참고문헌
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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. https://doi.org/10.1177/1045389X17721039
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells Theory and Analysis, 2nd Ed., CRC Press, Florida, USA.
- 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.
- 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.
- 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.
- 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.