Investigation of Imperfection Effects in Dynamic Behavior of FG Strucure

Document Type : Original Article

Authors
Mohammad Meskini 1
Mostafa Livani 1
Mohammad Hosein Habibi 2
1 Assistant Professor, Department of Aerospace Engineering, Shahid Sattari Aeronautical University of Science and Technology
2 MS student, Department of Graduate Studies, Shahid Sattari Aeronautical University of Science and Technology
10.22034/stme.2023.401410.1037
Abstract
In this study, the effect of material imperfection on the free vibration response of perfect and imperfect FG plate is studied. A new hyperbolic shear deformation function is presented in this paper. The new hyperbolic function is chosen in such a way that the degree of the function is reduced as much as possible, despite the sufficient accuracy, so that the calculation speed is greatly reduced. The properties of the FG plate varied along the thickness according to power law. The material composition in production process cannot be completely in accordance with the expected pattern, which leads to the production of imperfect FG material. The governing differential equations are derived using the Hamilton’s principle. The obtained equations were solved using the Navier method with simple boundary conditions. The effects of important geometric and mechanical parameters of perfect model and two types of imperfect model, including length to thickness ratio, length to width ratio, wave number and power-law exponent on natural frequency response of imperfect FG plate are investigated. To verification, the analytical results obtained in this study are compared with the results presented in the literature, and in this comparison, a good agreement was obtained, which shows the correctness theory, deriving and solving equations.
Keywords
Keywords
Free Vibration
Imperfect FGM
New hyperbolic theory
Hamilton’s Principal
Navier method
Subjects
[1] M. Arefi, and M. Meskini, “Application of hyperbolic shear deformation theory to free vibration analysis of functionally graded porous plate with piezoelectric face-sheets”, Structural Engineering and Mechanics, Vol. 71, No. 5, 2019, pp. 459-467.
[2] A. R. Setoodeh, and M. Shojaee, “Application of TW-DQ method to nonlinear free vibration analysis of FG carbon nanotube-reinforced composite quadrilateral plates”, Thin-Walled Structures, Vol. 108, 2016, pp. 1-11. 
[3] M. Livani, and K. Malekzadeh Fard, “Free vibration analysis of doubly curved composite sandwich panels with variable thickness”, Amirkabir Journal of Mechanical Engineering, Vol. 52, No. 8, pp. 2195–2212, 2019. (in Persian)
[4] M. Rezaee, and V. Shaterian alghalandis, “An Analytical Method for Damped Free Vibration Analysis of a Cracked Beam Considering the Coupled Multimode Equations”, Amirkabir Journal of Mechanical Engineering, Vol. 52, No. 1, pp. 155-172, 2020. (in Persian)
[5] M. Sobhy, and A. F. Radwan. “A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates”, International Journal of Applied Mechanics, Vol. 9, No.1, 2017.
[6] A. Ebrahimi-Mamaghani, R. Sotudeh-Gharebagh, R. Zarghami, and N. Mostoufi, “Thermomechanical stability of axially graded Rayleigh pipes”, Mechanics Based Design of Structures and Machines , Vol.50, No. 2, 2022, pp. 412-441.
[7] S. E. Kim, N. D. Duc, V. H. Nam, and N. V. Sy, “Nonlinear vibration and dynamic buckling of eccentrically oblique stiffened FGM plates resting on elastic foundations in thermal environment”, Thin-Walled Structures, Vol. 142, 2019, pp. 287-296.
[8] X. Zhu, Z. Lu, Z. Wang, L. Xue, and A. Ebrahimi-Mamaghani, “A  Vibration of spinning functionally graded nanotubes conveying fluid”, Engineering with Computers, Vol. 38, 2022, pp.1771–1792.
[9] R. Ansari, J. Torabi, and M. Faghih Shojaei, “Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading”, Composites Part B: Engineering, Vol. 109, 2017, pp. 197-213.
[10] T. T.Thom, and N. D. Kien, “Free vibration analysis of 2-D FGM beams in thermal environment based on a new third-order shear deformation theory”, Vietnam Journal of Mechanics, VAST, Vol. 40, No. 2, 2018, pp. 121-140.
[11] H. Shafiei and A. R. Setoodeh “Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation”, Steel and Composite Structures, Vol. 24, 2017, pp. 65-77.
[12] A. R. Rahimi, M. Livani, and A. Negahban Boron, “Free vibration analysis of functionally graded material beams with transverse crack”, Journal of Mechanical Engineering, Vol. 51, No. 1, 2021, pp. 277-281.
[13] Y. Wang, K. Xie, T. Fu, and W. Zhang, “A unified modified couple stress model for sizedependent free vibrations of FG cylindrical microshells based on high-order shear deformation theory”, European Physical Journal - Plus, Vol. 135, No. 1, 2020.
[14] R. Meksi, S. Benyoucef, A. Mahmoudi, A. Tounsi, and et al., “An analytical solution for bending, buckling and vibration responses of FGM sandwich plates”, Journal of Sandwich Structures & Materials,Vol. 21, No. 2, 2019, pp. 727-757. 
[15] J. Ehyaei, H. Safarpour, and E. Shahabinejad, “Vibration analysis of a double layer microshell utilizing a modified couple stress theory”, Iranian Journal of Mechanical Engineering Transactions of the ISME, Vol. 21, No. 1, 2020, pp. 21-44.
[16] H. Safarpour, Z. Esmailpoor Hajilak, and M. Habibi, “A size-dependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation”, International Journal of Mechanics and Materials in Design, Vol. 15, No. 3, 2019, pp. 569–583.
[17] S. C. Chikr, A. Kaci, A. A. Bousahla and ..., “A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin’s approach”, Geomechanics and Engineering, Vol. 21, No. 5, 2020.
[18] D. S. Mashat, A. M. Zenkour, and A. F. Radwan, “A quasi-3D higher-order plate theory for bending of FG plates resting on elastic foundations under hygro-thermo-mechanical loads with porosity”,  European Journal of Mechanics-A/Solids, Vol. 82, 2020. 
[19] L. Hadji, M. Avcar, and N. Zouatnia, “Natural frequency analysis of imperfect FG sandwich plates resting on Winkler-Pasternak foundation”, Materials Today: Proceedings, Vol. 53, No. 1, 2022, pp. 153-160. 
[20] D. Singh, and A. Gupta, “Influence of geometric imperfections on the free vibrational response of the functionally graded material sandwich plates with circular cut-outs”, Materials Today: Proceedings, Vol. 62, No. 3, 2022, pp. 1496-1499.
[21] X. Chen, Y. Lu, Z. Wu, Y. Shao, X. Xue, and Y. Wu, “Free vibration of in-plane bi-directional functionally graded materials rectangular plates with geometric imperfections and general elastic restraints”,  Aerospace Science and Technology, Vol. 132, 2023.
[22] H. Chaabani, S. Mesmoudi, L. Boutahar, and K. El Bikri, “A high-order finite element continuation for buckling analysis of porous FGM plates”,  Engineering Structures, Vol. 279, 2023.
[23] Abualnour, Moussa, and et al., “A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates”, Composite Structures, Vol. 184, 2018, pp. 688-697.
[24] Z. Belabed, M. S. A. Houari, and et al., “An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM)plates”, Composites Part B: Engineering, Vol. 60, 2014, pp. 274-283.
A. M. A. Neves, A. J. M. Ferreira, and et al., “A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates”, Composites Part B: Engineering, Vol. 43, 2012, pp. 711-7.

  • Receive Date 09 June 2023
  • Revise Date 14 July 2023
  • Accept Date 26 August 2023
  • First Publish Date 26 August 2023
  • Publish Date 22 June 2023