Abstract
This study investigates the buckling and free vibration behavior of functionally graded saturated porous (FGSP) using a refined quasi-3D theory that ensures zero transverse shear stress at the top and bottom surfaces of the plate. The material properties depend on the porosity coefficient according to three patterns. Hamilton's principle and Biot's poroelasticity theory are employed to derive the equations of motion, which are then solved using Navier's technique. After examining the accuracy of the suggested approach, the effect of fluid compressibility on natural frequency and critical buckling load is investigated in the undrained condition. Also, the effect of porosity, geometrical parameters, and elastic foundation on the vibration and buckling response of FGSP plates are examined. The study reveals that saturating the pores with fluid leads to increased plate stiffness. This translates to higher critical buckling loads and fundamental frequencies.
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References
Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. J. Appl. Phys. 26(2), 182–185 (1955)
Arefi, M., Meskini, M.: Application of hyperbolic shear deformation theory to free vibration analysis of functionally graded porous plate with piezoelectric face-sheets. Struct. Eng. Mech. 71(5), 459–467 (2019)
Ghorbanpour Arani, A., Khani, M., Khoddami Maraghi, Z.: Dynamic analysis of a rectangular porous plate resting on an elastic foundation using high-order shear deformation theory. J. Vib. Control. Vib. Control 24(16), 3698–3713 (2018)
Tu, T.M., Hoa, L.K., Hung, D.X., Hai, L.T.: Nonlinear buckling and post-buckling analysis of imperfect porous plates under mechanical loads. J. Sandwich Struct. Mater. 22(6), 1910–1930 (2020)
Zghal, S., Dammak, F.: Buckling responses of porous structural components with gradient power-based and sigmoid material variations under different types of compression loads. Compos. Struct. 273, 114313 (2021)
Theodorakopoulos, D., Beskos, D.: Flexural vibrations of poroelastic plates. Acta Mech. 103(1), 191–203 (1994)
Leclaire, P., Horoshenkov, K., Cummings, A.: Transverse vibrations of a thin rectangular porous plate saturated by a fluid. J. Sound Vib. 247(1), 1–18 (2001)
Jabbari, M., Mojahedin, A., Khorshidvand, A.R., Eslami, M.R.: Buckling analysis of a functionally graded thin circular plate made of saturated porous materials. J. Eng. Mech. 140(2), 287–295 (2014)
Jabbari, M., Hashemitaheri, M., Mojahedin, A., Eslami, M.R.: Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials. J. Therm. Stresses 37(2), 202–220 (2014)
Jabbari, M., Mojahedin, A., Joubaneh, E.F.: Thermal buckling analysis of circular plates made of piezoelectric and saturated porous functionally graded material layers. J. Eng. Mech. 141(4), 04014148 (2015)
Jabbari, M., Rezaei, M., Mojahedin, A.: Mechanical buckling of FG saturated porous rectangular plate with piezoelectric actuators. Iran. J. Mech. Eng. Trans. ISME 17(2), 46–66 (2016)
Rezaei, A., Saidi, A.: An analytical study on the free vibration of moderately thick fluid-infiltrated porous annular sector plates. J. Vib. Control 24(18), 4130–4144 (2018)
Rezaei, A., Saidi, A.: Buckling response of moderately thick fluid-infiltrated porous annular sector plates. Acta Mech. 228(11), 3929–3945 (2017)
Rezaei, A., Saidi, A.: On the effect of coupled solid-fluid deformation on natural frequencies of fluid saturated porous plates. Eur. J. Mech. A/Solids 63, 99–109 (2017)
Chen, D., Yang, J., Kitipornchai, S.: Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev–Ritz method. Arch. Civ. Mech. Eng. 19(1), 157–170 (2019)
Zhao, J., Wang, Q., Deng, X., Choe, K., Zhong, R., Shuai, C.: Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions. Compos. B Eng. 168, 106–120 (2019)
Bemani Khouzestani, L., Khorshidvand, A.R.: Axisymmetric free vibration and stress analyses of saturated porous annular plates using generalized differential quadrature method. J. Vib. Control. Vib. Control 25(21–22), 2799–2818 (2019)
Sharifan, M.H., Jabbari, M.: Mechanical buckling analysis of saturated porous functionally graded elliptical plates subjected to in-plane force resting on two parameters elastic foundation based on HSDT. J. Pressure Vessel Technol. 142(4), 041302 (2020)
Mojahedin, A., Jabbari, M., Khorshidvand, A.R., Eslami, M.R.: Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory. Thin Wall. Struct. 99, 83–90 (2016)
Rad, E.S., Saidi, A.R., Rezaei, A.S., Askari, M.: Shear deformation theories for elastic buckling of fluid-infiltrated porous plates: an analytical approach. Compos. Struct. 254, 112829 (2020)
Rezaei, A., Saidi, A.: Exact solution for free vibration of thick rectangular plates made of porous materials. Compos. Struct. 134, 1051–1060 (2015)
Kiarasi, F., Babaei, M., Asemi, K., Dimitri, R., Tornabene, F.: Three-dimensional buckling analysis of functionally graded saturated porous rectangular plates under combined loading conditions. Appl. Sci. 11(21), 10434 (2021)
Babaei, M., Asemi, K., Kiarasi, F.: Static response and free-vibration analysis of a functionally graded annular elliptical sector plate made of saturated porous material based on 3D finite element method. Mech. Based Des. Struct. Mach.. Based Des. Struct. Mach. 51, 1–25 (2020)
Babaei, M., Hajmohammad, M.H., Asemi, K.: Natural frequency and dynamic analyses of functionally graded saturated porous annular sector plate and cylindrical panel based on 3D elasticity. Aerosp. Sci. Technol. 96, 105524 (2020)
Carrera, E., Brischetto, S., Cinefra, M., Soave, M.: Effects of thickness stretching in functionally graded plates and shells. Compos. B Eng. 42(2), 123–133 (2011)
Bouafia, K., Selim, M.M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Bedia, E.A.A., Tounsi, A.: Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model. Steel Compos. Struct. Int. J. 41(4), 487–503 (2021)
Lafi, D.E., Bouhadra, A., Mamen, B., Menasria, A., Bourada, M., Bousahla, A.A., Bourada, F., Tounsi, A., Tounsi, A., Yaylaci, M.: Combined influence of variable distribution models and boundary conditions on the thermodynamic behavior of FG sandwich plates lying on various elastic foundations. Struct. Eng. Mech. 89(2), 103 (2024)
Zaitoun, M.W., Chikh, A., Tounsi, A., Al-Osta, M.A., Sharif, A., Al-Dulaijan, S.U., Al-Zahrani, M.M.: Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment. Thin Wall. Struct. 170, 108549 (2022)
Tahir, S.I., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Dulaijan, S.U., Al-Zahrani, M.M.: The effect of three-variable viscoelastic foundation on the wave propagation in functionally graded sandwich plates via a simple quasi-3D HSDT. Steel Compos. Struct. 42(4), 501 (2022)
Zaitoun, M.W., Chikh, A., Tounsi, A., Sharif, A., Al-Osta, M.A., Al-Dulaijan, S.U., Al-Zahrani, M.M.: An efficient computational model for vibration behavior of a functionally graded sandwich plate in a hygrothermal environment with viscoelastic foundation effects. Eng. Comput. 39(2), 1127–1141 (2023)
Bennedjadi, M., Aldosari, S.M., Chikh, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A.: Visco-elastic foundation effect on buckling response of exponentially graded sandwich plates under various boundary conditions. Geomech. Eng. 32(2), 159 (2023)
Bounouara, F., Aldosari, S.M., Chikh, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Albalawi, H., Tounsi, A.: The effect of visco-Pasternak foundation on the free vibration behavior of exponentially graded sandwich plates with various boundary conditions. Steel Compos. Struct. Int. J. 46(3), 367–383 (2023)
Mudhaffar, I.M., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Zahrani, M.M., Al-Dulaijan, S.U.: Impact of viscoelastic foundation on bending behavior of FG plate subjected to hygro-thermo-mechanical loads. Struct. Eng. Mech. Int. J. 86(2), 167–180 (2023)
Tounsi, A., Mostefa, A.H., Bousahla, A.A., Tounsi, A., Ghazwani, M.H., Bourada, F., Bouhadra, A.: Thermodynamical bending analysis of P-FG sandwich plates resting on nonlinear visco-Pasternak’s elastic foundations. Steel Compos. Struct. 49(3), 307–323 (2023)
Tounsi, A., Mostefa, A.H., Attia, A., Bousahla, A.A., Bourada, F., Tounsi, A., Al-Osta, M.A.: Free vibration investigation of functionally graded plates with temperaturedependent properties resting on a viscoelastic foundation. Struct. Eng. Mech. Int. J. 86(1), 1–16 (2023)
Tounsi, A., Bousahla, A.A., Tahir, S.I., Mostefa, A.H., Bourada, F., Al-Osta, M.A., Tounsi, A.: Influences of different boundary conditions and hygro-thermal environment on the free vibration responses of FGM sandwich plates resting on viscoelastic foundation. Int. J. Struct. Stab. Dyn. 2450117 (2023)
Gawah, Q., Bourada, F., Al-Osta, M. A., Tahir, S. I., Tounsi, A., Yaylacı, M.: An improved first-order shear deformation theory for wave propagation analysis in FG-CNTRC beams resting on a viscoelastic substrate (2024)
Neves, A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N., Soares, C.M.: Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Compos. B Eng. 44(1), 657–674 (2013)
Mashat, D.S., Zenkour, A.M., Radwan, A.F.: A quasi-3D higher-order plate theory for bending of FG plates resting on elastic foundations under hygro-thermo-mechanical loads with porosity. Eur. J. Mech. A. Solids 82, 103985 (2020)
Tru, V.N., Long, N.V., Tu, T.M., Trang, V.T.T.: Static analysis of functionally graded saturated porous plate rested on Pasternak elastic foundation by using a new quasi-3D higher-order shear deformation theory. Arch. Appl. Mech.. Appl. Mech. 93(6), 2565–2583 (2023)
Chen, D., Gao, K., Yang, J., Kitipornchai, S.: An introduction to functionally graded porous materials and composite structures. In: Machine Learning Aided Analysis Design and Additive Manufacturing of Functionally Graded Porous Composite Structures, pp. 3–15. Elsevier (2024)
Chen, D., Yang, J., Kitipornchai, S.: Free and forced vibrations of shear deformable functionally graded porous beams. Int. J. Mech. Sci. 108, 14–22 (2016)
Barati, M.R., Zenkour, A.M.: Investigating post-buckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions. Compos. Struct. 182, 91–98 (2017)
Magnucki, K., Stasiewicz, P.: Elastic buckling of a porous beam. J. Theor. Appl. Mech. 42(4), 859–868 (2004)
Chen, D., Yang, J., Kitipornchai, S.: Elastic buckling and static bending of shear deformable functionally graded porous beam. Compos. Struct. 133, 54–61 (2015)
Gibson, I., Ashby, M.F.: The mechanics of three-dimensional cellular materials. Proc. Roy. Soc. Lond. A Math. Phys. Sci. 382(1782), 43–59 (1982)
Choi, J., Lakes, R.: Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson’s ratio. Int. J. Mech. Sci. 37(1), 51–59 (1995)
Detournay, E., Cheng, A.H.D.: 5-Fundamentals of poroelasticity. In: Fairhurst, C. (ed.) Analysis and Design Methods, pp. 113–171. Pergamon, Oxford (1993)
Reddy, J.N.: Energy Principles and Variational Methods in Applied Mechanics. Wiley, New York (2017)
Huang, Z., Lü, C., Chen, W.: Benchmark solutions for functionally graded thick plates resting on Winkler–Pasternak elastic foundations. Compos. Struct. 85(2), 95–104 (2008)
Swaminathan, K., Naveenkumar, D.: Higher order refined computational models for the stability analysis of FGM plates–analytical solutions. Eur. J. Mech. A. Solids 47, 349–361 (2014)
Rezaei, A., Saidi, A.: Application of carrera unified formulation to study the effect of porosity on natural frequencies of thick porous–cellular plates. Compos. B Eng. 91, 361–370 (2016)
Thai, H.-T., Choi, D.-H.: An efficient and simple refined theory for buckling analysis of functionally graded plates. Appl. Math. Model. 36(3), 1008–1022 (2012)
Ebrahimi, F., Habibi, S.: Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate. Steel Compos. Struct. 20(1), 205–225 (2016)
Thai, H.-T., Choi, D.-H.: A refined plate theory for functionally graded plates resting on elastic foundation. Compos. Sci. Technol. 71(16), 1850–1858 (2011)
Uymaz, B., Aydogdu, M.: Three dimensional mechanical buckling of FG plates with general boundary conditions. Compos. Struct. 96, 174–193 (2013)
Uymaz, B., Aydogdu, M.: Three-dimensional vibration analyses of functionally graded plates under various boundary conditions. J. Reinf. Plast. Compos. 26(18), 1847–1863 (2007)
Detournay, E., Cheng, A.H.-D.: Fundamentals of poroelasticity. In: Analysis and Design Methods, pp. 113–171. Elsevier (1993)
Ebrahimi, F., Habibi, S.: Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate. Steel Compos. Struct. 20, 205–225 (2016)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, London (2003)
Acknowledgements
This research is funded by Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) under grant number: 107.02-2021.16.
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Vu Thi Thu Trang: Methodology, Supervision, Writing – original draft. Nguyen Van Long: Methodology, Project administration, Software, Writing – original draft, Writing – review & editing. Tran Minh Tu: Formal analysis, Software, Supervision, Writing – review & editing. Le Thanh Hai: Data curation, Investigation, Validation, Writing – review & editing.
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Appendix: The global linear stiffness matrix [S], and global mass matrix [M] Coefficients of matrix [S]:
Appendix: The global linear stiffness matrix [S], and global mass matrix [M] Coefficients of matrix [S]:
with \(\xi = k_{w} + k_{sx} \alpha^{2} + k_{sy} \beta^{2} .\)
1.1 Coefficients of matrix [M]:
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Trang, V.T.T., Van Long, N., Tu, T.M. et al. A refined quasi-3D model for buckling and free vibration of functionally graded saturated porous plate resting on elastic foundation. Arch Appl Mech (2024). https://doi.org/10.1007/s00419-024-02613-6
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DOI: https://doi.org/10.1007/s00419-024-02613-6