Abstract
This paper aims to present free vibration of porous functionally graded thick rectangular plates using a quasi-3D refined theory. This theory considers the thickness stretching effect for vibration analysis of porous plates. It is assumed that the material properties of the porous plate are varying across the plate thickness according to a modified polynomial material law. The equations of motion of the porous plate are obtained via the Hamilton principle. Navier’s technique is applied to obtain the closed-form solution for simply-supported functionally graded materials porous plates. Some numerical validations are presented to prove the accuracy of the present quasi-3D refined theory in predicting the free vibration response of porous plates. The influence of porosity parameter, aspect ratio, side-to-thickness ratio, and exponent graded factor are discussed.
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REFERENCES
Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H., and Omidi, M., Free Vibration of Functionally Graded Rectangular Plates Using First-Order Shear Deformation Plate Theory, Appl. Math. Model., 2010, vol. 34, no. 5, pp. 1276–1291.
Fares, M., Elmarghany, M.K., and Atta, D., An Efficient and Simple Refined Theory for Bending and Vibration of Functionally Graded Plates, Compos. Struct., 2009, vol. 91, no. 3, pp. 296–305.
Thai, H.-T. and Choi, D.-H., A Refined Shear Deformation Theory for Free Vibration of Functionally Graded Plates on Elastic Foundation, Compos. B. Eng., 2012, vol. 43, no. 5, pp. 2335–2347.
Neves, A., Ferreira, A., Carrera, E., Roque, C., Cinefra, M., Jorge, R., and Soares, C., A Quasi-3D Sinusoidal Shear Deformation Theory for the Static and Free Vibration Analysis of Functionally Graded Plates, Compos. B. Eng., 2012, vol. 43, no. 2, pp. 711–725.
Thai, H.-T. and Vo, T.P., A New Sinusoidal Shear Deformation Theory for Bending, Buckling, and Vibration of Functionally Graded Plates, Appl. Math. Model., 2013, vol. 37, no. 5, pp. 3269–3281.
Neves, A., Ferreira, A., Carrera, E., Cinefra, M., Roque, C., Jorge, R., and Soares, C., A Quasi-3D Hyperbolic Shear Deformation Theory for the Static and Free Vibration Analysis of Functionally Graded Plates, Compos. Struct., 2012, vol. 94, no. 5, pp. 1814–1825.
Thai, H.-T., Park, T., and Choi, D.-H., An Efficient Shear Deformation Theory for Vibration of Functionally Graded Plates, Arch. Appl. Mech., 2013, vol. 83, no. 1, pp. 137–149.
Zaoui, F.Z., Tounsi, A., and Ouinas, D., Free Vibration of Functionally Graded Plates Resting on Elastic Foundations Based on Quasi-3D Hybrid-Type Higher Order Shear Deformation Theory, Smart Struct. Syst., 2017, vol. 20, no. 4, pp. 509–524.
Zenkour, A.M., On Vibration of Functionally Graded Plates According to a Refined Trigonometric Plate Theory, Int. J. Struct. Stab. Dy., 2005, vol. 5, no. 2, pp. 279–297.
Hebali, H., Bakora, A., Tounsi, A., and Kaci, A., A Novel Four Variable Refined Plate Theory for Bending, Buckling, and Vibration of Functionally Graded Plates, Steel Compos. Struct., 2016, vol. 22, no. 3, pp. 473–495.
Jha, D., Kant, T., and Singh, R., Free Vibration of Functionally Graded Plates with a Higher-Order Shear and Normal Deformation Theory, Int. J. Struct. Stab. Dy., 2013, vol. 13, no. 1, p. 1350004.
Djedid, I.K., Benachour, A., Houari, M.S.A., Tounsi, A., and Ameur, M., A N-Order Four Variable Refined Theory for Bending and Free Vibration of Functionally Graded Plates, Steel Compos. Struct., 2014, vol. 17, no. 1, pp. 21–46.
Galeban, M., Mojahedin, A., Taghavi, Y., and Jabbari, M., Free Vibration of Functionally Graded Thin Beams Made of Saturated Porous Materials, Steel Compos. Struct., 2016, vol. 21, no. 5, pp. 999–1016.
Chen, D., Yang, J., and Kitipornchai, S., Free and Forced Vibrations of Shear Deformable Functionally Graded Porous Beams, Int. J. Mech. Sci., 2016, vol. 108, pp. 14–22.
Ayache, B., Bennai, R., Fahsi, B., Fourn, H., Atmane, H.A., and Tounsi, A., Analysis of Wave Propagation and Free Vibration of Functionally Graded Porous Material Beam with a Novel Four Variable Refined Theory, Earthq. Struct., 2018, vol. 15, no. 4, pp. 369–382.
Shafiei, N., Mirjavadi, S.S., Mohasel Afshari, B., Rabby, S., and Kazemi, M., Vibration of Two-Dimensional Imperfect Functionally Graded (2D-FG) Porous Nano-/Micro-Beams, Comput. Method Appl. M, 2017, vol. 322, pp. 615–632.
Berghouti, H., Adda Bedia, E., Benkhedda, A., and Tounsi, A., Vibration Analysis of Nonlocal Porous Nanobeams Made of Functionally Graded Material, Adv. Nano Res., 2019, vol. 9, no. 5, pp. 351–364.
Li, H., Pang, F., Chen, H., and Du, Y., Vibration Analysis of Functionally Graded Porous Cylindrical Shell with Arbitrary Boundary Restraints by Using a Semianalytical Method, Compos. B. Eng., 2019, vol. 164, pp. 249–264.
Wang, Y. and Wu, D., Vibration Analysis of Functionally Graded Porous Cylindrical Shell with Arbitrary Boundary Restraints by Using a Semianalytical Method, Aerosp. Sci. Technol., 2017, vol. 66, pp. 83–91.
Zhao, J., Xie, F., Wang, A., Shuai, C., Tang, J., and Wang, Q., A Unified Solution for the Vibration Analysis of Functionally Graded Porous (FGP) Shallow Shells with General Boundary Conditions, Compos. B. Eng., 2019, vol. 156, pp. 406–424.
Akbaş, Ş.D., Vibration and Static Analysis of Functionally Graded Porous Plates, J. Appl. Comput. Mech., 2017, vol. 3, no. 3, pp. 199–207.
Rezaei, A., Saidi, A., Abrishamdari, M., and Mohammadi, M.P., Natural Frequencies of Functionally Graded Plates with Porosities via a Simple Four Variable Plate Theory: An Analytical Approach, Thin-Walled Struct., 2017, vol. 120, pp. 366–377.
Zhao, J., Choe, K., Xie, F., Wang, A., Shuai, C., and Wang, Q., Three-Dimensional Exact Solution for Vibration Analysis of Thick Functionally Graded Porous (FGP) Rectangular Plates with Arbitrary Boundary Conditions, Compos. B. Eng., 2018, vol. 155, pp. 369–381.
Demirhan, P.A. and Taskin, V., Bending and Free Vibration Analysis of Levy-Type Porous Functionally Graded Plate Using State Space Approach, Compos. B. Eng., 2019, vol. 160, pp. 661–676.
Daikh, A.A. and Zenkour, A.M., Free Vibration and Buckling of Porous Power-Law and Sigmoid Functionally Graded Sandwich Plates Using a Simple Higher-Order Shear Deformation Theory, Mater. Res. Express, 2019, vol. 6, no. 11, p. 115707.
Farrokh, M., Afzali, M., and Carrera, E., Mechanical and Thermal Buckling Loads of Rectangular FG Plates by Using Higher-Order Unified Formulation, Mech. Adv. Mater. Struct., 2019, pp. 1–10.
Zenkour, A.M., Quasi-3D Refined Theory for Functionally Graded Porous Plates: Displacements and Stresses, Phys. Mesomech., 2020, vol. 23, no. 1, pp. 39–53. https://doi.org/10.1134/S1029959920010051
Karamanli, A. and Aydogdu, M., Vibration of Functionally Graded Shear and Normal Deformable Porous Microplates via Finite Element Method, Compos. Struct., 2020, vol. 237, p. 111934.
Matsunaga, H., Free Vibration and Stability of Functionally Graded Plates According to a 2-D Higher-Order Deformation Theory, Compos. Struct., 2008, vol. 82, no. 2, pp. 499–512.
Zenkour, A.M. and Aljadani, M.H., Porosity Effect on Thermal Buckling Behavior of Actuated Functionally Graded Piezoelectric Nanoplates, Eur. J. Mech. A. Solids, 2019, vol. 78, p. 103835.
Zenkour, A. and Aljadani, M., Mechanical Buckling of Functionally Graded Plates Using a Refined Higher-Order Shear and Normal Deformation Plate Theory, Adv. Aircr. Spacecr. Sci., 2018, vol. 5, no. 6, pp. 615–632.
Thinh, T.I., Tu, T.M., Quoc, T.H., and Long, N.V., Vibration and Buckling Analysis of Functionally Graded Plates Using New Eight-Unknown Higher Order Shear Deformation Theory, Lat. Am. J. Solids Struct., 2016, vol. 13, no. 3, pp. 456–477.
Zhao, X., Lee, Y., and Liew, K.M., Free Vibration Analysis of Functionally Graded Plates Using the Element-Free KP-Ritz Method, J. Sound Vib., 2009, vol. 319, no. 3–5, pp. 918–939.
Hosseini-Hashemi, S., Fadaee, M., and Atashipour, S.R., Study on the Free Vibration of Thick Functionally Graded Rectangular Plates According to a New Exact Closed-Form Procedure, Compos. Struct., 2011, vol. 93, no. 2, pp. 722–735.
Hosseini-Hashemi, S., Fadaee, M., and Atashipour, S.R., A New Exact Analytical Approach for Free Vibration of Reissner–Mindlin Functionally Graded Rectangular Plates, Int. J. Mech. Sci., 2011, vol. 53, no. 1, pp. 11–22.
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Translated from in Fizicheskaya Mezomekhanika, 2021, Vol. 24, No. 2, pp. 56–70.
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Zenkour, A.M., Aljadani, M.H. Quasi-3D Refined Theory for Functionally Graded Porous Plates: Vibration Analysis. Phys Mesomech 24, 243–256 (2021). https://doi.org/10.1134/S1029959921030036
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DOI: https://doi.org/10.1134/S1029959921030036