Geomechanics and Engineering

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Free vibrational behavior of perfect and imperfect multi-directional FG plates and curved structures

  • Pankaj S. Ghatage (School of Mechanical Engineering, Vellore Institute of Technology) ;
  • P. Edwin Sudhagar (School of Mechanical Engineering, Vellore Institute of Technology) ;
  • Vishesh R. Kar (Department of Mechanical Engineering, National Institute of Technology Jamshedpur)
  • Received : 2023.03.26
  • Accepted : 2023.10.30
  • Published : 2023.11.25
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Abstract

The present paper examines the natural frequency responses of the bi-directional (nx-ny, ny-nz and nz-nx) and multidirectional (nx-ny-nz) functionally graded (FG) plate and curved structures with and without porosity. The even and uneven kind of porosity pattern are considered to observe the influence of porosity type and porosity index. The numerical findings have been obtained using a higher order shear deformation theory (HSDT) based isometric finite element (FE) approach generated in a MATLAB platform. According to the convergence and validation investigation, the proposed HSDT based FE model is adequate to predict free vibrational responses of multidirectional porous FG plates and curved structures. Further a parametric analysis is carried out by taking various design parameters into account. The free vibrational behavior of bidirectional (2D) and multidirectional (3D) perfect-imperfect FGM structure is examined against various power law index, support conditions, aspect, and thickness ratio, and for the curvature of curved structures. The results indicate that the maximum non-dimensional fundamental frequency (NFF) value is observed in perfect FGM plates and curved structures compared to porous FGM plates and curved structures and it is maximum for FGM plates and curved structures with uneven kind of porosity than even porosity.

Keywords

References

  1. Ahlawat, N. and Lal, R. (2016), "Buckling and vibrations of multidirectional functionally graded circular plate resting on elastic foundation", Proc. Eng., 144, 85-93. https://doi.org/10.1016/j.proeng.2016.05.010.
  2. Al Rjoub, Y.S. and Alshatnawi, J.A. (2020), "Free vibration of functionally-graded porous cracked plates", In Struct., 28, 2392-2403. https://doi.org/10.1016/j.istruc.2020.10.059.
  3. Bansal, G., Gupta, A. and Katiyar, V. (2020), "Vibration of porous functionally graded plates with geometric discontinuities and partial supports", Proc. of the Instit. of Mech. Enginrs., Part C: J. of Mech. Engg. Sci., 234(21), 4149-4170. https://doi.org/10.1177/0954406220920660.
  4. Bathini, S.R. (2020), "Free vibration behavior of bi-directional functionally graded plates with porosities using a refined first order shear deformation theory", J. Comput. Appl. Mech., 51(2), 374-388. https://doi.org/10.22059/JCAMECH.2020.303046.510.
  5. Chen, M., Jin, G., Ma, X., Zhang, Y., Ye, T. and Liu, Z. (2018), "Vibration analysis for sector cylindrical shells with bidirectional functionally graded materials and elastically restrained edges", Compos. Part B: Eng., 153, 346-363. https://doi.org/10.1016/j.compositesb.2018.08.129.
  6. Cuong-Le, T., Nguyen, K.D., Lee, J., Rabczuk, T. and Nguyen-Xuan, H. (2021), "A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotech., 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  7. Ebrahimi, M.J. and Najafizadeh, M.M. (2014), "Free vibration analysis of two-dimensional functionally graded cylindrical shells", Appl. Math. Model., 38(1), 308-324. https://doi.org/10.1016/j.apm.2013.06.015.
  8. Esmaeilzadeh, M. and Kadkhodayan, M. (2019), "Dynamic analysis of stiffened bi-directional functionally graded plates with porosities under a moving load by dynamic relaxation method with kinetic damping", Aerosp. Sci. Tech., 93,105333. https://doi.org/10.1016/j.ast.2019.105333.
  9. Ghatage, P.S., Kar, V.R. and Sudhagar, P.E. (2020), "On the numerical modelling and analysis of multi-directional functionally graded composite structures: A review", Compos. Struct., 236, 111837. https://doi.org/10.1016/j.compstruct.2019.111837.
  10. Ghatage, P.S. and Sudhagar, P.E. (2023), "Free vibrational behavior of bi-Directional functionally graded composite panel with and without porosities using 3D finite element approximations", Int. J. Integra. Eng., 15(1), 131-144. https://doi.org/10.30880/ijie.2023.15.01.012.
  11. Ghatage, P.S. and Sudhagar, P.E. (2023), "Free vibrational behavior of bi-directional perfect and imperfect axially graded cylindrical shell panel under thermal environment", Struct. Eng. Mecha., 85(1), 135. https://doi.org/10.12989/sem.2023.85.1.135..
  12. Hadji, L., Bernard, F., Safa, A. and Tounsi, A. (2021), "Bending and free vibration analysis for FGM plates containing various distribution shape of porosity", Adv. Mater. Res., 10(2), 115-135. https://doi.org/10.12989/amr.2021.10.2.115.
  13. Hosseini-Hashemi, S., Salehipour, H., Atashipour, S.R. and Sburlati, R. (2013), "On the exact in-plane and out-of-plane free vibration analysis of thick functionally graded rectangular plates: Explicit 3-D elasticity solutions", Compos. Part B: Eng., 46, 108-115. https://doi.org/10.1016/j.compositesb.2012.10.008.
  14. Kang, R., Xin, F., Shen, C. and Lu, T.J. (2022), "3D free vibration analysis of functionally graded plates with arbitrary boundary conditions in thermal environment", Adv. Eng. Materi., 24(5), 2100636. https://doi.org/10.1002/adem.202100636.
  15. Kar, V.R. and Panda, S.K. (2015a), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Sol. Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691.
  16. Kar, V.R. and Panda, S.K. (2015b), "Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method", Compos. Struct., 129, 202-212. https://doi.org/10.1016/j.compstruct.2015.04.006.
  17. Kar, V.R. and Panda, S.K. (2016), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chine. J. Aeron., 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007
  18. Keddouri, A., Hadji, L. and Tounsi, A. (2019), "Static analysis of functionally graded sandwich plates with porosities", Adv. Mater. Res., 8(3), 155-177. https://doi.org/10.12989/amr.2019.8.3.155.
  19. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2020), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. with Comput., 36(3), 807-821. https://doi.org/10.1007/s00366-019-00732-1.
  20. Li, S., Zheng, S. and Chen, D> (2020), "Porosity dependent isogeometric analysis of bi-directional functionally graded plates", Thin-Walled Struct., 156, 106999. https://doi.org/10.1016/j.tws.2020.106999.
  21. Lieu, Q.X., Lee, D., Kang, J. and Lee, J. (2019), "NURBS-based modeling and analysis for free vibration and buckling problems of in-plane bi-directional functionally graded plates", Mech. Adv. Mater. Struct., 26(12), 1064-1080. https://doi.org/10.1080/15376494.2018.1430273.
  22. Lieu, Q.X., Lee, S., Kang, J. and Lee, J. (2018), "Bending and free vibration analyses of in-plane bi-directional functionally graded plates with variable thickness using isogeometric analysis", Compos. Struct., 192, 434-451. https://doi.org/10.1016/j.compstruct.2018.03.021.
  23. Mehrabadi, S.J. and Aragh, B.S. (2013), "On the thermal analysis of 2-D temperature-dependent functionally graded open cylindrical shells", Compos. Struct., 96, 773-785. https://doi.org/10.1016/j.compstruct.2012.09.036.
  24. Molla-Alipour, M., Shariyat, M. and Shaban, M. (2020), "Free vibration analysis of bidirectional functionally graded conical/cylindrical shells and annular plates on nonlinear elastic foundations, based on a unified differential transform analytical formulation", J. Solid Mech., 12(2), 385-400. https://doi.org/10.22034/JSM.2019.1869981.1450.
  25. Nemat-Alla, M. (2003), "Reduction of thermal stresses by developing two-dimensional functionally graded materials", Int. J. Solids Struct., 40(26), 7339-7356. https://doi.org/10.1016/j.ijsolstr.2003.08.017.
  26. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib., 318(1-2), 176-92. https://doi.org/10.1016/j.jsv.2008.03.056.
  27. Punera, D. and Kant, T. (2017), "Free vibration of functionally graded open cylindrical shells based on several refined higher order displacement models", Thin-Walled Struct., 119, 707-726. https://doi.org/10.1016/j.tws.2017.07.016.
  28. Ramteke, P.M., Panda, S.K. and Nitin, S> (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865.
  29. Ramteke, P.M. and Panda, S.K. (2021), "Free vibrational behaviour of multi-directional porous functionally graded structures", Arab. J. Sci. Eng., 46(8), 7741-7756. https://doi.org/10.1007/s13369-021-05461-6.
  30. Ramteke, P.M., Panda, S.K. and Patel, B. (2022), "Nonlinear eigenfrequency characteristics of multi-directional functionally graded porous panels", Compos. Struct., 279, 114707. https://doi.org/10.1016/j.compstruct.2021.114707.
  31. Sah, S.K. and Ghosh, A. (2022), "Influence of porosity distribution on free vibration and buckling analysis of multidirectional functionally graded sandwich plates", Compos. Struct., 279, 114795. https://doi.org/10.1016/j.compstruct.2021.114795.
  32. Salehipour, H., Nahvi, H. and Shahidi, A.R. (2015), "Exact closed-form free vibration analysis for functionally graded micro/nano plates based on modified couple stress and three-dimensional elasticity theories", Compos. Struct., 124, 283-291. https://doi.org/10.1016/j.compstruct.2015.01.015.
  33. Salehipour, H. and Shahsavar, A. (2018), "A three-dimensional elasticity model for free vibration analysis of functionally graded micro/nano plates: Modified strain gradient theory", Compos. Struct., 206, 415-424. https://doi.org/10.1016/j.compstruct.2018.08.033.
  34. Salehipour, H., Shahsavar, A. and Civalek, O. (2019), "Free vibration and static deflection analysis of functionally graded and porous micro/nanoshells with clamped and simply supported edges", Compos. Struct., 221, 110842. https://doi.org/10.1016/j.compstruct.2019.04.014.
  35. Salehipour, H., Shahgholian-Ghahfarokhi, D., Shahsavar, A., Civalek, O. and Edalati, M. (2022), "Static deflection and free vibration analysis of functionally graded and porous cylindrical micro/nano shells based on the three-dimensional elasticity and modified couple stress theories", Mech. Based Des. Struct. Mach., 50(6), 2184-2205. https://doi.org/10.1080/15397734.2020.1775095.
  36. Sayyad, A.S. and Ghugal, Y.M. (2021), "Static and free vibration analysis of doubly-curved functionally graded material shells", Compos. Struct., 269, 114045. https://doi.org/10.1016/j.compstruct.2021.114045.
  37. Sharma, N., Tiwari, P., Maiti, D.K. and Maity, D. (2021), "Free vibration analysis of functionally graded porous plate using 3-D degenerated shell element", Compos. Part C: Open Access, 6, 100208. https://doi.org/10.1016/j.jcomc.2021.100208.
  38. Simsek, M. (2015), "Bi-directional functionally graded materials (BDFGM) for free and forced vibration of timoshenko beams with various boundary conditions", Compos. Struct., 133, 968-78. https://doi.org/10.1016/j.compstruct.2015.08.021.
  39. Sobhy, M. and Zenkour, A.M. (2019), "Porosity and inhomogeneity effects on the buckling and vibration of double-fgm nanoplates via a quasi-3d refined theory", Compos. Struct., 220, 289-303. https://doi.org/10.1016/j.compstruct.2019.03.096.
  40. Tahouneh, V. and Naei, M.H. (2016), "The effect of multidirectional nanocomposite materials on the vibrational response of thick shell panels with finite length and rested on two-parameter elastic foundations", Int. J. Adv. Struct. Eng., 8(1), 11-28. https://doi.org/10.1007/s40091-016-0110-4.
  41. Talebizadehsardari, P., Salehipour, H., Shahgholian-Ghahfarokhi, D., Shahsavar, A. and Karimi, M. (2022), "Free vibration analysis of the macro-micro-nano plates and shells made of a material with functionally graded porosity: A closed-form solution", Mech. Based Des. Struct. Mach., 50(3), 1054-1080. https://doi.org/10.1080/15397734.2020.1744002.
  42. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Method. Appl. M., 198(37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011.
  43. Tornabene, F., Viola, E. and Inman, D.J. (2009) "2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annul plate structures", J. Sound Vib., 328(3), 259-290. https://doi.org/10.1016/j.jsv.2009.07.031.
  44. Wu, C.P. and Yu, L.T. (2019), "Free vibration analysis of bidirectional functionally graded annular plates using finite annular prism methods", J. Mech. Sci. Tech., 33(5), 2267-2279. https://doi.org/10.1007/s12206-019-0428-5.