Abstract
This article deals with free vibration response of functionally graded cylindrical and spherical porous shells in thermal environments with temperature-dependent material properties. The effective material properties are determined via the rule of mixture with porosity phases. The equation of motion is developed based on a curved 8-node degenerated shell element formulation using the principle of virtual work. Two different material mixtures are considered, the first one is zirconium oxide and titanium alloy referred to as ZrO2/Ti-6AL-4V, and the second one is silicon nitride and stainless steel referred to as Si3N4/SUS304. The influence of material constituents, power-law indexes, boundary conditions, radius to thickness ratio, porosity parameter, and temperature gradient on the natural frequencies is studied in detail. It is found that the porosity of the constituent material has a significant consequence on the vibration response of FGM shells, especially in high temperatures.
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References
Huang, X.L., Shen, H.S.: Nonlinear vibration and dynamic response of functionally graded plates in thermal environments. Int. J. Solids Struct. 41, 2403–2427 (2004)
Kim, Y.W.: Temperature dependent vibration analysis of functionally graded rectangular plates. J. Sound Vib. 284, 531–549 (2005)
Kadoli, R., Ganesan, N.: Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition. J. Sound Vib. 289, 450–480 (2006)
Matsunaga, H.: Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory. Compos. Struct. 82, 499–512 (2008)
Han, S.C., Lomboy, G.R., Kim, K.D.: Mechanical vibration and buckling analysis of FGM plates and shells using a four-node quasi-conforming shell element. Int. J. Struct. Stab. Dyn. 8(2), 203–229 (2008)
Zhao, X., Lee, Y.Y., Liw, K.M.: Free vibration analysis of functionally graded plates using the element-free kp-Ritz method. J. Sound Vib. 319, 918–939 (2009)
Shahrjerdi, A., Mustapha, F., Bayat, M., Majid, D.L.A.: Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory. J. Mech. Sci. Technol. 25(9), 2195–2209 (2011)
Nguyen-Xuan, H., Tran Loc, V., Thai Chien, H., Nguyen-Thoi, T.: Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing. Thin-Walled Struct. 54, 1–18 (2012)
Kar, V.R., Panda, S.K.: Free vibration responses of temperature dependent functionally graded curved panels under thermal environment. Latin Am. J. Solids Struct. 12, 2006–2024 (2015)
Fazzolari, F.A.: Modal characteristics of P- and S-FGM plates with temperature-dependent materials in thermal environment. J. Therm. Stresses 39(7), 854–873 (2016)
Parida, S., Mohanty, S.C.: Free vibration analysis of rotating functionally graded material plate under nonlinear thermal environment using higher order shear deformation theory. J. Mech. Eng. Sci. 233(6), 1–18 (2018)
Parida, S., Mohanty, S.C.: Free vibration analysis of functionally graded skew plate in thermal environment using higher order theory. Int. J. Appl. Mech. 10(1), 1–26 (2018)
Burlayenko, V.N., Sadowski, T., Dimitrova, S.: Three-dimensional free vibration analysis of thermally loaded FGM sandwich plates. Materials. 12(15), 1–20 (2019)
Shakouri, M.: Free vibration analysis of functionally graded rotating conical shells in thermal environment. Compos. B 163, 574–584 (2019)
Hong, N.T.: Nonlinear static bending and free vibration analysis of bidirectional functionally graded material plates. Int. J. Aerosp. Eng. 4, 1–16 (2020)
Moita, J.S., Araújo, A.L., Correia, V.F., Soares, C.M.M.: Vibrations of functionally graded material axisymmetric shells. Compos. Struct. 248, 112489 (2020)
Wattanasakulpong, N., Ungbhakorn, V.: Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerosp. Sci. Technol. 32, 111–120 (2014)
Ebrahimi, F., Ghasemi, F., Salari, E.: Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica 51, 223–249 (2016)
Ghadiri, M., Safar, P.H.: Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment. J. Therm. Stresses 40(1), 1–17 (2017)
Trinh, M.C., Nguyen, D.D., Kim, S.E.: Effects of porosity and thermomechanical loading on free vibration and nonlinear dynamic response of functionally graded sandwich shells with double curvature. Aerosp. Sci. Technol. 87, 119–132 (2019)
Talebizadehsardari, P., Salehipour, H., Ghahfarokhi, D.S., Shahsavar, A., Karimi, M.: 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. 996, 1–27 (2020)
Tran, T.T., Tran, V.K., Pham, Q.H., Zenkour, A.M.: Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation. Compos. Struct. 264, 777 (2021)
Katiyar, V., Gupta, A.: Vibration response of a geometrically discontinuous bi-directional functionally graded plate resting on elastic foundations in thermal environment with initial imperfections. Mech. Based Des. Struct. Mach. 5, 3100 (2021)
Tran, Q.H., Duong, H.T., Tran, T.M.: Free vibration analysis of functionally graded doubly curved shell panels resting on elastic foundation in thermal environments. Int. J. Adv. Struct. Eng. 10(3), 275–283 (2018)
Rezaei, A.S., Saidi, A.R., Abrishamdari, M., Pour Mohammadi, M.H.: Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: an analytical approach. Thin-Walled Struct. 120, 366–377 (2017)
Kiani, Y., Akbarzadeh, A.H., Chen, Z.T., Eslami, M.R.: Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak-type elastic foundation. Compos. Struct. 94, 2474–2484 (2012)
Zhao, X., Lee, Y.Y., Liew, K.M.: Thermoelastic and vibration analysis of functionally graded cylindrical shells. Int. J. Mech. Sci. 51, 694–707 (2009)
Wang, Y., Wu, D.: Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory. Aerosp. Sci. Technol. 66, 83–91 (2017)
Zghal, S., Dammak, F.: Vibration characteristics of plates and shells with functionally graded pores imperfections using an enhanced finite shell element. Comput. Math. Appl. 99, 52–72 (2021)
Khan, T., Zhang, N., Akram, A.: State of the art review of functionally graded materials. In: International Conference on Computing, Mathematics and Engineering Technologies – iCoMET, (2019) Doi: https://doi.org/10.1109/ICOMET.2019.8673489
Wang, Y.Q., Zu, J.W.: Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment. Aerosp. Sci. Technol. 69, 550–562 (2017)
Wattanasakulpong, N., Chaikittiratana, A.: Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method. Meccanica 50, 1331–1342 (2015)
Akbaş, ŞD.: Vibration and static analysis of functionally graded porous plates. J. Appl. Comput. Mech. 3(3), 199–207 (2017)
Wang, Y., Ye, C., Zu, J.W.: Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities. Appl. Math. Mech. 39(11), 1587–1604 (2018)
Abuteir, B.W., Harkati, E., Boutagouga, D., Mamouri, S., Djeghaba, K.: Thermo-mechanical nonlinear transient dynamic and dynamic-buckling analysis of functionally graded material shell structures using an implicit conservative/decaying time integration scheme. Mech. Adv. Mater. Struct. 4, 1–20 (2021)
Oñate, E.: Structural analysis with the finite element method linear statics. Beams Plates Shells. 2, 178–212 (2013)
Tuan, T.A., Quoc, T.H., Tu, T.M.: Free vibration analysis of laminated stiffened cylindrical panels using finite element method. J. Sci. Technol. 6, 99 (2016)
Wong, Y.Y., Crouch, R.S.: A compact geometrically nonlinear FE shell code for cardiac analysis: shell formulation. In: 7th European Conf on Computational Fluid Dynamics (ECFD 7), pp. 1–12 (2018)
Hajlaoui, A., Jarraya, A., El BikriDammak, K.F.: Buckling analysis of functionally graded materials structures with enhanced solid-shell elements and transverse shear correction. Compos. Struct. 132, 87–97 (2015)
Nguyen, T.K., Sab, K., Bonnet, G.: First-order shear deformation plate models for functionally graded materials. Compos. Struct. 83(1), 25–36 (2008)
Boutagouga, D.: A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions. Int. J. Numer. Meth. Eng. 110(6), 573–600 (2017)
Groenwold, A.A., Stander, N.: An efficient 4-node 24 D.O.F thick shell finite element with 5-point quadrature. Eng. Comput. 12(8), 723–747 (1995)
Huang, X.L., Shen, H.S.: Nonlinear vibration and dynamic response of functionally graded plates in thermal environments. Int. J. Solids Struct. 41(9–10), 2403–2427 (2004)
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Abuteir, B.W., Boutagouga, D. Free-vibration response of functionally graded porous shell structures in thermal environments with temperature-dependent material properties. Acta Mech 233, 4877–4901 (2022). https://doi.org/10.1007/s00707-022-03351-y
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DOI: https://doi.org/10.1007/s00707-022-03351-y