Browse > Article
http://dx.doi.org/10.12989/sem.2019.71.5.459

Application of hyperbolic shear deformation theory to free vibration analysis of functionally graded porous plate with piezoelectric face-sheets  

Arefi, M. (Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan)
Meskini, M. (Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan)
Publication Information
Structural Engineering and Mechanics / v.71, no.5, 2019 , pp. 459-467 More about this Journal
Abstract
In this paper, hyperbolic shear deformation theory is used for free vibration analysis of piezoelectric rectangular plate made of porous core. Various types of porosity distributions for the porous material is used. To obtain governing equations of motion, Hamilton's principle is used. The Navier's method is used to obtain numerical results of the problem in terms of significant parameters. One can conclude that free vibration responses are changed significantly with change of important parameters such as various porosities and dimensionless geometric parameters such as thickness to side length ratio and ratio of side lengths.
Keywords
free vibration; porous material; hyperbolic shear deformation theory; Hamilton's principle; porosity distribution;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Abbas, I., Hamdy, A. and Youssef, M. (2015), "Two-dimensional fractional order generalized thermoelastic porous material", Lat. Am. J. Solid. Struct., 12(7), 1415-1431. http://doi.org/10.1590/1679-78251584.   DOI
2 Ait Atmane, H., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x.   DOI
3 Arefi, M. and Rahimi, G.H. (2012), "Three-dimensional multifield equations of a functionally graded piezoelectric thick shell with variable thickness, curvature and arbitrary nonhomogeneity", Acta. Mech. 223(1), 63-79. https://doi.org/10.1007/s00707-011-0536-5.   DOI
4 Arefi, M. (2016), "Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials", Acta. Mech., 227(9), 2529-2542. https://doi.org/10.1007/s00707-016-1584-7.   DOI
5 Arefi, M. and Zenkour, A.M. (2017a), "Effect of thermos magneto-electro mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear deformation plate theory", J. Sandw. Struct. Mater., 56, 1-31. https://doi.org/10.1177/1099636217697497.
6 Arefi, M. and Zenkour, A.M. (2017b), "Influence of micro-lengthscale parameters and inhomogeneities on the bending, free vibration and wave propagation analyses of a FG Timoshenko's sandwich piezoelectric microbeam", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636217714181.
7 Arefi, M. and Zenkour, A.M. (2017c), "Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation", Phys. B: Cond. Mat., 521, 188-197. https://doi.org/10.1016/j.physb.2017.06.066.   DOI
8 Mehralian, F., Beni, Y.T. and Zeverdejani, M.K. (2017), "Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes", Phys. B. Condens. Matter, 514, 61-69. https://doi.org/10.1016/j.physb.2017.03.030.   DOI
9 Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells Theory and Analysis, 2nd Ed., CRC Press, Florida, USA.
10 Mirjavadi, S.S. Afshari, B.M. Shafiei, N. Hamouda, A.M.S. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel. Compos. Struct. 25(4), 55-67. https://doi.org/10.12989/scs.2017.25.4.415.
11 Rezaei, A.S. and Saidi, A.R. (2016), "Application of Carrera Unified Formulation to study the effect of porosity on natural frequencies of thick porous-cellular plates", 91, Compos. Part B Eng., 91, 361-370. https://doi.org/10.1016/j.compositesb.2015.12.050.   DOI
12 Wu, X.H., Chen, C.Q., Shen, Y.P. and Tian, X.G. (2002), "A high order theory for functionally graded piezoelectric shells", J. Solid. Struct., 39(20), 5325-5344. https://doi.org/10.1016/S0020-7683(02)00418-3.   DOI
13 Zhao, J., Wang, Q., Deng, X., Choe, K., Zhong, R. and Shuai, C. (2018), "Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions", Compos. Part B, 168, 106-120. https://doi.org/10.1016/j.compositesb.2018.12.044.
14 Arefi, M. (2018b), "Buckling analysis of the functionally graded sandwich rectangular plates integrated with piezoelectric layers under bi-axial loads", J. Sandw. Struct. Mater., 19(6), 712-735. https://doi.org/10.1177/1099636216642393.   DOI
15 Arefi, M. and Zenkour, A.M. (2018), "Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric love nanorod model", J. Intel. Mater. Syst. Struct., 28(17), 2403-2413. https://doi.org/10.1177/1045389X17689930.   DOI
16 Arefi, M., Zamani, M.H. and Kiani, M. (2018), "Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak's foundation", J. Intel. Mater. Syst. Struct., 29(5), 774-786.   DOI
17 Arefi, M. (2018a), "Analysis of a doubly curved piezoelectric nano shell: nonlocal electro-elastic bending solution", Eur. J. Mech-A/Solids, 70, 226-237. https://doi.org/10.1016/j.euromechsol.2018.02.012.   DOI
18 Barati, M.R. and Zenkour, A.M. (2017), "Investigating postbuckling of geometrically imperfect metal foam Nano beams with symmetric and asymmetric porosity distributions", Compos. Struct., 182, 91-98. https://doi.org/10.1016/j.compstruct.2017.09.008.   DOI
19 Benahmed, A., Houari, M.S.A., Benyoucef, S., Elakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009.   DOI
20 Benachour, A., Tahar, H.D., Atmane, H.A., Tounsi, A. and Ahmed, M.S. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B. Eng., 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032.   DOI
21 Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel. Compos. Struct., 20(1), 150-162. http://dx.doi.org/10.12989/scs.2016.20.1.205.
22 Chen, D., Yang, J. and Kitipornchai, S. (2019), "Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method", Civil Mech. Eng., 19(1), 157-170. https://doi.org/10.1016/j.acme.2018.09.004.   DOI
23 Chen, L.W., Lin, C.Y. and Wang, C.C. (2002), "Dynamic stability analysis and control of a composite beam with piezoelectric layers", Compos. Struct., 56(1), 97-109. https://doi.org/10.1016/S0263-8223(01)00183-0.   DOI
24 Demirhan, P.A. and Taskin, V. (2018), "Bending and free vibration of levy-type porous functionally graded plate using state space approach", Compos. Part B, 160, https://doi.org/10.1016/j.compositesb.2018.12.020.
25 Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech. 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665.   DOI
26 El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Bedia, E.A.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004.   DOI
27 Fakhari, V., Ohadi, A. and Yousefian, P. (2011), "Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layer in thermal environment", Compos. Struct., 93(9), 2310-2321. https://doi.org/10.1016/j.compstruct.2011.03.019.   DOI
28 Galeban, M.R. Mojahedin, A. Taghavi Y. and Jabbari, M. (2016), "Free vibration of functionally graded thin beams made of saturated porous materials", Steel. Compos. Struct., 21(5), 25-36. https://doi.org/10.12989/scs.2016.21.5.999.
29 Kim, J., Zur, K.K. and Reddy, J. N (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Comp. Struct., 209, 879-888. https://doi.org/10.1016/j.compstruct.2018.11.023.   DOI
30 Khorshidi, K., Asgari, T. and Fallah, A. (2015), "Free vibrations analysis of functionally graded rectangular nano-plates based on nonlocal exponential shear deformation theory", Mech. Adv. Compos. Struct. , 2(2), 79-93. http://dx.doi.org/10.22075/macs.2015.395.
31 Li, K., Wu, D., Chen, X., Cheng, J., Liu, Z., Gao, W. and Liu, M. (2018), "Isogeometric Analysis of functionally graded porous plates reinforced by graphene platelets", Comp. Struct., 204, 114-130. https://doi.org/10.1016/j.compstruct.2018.07.059.   DOI
32 Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, BB. (2016), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Braz. Soc. Mech. Sci. Eng., 38(8), 2193-2211. https://doi.org/10.1007/s40430-015-0482-6.   DOI
33 Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 1(133), 1079-1092. https://doi.org/10.1016/j.compstruct.2015.08.014.
34 Li, L., Hu, Y. and Ling, L. (2016), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Phys. E., 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028.   DOI
35 Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.   DOI