354150 DOI: 10.1155/2019/1354150.
  9. Wu, C.P. and Yu, L.T., 2019. Free vibration analysis of bi-directional functionally graded annular plates using finite annular prism methods. Journal of Mechanical Science and Technology, 33(5), pp.2267-2279. DOI: 10.1007/s12206-019-0428-5.
  10. Tash, F.Y. and Neya, B.N., 2020. An analytical solution for bending of transversely isotropic thick rectangular plates with variable thickness. Applied Mathematical Modelling, 77, pp.1582-1602. DOI: 10.1016/j.apm.2019.08.017.
  11. Eshraghi, I. and Dag, S., 2020. Forced vibrations of functionally graded annular and circular plates by domain‐boundary element method. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 100(8), p.e201900048. HYPERLINK https://doi.org/10.1002/zamm.201900048 DOI: 1002/zamm.201900048.
  12. Hashemi, S. and Jafari, A.A., 2021. An analytical solution for nonlinear vibration analysis of functionally graded rectangular plate in contact with fluid. Appl. Math. Mech., 13(4), pp.914-941. DOI: 10.4208/aamm.OA-2019-0333.
  13. Javani, M., Kiani, Y. and Eslami, M.R., 2021. Rapid heating vibrations of FGM annular sector plates. Engineering with Computers, 37(1), pp.305-322. DOI: 10.1007/s00366-019-00825-x.
  14. Arefi, M., Moghaddam, S.K., Bidgoli, E.M.R., Kiani, M. and Civalek, O., 2021. Analysis of graphene nanoplatelet reinforced cylindrical shell subjected to thermo-mechanical loads. Composite Structures, 255, p.112924. HYPERLINK https://doi.org/10.1142/S0219455426501300 DOI: 10.1142/S0219455426501300
  15. Shahsavari, M., Asemi, K., Babaei, M. and Kiarasi, F., 2021. Numerical investigation on thermal post-buckling of annular sector plates made of FGM via 3D finite element method. Mechanics of Advanced Composite Structures, 8(2), pp.309-320. DOI: 10.22075/macs.2021.21158.1293.
  16. Kiarasi, F., Babaei, M., Asemi, K., Dimitri, R. and Tornabene, F., 2022. Free vibration analysis of thick annular functionally graded plate integrated with piezo-magneto-electro-elastic layers in a hygrothermal environment. Applied Sciences, 12(20), p.10682. HYPERLINK https://doi.org/10.3390/app122010682 DOI: 10.3390/app122010682.
  17. Sobhani, E., Masoodi, A.R., Civalek, O. and Ahmadi-Pari, A.R., 2022. Agglomerated impact of CNT vs. GNP nanofillers on hybridization of polymer matrix for vibration of coupled hemispherical-conical-conical shells. Aerospace Science and Technology, 120, p.107257. HYPERLINK https://doi.org/10.1016/j.ast.2021.107257 DOI: 10.1016/j.ast.2021.107257.
  18. Vasara, D., Khare, S., Sharma, H.K. and Kumar, R., 2022. Free vibration analysis of functionally graded porous circular and annular plates using differential quadrature method. Forces in Mechanics, 9, p.100126. DOI: 10.1016/j.finmec.2022.100126.
  19. Huang, C.S. and Chung, W.C., 2023. Analytical solution for the three-dimensional vibration of a rectangular functionally graded material plate with two simply supported opposite faces. International Journal of Structural Stability and Dynamics, 23(02), p.2350014. DOI: 10.1142/S0219455423500141.
  20. Shariati, M., Shishehsaz, M. and Mosalmani, R., 2023. Stress-driven Approach to Vibrational Analysis of FGM Annular‎ Nano-plate based on First-order Shear Deformation Plate Theory. Journal of Applied and Computational Mechanics, 9(3), pp.637-655. HYPERLINK https://doi.org/10.22055/jacm.2022.41125.3704 DOI: 10.22055/JACM.2022.41125.3704.
  21. Khatoonabadi, M., Jafari, M., Kiarasi, F., Hosseini, M., Babaei, M. and Asemi, K., 2023. Shear buckling response of FG porous annular sector plate reinforced by graphene platelet subjected to different shear loads. Journal of Computational Applied Mechanics, 54(1), pp.68-86. DOI: 10.22059/jcamech.2023.352182.784.
  22. Sharma, S.K. and Ahlawat, N., 2024. Free axisymmetric vibrations of functionally graded material annular plates via DTM. International Journal of Structural Stability and Dynamics, 24(03), p.2450027. DOI: 10.1142/S0219455424500275.
  23. Bridjesh, P., Geetha, N.K. and Yelamasetti, B., 2024. Numerical investigation on buckling of two-directional porous functionally graded beam using higher order shear deformation theory. International Journal on Interactive Design and Manufacturing (IJIDeM), 18(5), pp.2805-2818. HYPERLINK http://dx.doi.org/10.1007/s12008-023-01332-6 DOI: 10.1007/s12008-023-01332-6.
  24. Lal, R. and Sharma, S., 2004. Axisymmetric vibrations of non-homogeneous polar orthotropic annular plates of variable thickness. Journal of sound and vibration, 272(1-2), pp.245-265. DOI: 10.1016/S0022-460X(03)00329-8.
  25. Alipour, M.M., Shariyat, M. and Shaban, M., 2010. A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations. International Journal of Mechanics and Materials in Design, 6(4), pp.293-304. DOI: 10.1007/s10999-010-9134-2.
  26. Hosseini-Hashemi, S., Taher, H.R.D. and Akhavan, H., 2010. Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations. Composite Structures, 92(7), pp.1734-1743. DOI: 10.1016/j.compstruct.2009.12.016.
  27. Lal, R. and Ahlawat, N., 2015. Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method. European Journal of Mechanics-A/Solids, 52, pp.85-94. DOI: 10.1016/j.euromechsol.2015.02.004.
  28. Lal, R. and Rani, R., 2016. On the use of differential quadrature method in the study of free axisymmetric vibrations of circular sandwich plates of linearly varying thickness. Journal of vibration and control, 22(7), pp.1729-1748. HYPERLINK https://doi.org/10.1177/1077546314544695 DOI: 10.1177/1077546314544.
  29. Gupta, A., Jain, N.K., Salhotra, R. and Joshi, P.V., 2018. Effect of crack location on vibration analysis of partially cracked isotropic and FGM micro-plate with non-uniform thickness: an analytical approach. International Journal of Mechanical Sciences, 145, pp.410-429. DOI: 10.1016/j.ijmecsci.2018.07.015.
  30. Lal, R. and Saini, R., 2019. Thermal effect on radially symmetric vibrations of temperature-dependent FGM circular plates with nonlinear thickness variation. Materials Research Express, 6(8), p.0865f1. DOI: 10.1088/2053-1591/ab24ee.
  31. Ahlawat, N. and Lal, R., 2020. Effect of Winkler foundation on radially symmetric vibrations of bi-directional FGM non-uniform Mindlin's circular plate subjected to in-plane peripheral loading. Journal of Solid Mechanics, 12(2), pp.455-475. DOI: 10.22034/jsm.2019.1873720.1466.
  32. Talebitooti, R., Zarastvand, M. and Rouhani, A.S., 2019. Investigating hyperbolic shear deformation theory on vibroacoustic behavior of the infinite functionally graded thick plate. Latin American Journal of Solids and Structures, 16(01), p.e139. DOI: 10.1590/1679-78254883.
  33. Lal, R. and Saini, R., 2020. Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method. Journal of Vibration and Control, 26(1-2), pp.73-87. DOI https://doi.org/10.1177/1077546319876.
  34. Jalali, S.K. and Heshmati, M., 2020. Vibration analysis of tapered circular poroelastic plates with radially graded porosity using pseudo-spectral method. Mechanics of Materials, 140, p.103240. DOI: 10.1016/j.mechmat.2019.103240.
  35. Tran, M.T. and Thai, S., 2023. Transient analysis of variable thickness multi-directional functionally graded plates using isogeometric analysis. Multidiscipline Modeling in Materials and Structures, 19(4), pp.652-679. DOI: 10.1108/MMMS-12-2022-0283.
  36. Zhong, S., Jin, G., Ye, T., Zhang, J., Xue, Y. and Chen, M., 2020. Isogeometric vibration analysis of multi-directional functionally gradient circular, elliptical and sector plates with variable thickness. Composite Structures, 250, p.112470. DOI: 10.1016/j.compstruct.2020.112470.
  37. Hashemi, S. and Jafari, A.A., 2021. An analytical solution for nonlinear vibration analysis of functionally graded rectangular plate in contact with fluid. Appl. Math. Mech., 13(4), pp.914-941. DOI: 10.4208/aamm.OA-2019-0333.
  38. Kumar, V., Singh, S.J., Saran, V.H. and Harsha, S.P., 2021. Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov's method. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 235(4), pp.880-897. DOI: 10.1177/146442072098049.
  39. Minh, P.P., Manh, D.T. and Duc, N.D., 2021. Free vibration of cracked FGM plates with variable thickness resting on elastic foundations. Thin-Walled Structures, 161, p.107425. DOI:  https://doi.org/10.1016/j.tws.2020.107425.
  40. Zarastvand, M.R., Ghassabi, M. and Talebitooti, R., 2021. A review approach for sound propagation prediction of plate constructions. Archives of Computational Methods in Engineering, 28(4), pp.2817-2843. DOI: 10.1007/s11831-020-09482-6.
  41. Zarastvand, M.R., Ghassabi, M. and Talebitooti, R., 2022. Prediction of acoustic wave transmission features of the multilayered plate constructions: A review. Journal of Sandwich Structures & Materials, 24(1), pp.218-293. DOI: 10.1177/1099636221993891.
  42. Ghafouri, M., Ghassabi, M., Zarastvand, M.R. and Talebitooti, R., 2022. Sound propagation of three-dimensional sandwich panels: influence of three-dimensional re-entrant auxetic core. Aiaa Journal, 60(11), pp.6374-6384. DOI: 10.2514/1.J061219.
  43. Kumar, V., Singh, S.J., Saran, V.H. and Harsha, S.P., 2023. Vibration response analysis of tapered porous FGM plate resting on elastic foundation. International Journal of Structural Stability and Dynamics, 23(02), p.2350024. DOI: 10.1142/S0219455423500244.
  44. Saini, R., Saini, R., Kumar, A. and Khadimallah, M.A., 2023. Free axisymmetric vibrations of heated non-uniform Bi-directional FGM Mindlin rings employing quadrature approaches. Thin-Walled Structures, 184, p.110482. DOI: https://doi.org/10.1016/j.tws.2022.110482.
  45. Hadji, L., Plevris, V., Madan, R. and Ait Atmane, H., 2024. Multi-directional functionally graded sandwich plates: buckling and free vibration analysis with refined plate models under various boundary conditions. Computation, 12(4), p.65. DOI: 10.3390/computation12040065.
  46. Islam, T.F. and Kedar, G.D., 2024. Hygrothermal buckling analysis of thin rectangular FGM plate with variable thickness. Engineering Computations, 41(3), pp.710-726. HYPERLINK https://doi.org/10.1108/EC-09-2023-0601 DOI: 10.1108/EC-09-2023-0601.
  47. Ahlawat, N. and Saini, R., 2024. Vibration and buckling analysis of elastically supported bi-directional FGM mindlin circular plates having variable thickness. Journal of Vibration Engineering & Technologies, 12(1), pp.513-532. DOI: 10.1007/s42417-023-00856-1.
  48. Mandal, R., Singha, T.D., Bandyopadhyay, T. and Karmakar, A., 2025. Influence of porosity on thermal free vibration of rotating porous sigmoid functionally graded plate with bi-directional thickness variation. Journal of Vibration Engineering & Technologies, 13(1), p.109. DOI: 10.1007/s42417-024-01639-y.
  49. Jafari Maryaki, F. and Shaterzadeh, A., 2025. Free vibration analysis of functionally graded porous materials complex shells with variable thickness. AUT Journal of Mechanical Engineering, 9(2), pp.99-112. DOI: 10.22060/ajme.2025.23494.6137.
  50. Zhou, J.K., 1986. Differential transformation and its applications for electronic circuits. Huazhong Science & Technology University Press, China.
  51. Leissa, A.W., 1969. Scientific and Technical Information Division, National Aeronautics and Space Administration. Vibration of plates,
  52. Dong, C.Y., 2008. Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev -Ritz method. Materials & Design, 29(8), pp.1518-1525. DOI: 10.1016/j.matdes.2008.03.001.
  53. Shariyat, M. and Alipour, M.M., 2014. A novel shear correction factor for stress and modal analyses of annular FGM plates with non-uniform inclined tractions and non-uniform elastic foundations. International Journal of Mechanical Sciences, 87, pp.60-71. DOI: 10.1016/j.ijmecsci.2014.05.032.
  54. Sharma, S., Gupta, U.S. and Lal, R., 2010. Effect of Pasternak foundation on axisymmetric vibration of polar orthotropic annular plates of varying thickness. Journal of Vibration and Acoustics, 132(4), p.041001. HYPERLINK https://doi.org/10.1115/1.4001495 DOI: 10.1115/1.4001495.
  55. Soni, S.R. and Amba-Rao, C.L., 1975. Axisymmetric vibrations of annular plates of variable thickness. Journal of Sound and Vibration, 38(4), pp.465-473. DOI: 10.1016/S0022-460X(75)80134-9.
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