Journal of Vibration and Sound

Journal of Vibration and Sound

Vibration analysis of functionally graded folded plate: A differential quadrature approach and first-order shear deformation theory

Document Type : research article

Authors
Nima Mohandesi 1
Mostafa Talebitooti 2
Mohammad Fadaee 3
1 Department of Mechanical Engineering, Qom University of Technology
2 Department of Mechanical Engineering, Qom University of Technology, Qom, Iran
3 Department of Mechanical Engineering, Qom University of Mechanical Engineering, Qom, Iran
Abstract
This research investigates the vibration behavior of folded plates made of functionally graded materials (FGMs). FGMs, as an advanced material class, possess a heterogeneous structure with mechanical properties that continuously vary through the thickness. Folded plates are utilized in various industries due to their ease of manufacturing and low production cost. A novel application of these plates is in the design and construction of fifth-generation stealth fighter aircraft. In this study, the elastic moduli and density of the FGM folded plate were initially considered. Subsequently, using Hamilton's principle, the governing dynamic equations and boundary conditions for each layer of the folded plate were separately derived. By applying continuity conditions at the folded region, the governing equations, boundary conditions, and continuity equations were formulated in a unified manner. To analyze this equation set, a combined Levy-Ritz method was employed, and the natural frequencies of the FGM folded plate were calculated by solving the eigenvalue problem. For validation purposes, the FGM folded plate was modeled and analyzed in COMSOL simulation software (based on the finite element method). Comparison of the finite element results with those obtained from the combined Levy-Ritz method demonstrates the high accuracy of the mathematical modeling and analytical solution method presented in this research.
Keywords
Functionally graded materials
vibrations
folded plate
differential quadrature method
Subjects
[[1]] M. Koizumi, concept of FGM, Ceram. Trans., 34, 1993, 3–10.
[2] hen HS, Xiang Y, Lin F. Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments. Comput Method Appl M 2017; 319: 175-193
[3] 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.
[4] Roque CMC, Ferreira AJM, Reddy JN. Analysis of Mindlin micro plates with a modified couple stress theory and a meshless method. Appl Math Model 2013;37(7):4626–4633
[5] Demirhan PA, Taskin V. Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach. Compos B Eng 2019; 160:661–676. 
[6] Baferani AH, Saidi AR, Ehteshami H. Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation. Compos Struct 2011;93(7):1842–1853.
[7] Hosseini-Hashemi S, Fadaee M, Atashipour SR. A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates. Int J Mech Sci 2011;53(1):11–22.
[8] Pham, Q. H., Tran, V. K., Tran, T. T., & Zenkour, A. M. (2023). Nonlocal higher-order finite element modeling for vibration analysis of viscoelastic orthotropic nanoplates resting on variable viscoelastic foundation. Composite Structures, 318, 117067.‏
[9] Pham, Q. H., Tran, V. K., & Nguyen, P. C. (2024). Dynamic response of magneto-electro-elastic composite plates lying on visco-Pasternak medium subjected to blast load. Composite Structures, 337, 118054.‏
[10] Tran, T. V., Tran, T. D., Hoa Pham, Q., Nguyen-Thoi, T., & Tran, V. K. (2020). An ES‐MITC3 Finite Element Method Based on Higher‐Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs. Mathematical Problems in Engineering, 2020(1), 7520209.
[1[1]] Pham, Q. H., Tran, V. K., & Nguyen, P. C. (2024). Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium. Defence Technology, 35, 77-99.‏
[12] Pham, Q. H., Nhan, H. T., Tran, V. K., & Zenkour, A. M. (2023). Hygro-thermo-mechanical vibration analysis of functionally graded porous curved nanobeams resting on elastic foundations. Waves in Random and Complex Media, 1-32.‏
[13] Thakur, B. R., Verma, S., Singh, B. N., & Maiti, D. K. (2021). Dynamic analysis of flat and folded laminated composite plates under hygrothermal environment using a nonpolynomial shear deformation theory. Composite Structures, 274, 114327.
[14] S.Y. Lee, S.C. Wooh, S.S. Yhim, Dynamic behavior of folded composite plates analyzed by the third order plate theory, Int. J. Solids Struct. 41 (2004) 1879-1892.
[15] Feri, M., Krommer, M., & Alibeigloo, A. (2025). Elasticity solution of functionally graded viscoelastic sandwich plates with piezoelectric layers under electrothermomechanical loading using DQM. Journal of Thermal Stresses, 48(1), 82-111.‏
[16]  معتضدیان، م.، جعفری، ا.، " ارتعاشات آزاد پنل و پوسته متصل کروی استوانه­ای به روش مربعات دیفرانسیلی تعمیم یافته دو بعدی "، نشریه­ علمی صوت و ارتعاش، 1402، شماره 23، دوره 12، صفحه 156- 176
[17] شکوری، م.، خادمی کوهی، م.، " تحلیل و بررسی اثر خواص مکانیکی الاستیک بر رفتار ارتعاشاتی پوسته­های استوانه­ای ساخته شده از مواد با خواص گرادیانی با شرایط مرزی مختلف"، نشریه علمی صوت و ارتعاش، 1401، شماره 21، دوره 11، صفحه 110- 118
[18] رحمانفر، ا.، جعفری، ا.، " ارتعاشات آزاد ورق مستطیلی چرخان با وصله پیزوالکتریک با روش عددی مربعات دیفرانسیلی تعمیم‌یافته "، نشریه علمی صوت و ارتعاش، 1403، شماره 25، دوره 13، صفحه 3- 32
[19] Guha Niyogi A, Laha MK, Sinha PK (1999) Finite element vibration analysis of laminated composite folded plate structures. Shock Vib 6:273–283.
[20] Mohandesi, N., Talebitooti, M., & Fadaee, M. (2024). Free vibration analysis of a folded auxetic plate using the Levy-differential quadrature method. Journal of Solid and Fluid Mechanics, 14(5), 155-165.‏
[2[1]] Peng, L.X., Kitipornchai, S. & Liew, K.M. Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method. Comput Mech 39, 799–814 (2007). https://doi.org/10.1007/s00466-006-0070-9
[22] Das S, Guha Niyogi A (2020) Free-vibration analysis of epoxy-based cross-ply laminated composite folded plates subjected to hygrothermal loading. J Inst Eng India Ser C.
[23] Javani M, Kiani Y, Eslami MR (2022) On the free vibrations of FG-GPLRC folded plates using GDQE procedure. Compos Struct.
[24] Mohammadi, H., & Setoodeh, A. R. (2021). Free vibration analysis of functionally graded carbon nanotubes reinforced composite skew folded plates using the isogeometric approach. Amirkabir Journal of Mechanical Engineering, 53(4), 2239-2260.‏
[25] Heidari-Soureshjani, A., Asadi, E., & Talebitooti, R. (2024). CNT-woven glass fiber laminated composite for folded plate application: 2D-GDQ and experimental study. Archives of Civil and Mechanical Engineering, 24(3), 163.
[26] Salehipour, H., Shahmohammadi, M. A., & Civalek, Ö. (2024). Natural frequencies and modal shapes of folded sandwich plates made of porous core and FG-CNTRC coating layers resting on two parameters elastic foundation. Aerospace science and technology, 148, 109077.‏