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Vibration characteristics of porous FGM plate with variable thickness resting on Pasternak’s foundation. (English) Zbl 1476.74055

Summary: In the paper, free vibration analysis of tapered Functionally Graded Material (FGM) plate with the inclusion of porosity has been performed. The tapered porous FGM plate is considered resting on a two-parameter (Winkler and Pasternak) elastic foundation. The displacement model of the kinematic equation for the plates in the present formulation is based on the First-order shear deformation theory (FSDT). The governing equation for free vibration analysis of FGM plates is obtained using Hamilton’s principle. Simple power-law, Exponential Law, and Sigmoid law are used for tailored the material properties in the thickness direction of FGM plates. The solution of the resulting partial differential equation is obtained by using Galerkin-Vlasov’s method with different boundary conditions. The solutions for uniform and uniform varying thick plates are investigated, and a comparative study is examined by comparing the results obtained with FSDT and Higher-order shear deformation theory (HSDT). The findings of the comparative study with the present approach provide pertinent outcomes for the vibration analysis of tapered FGM plates. The analytical solution for vibration analysis is presented to reveal the effects of porosity parameter, volume exponent, span ratio, aspect ratio, porosity distribution, and boundary conditions. Also, the elastic foundation parameter on tapered FGM plate increases the non-dimensional frequency, and the Pasternak foundation effect always dominates over the Winkler foundation.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74E05 Inhomogeneity in solid mechanics
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[1] Amini, M. H.; Soleimani, M.; Rastgoo, A., Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation, Smart Mater. Struct., 18 (2009)
[2] Baferani, A. H.; Saidi, A. R.; Ehteshami, H., Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation, Compos. Struct., 93, 7, 1842-1853 (2011)
[3] Benachour, A.; Tahar, H. D.; Atmane, H. A.; Tounsi, A.; Ahmed, M. S., A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient, Compos. B Eng., 42, 1386-1394 (2011)
[4] Bert, C. W.; Malik, M., Free vibration analysis of tapered rectangular plates by differential quadrature method: a semi-analytical approach, J. Sound Vib., 190, 41-63 (1996)
[5] Bouguenina, O.; Belakhdar, K.; Tounsi, A.; Bedia, E. A.A., Numerical analysis of FGM plates with variable thickness subjected to thermal buckling, Steel Compos. Struct., 19, 679-695 (2015)
[6] Chen, D.; Kitipornchai, S.; Yang, J., Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, Thin-Walled Struct., 107, 39-48 (2016)
[7] Chen, D.; Yang, J.; Kitipornchai, S., Elastic buckling and static bending of shear deformable functionally graded porous beam, Compos. Struct., 133, 54-61 (2015)
[8] Cheng, Z. Q.; Batra, R. C., Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates, J. Sound Vib., 229, 4, 879-895 (2000) · Zbl 1235.74209
[9] D Mindlin, R., Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, J. Appl. Mech., 18 (1951) · Zbl 0044.40101
[10] Demirhan, P. A.; Taskin, V., Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach, Compos. B Eng., 160, 661-676 (2019)
[11] Efraim, E.; Eisenberger, M., Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, J. Sound Vib., 299, 720-738 (2007)
[12] Gupta, A.; Talha, M.; Singh, B. N., Vibration characteristics of functionally graded material plate with various boundary constraints using higher order shear deformation theory, Compos. B Eng., 94, 64-74 (2016)
[13] Hao, Y. X.; Chen, L. H.; Zhang, W.; Lei, J. G., Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate, J. Sound Vib., 312, 862-892 (2008)
[14] Hao, Y. X.; Zhang, W.; Yang, J., Nonlinear dynamics of a FGM plate with two clamped opposite edges and two free edges, Acta Mech. Solida Sin., 27, 394-406 (2014)
[15] Jung, W. Y.; Han, S. C.; Park, W. T., Four-variable refined plate theory for forced-vibration analysis of sigmoid functionally graded plates on elastic foundation, Int. J. Mech. Sci., 111-112, 73-87 (2016)
[16] Koizumi, M., FGM activities in Japan, Compos. B Eng., 28, 1-4 (1997)
[17] Magnucka-Blandzi, E., Axi-symmetrical deflection and buckling of circular porous-cellular plate, Thin-Walled Struct., 46, 333-337 (2008)
[18] Malekzadeh, P.; Karami, G., Vibration of non-uniform thick plates on elastic foundation by differential quadrature method, Eng. Struct., 26, 1473-1482 (2004)
[19] Manna, M. C., Free vibration of tapered isotropic rectangular plates, JVC/Journal Vib. Control., 18, 76-91 (2012)
[20] Matsunaga, H., Free vibration and stability of functionally graded plates according to 2-D higher-order deformation theory, Compos. Struct. - Compos STRUCT., 84, 132-146 (2008)
[21] Nerantzaki, M. S.; Katsikadelis, J. T., An analog equation solution to dynamic analysis of plates with variable thickness, Eng. Anal. Bound. Elem., 17, 145-152 (1996)
[22] Pabst, W.; Tichá, G.; Gregorová, E.; Týnová, E., Effective elastic properties of alumina-zirconia composite ceramics part 5. Tensile modulus of alumina-zirconia composite ceramics, Ceram. - Silikaty., 49, 77-85 (2005)
[23] Pouladvand, M., Thermal stability of thin rectangular plates with variable thickness made of functionally graded materials, 1, 171-189 (2009)
[24] Reddy, J. N., Analysis of functionally graded plates. Int. J. Numer. METHODS Eng, Int. J. Numer. Methods Eng., 47, 663-684 (2000) · Zbl 0970.74041
[25] Reddy, J. N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (2003), CRC Press: CRC Press Boca Raton
[26] Reissner, E., On the theory of bending of elastic plates, J. Math. Phys., 23, 184-191 (1944) · Zbl 0061.42501
[27] Rezaei, A. S.; Saidi, A. R., Exact solution for free vibration of thick rectangular plates made of porous materials, Compos. Struct., 134, 1051-1060 (2015)
[28] Rezaei, A. S.; Saidi, A. R., 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)
[29] Rezaei, A. S.; Saidi, A. R., Buckling response of moderately thick fluid-infiltrated porous annular sector plates, Acta Mech., 228, 3929-3945 (2017) · Zbl 1380.74033
[30] Rezaei, A. S.; Saidi, A. R., On the effect of coupled solid-fluid deformation on natural frequencies of fluid saturated porous plates, Eur. J. Mech. Solid., 63, 99-109 (2017) · Zbl 1406.74204
[31] Rezaei, A. S.; Saidi, A. R.; Abrishamdari, M.; Mohammadi, M. H.P., 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)
[32] Sakiyama, T.; Huang, M., Free vibration analysis of rectangular plates with variable thickness, J. Sound Vib., 17, 705-713 (1998)
[33] Shahsavari, D.; Shahsavari, M.; Li, L.; Karami, B., A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation, Aero. Sci. Technol., 72, 134-149 (2018)
[34] Shufrin, I.; Eisenberger, M., Vibration of shear deformable plates with variable thickness - first-order and higher-order analyses, J. Sound Vib., 290, 465-489 (2006)
[35] Singh, S. J.; Harsha, S. P., Exact solution for free vibration and buckling of sandwich S-FGM plates on pasternak elastic foundation with various boundary conditions, Int. J. Struct. Stabil. Dynam., 19 (2019)
[36] Singh, S. J.; Harsha, S. P., Nonlinear dynamic analysis of sandwich S-FGM plate resting on pasternak foundation under thermal environment, Eur. J. Mech. Solid., 76, 155-179 (2019) · Zbl 1472.74093
[37] Singh, S. J.; Harsha, S. P., Analysis of porosity effect on free vibration and buckling responses for sandwich sigmoid function based functionally graded material plate resting on Pasternak foundation using Galerkin Vlasov’s method, J. Sandw. Struct. Mater. (2020)
[38] Singh, S. J.; Harsha, S. P., Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov’s method: a semi-analytical approach, Thin-Walled Struct., 150, 106668 (2020)
[39] Spriggs, R. M., Expression for effect of porosity on elastic modulus of polycrystalline refractory materials, particularly aluminum oxide, Sci. Sinter., 44, 628-629 (1961)
[40] Thai, H. T.; Choi, D. H., A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation, Compos. B Eng., 43, 2335-2347 (2012)
[41] Thai, H. T.; Choi, D. H., A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates, Compos. Struct., 101, 332-340 (2013)
[42] Vel, S. S.; Batra, R. C., Three-dimensional exact solution for the vibration of functionally graded rectangular plates, J. Sound Vib., 272, 703-730 (2004)
[43] Wang, Y. Q.; Zu, J. W., Large-amplitude vibration of sigmoid functionally graded thin plates with porosities, Thin-Walled Struct., 119, 911-924 (2017)
[44] Wattanasakulpong, N.; Ungbhakorn, V., Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aero. Sci. Technol., 32, 111-120 (2014)
[45] Xiang, Y.; Wang, C. M.; Kitipornchai, S., Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations, Int. J. Mech. Sci., 36, 311-316 (1994) · Zbl 0799.73048
[46] Yang, J.; Shen, H. S., Dynamic response of initially stressed functionally graded rectangular thin plates, Compos. Struct., 54, 4, 497-508 (2001)
[47] Zenkour, A. M., A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities, Compos. Struct., 201, 38-48 (2018)
[48] Zhang, W.; Yang, J.; Hao, Y., Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory, Nonlinear Dynam., 59, 619-660 (2010) · Zbl 1189.74053
[49] Zhang, W.; Hao, Y.; Guo, X.; Chen, L., Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations, Meccanica, 47, 985-1014 (2012) · Zbl 1284.74048
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