참고문헌
- Aghababaei, R. and Reddy, J.N. (2009), "Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates", J. Sound Vib., 326(1-2), 277-289. https://doi.org/10.1016/j.jsv.2009.04.044
- Anh, V.T.T., Bich, D.H. and Duc, N.D. (2015), "Nonlinear stability analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads", Eur. J. Mech. - A/Solids, 50, 28-38. https://doi: 10.1016/j.euromechsol.2014.10.004
- Ansari, R. and Sahmani, S. (2011), "Surface stress effects on the free vibration behavior of nanoplates", Int. J. Eng. Sci., 49(11), 1204-1215. https://doi.org/10.1016/j.ijengsci.2011.06.005
- Arshid, E. and Khorshidvand, A.R. (2018), "Thin-Walled Structures Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method", Thin Wall. Struct., 125(January), 220-233. https://doi.org/10.1016/j.tws.2018.01.007
- Arshid, E., Khorshidvand, A.R. and Khorsandijou, S.M. (2019), "The effect of porosity on free vibration of SPFG circular plates resting on visco-Pasternak elastic foundation based on CPT, FSDT and TSDT", Struct. Eng. Mech., Int. J., 70(1), 97-112. https://doi.org/10.12989/sem.2019.70.1.097
- Barati, M.R. (2017), "Coupled effects of electrical polarization-strain gradient on vibration behavior of double-layered flexoelectric nanoplates", Smart Struct. Syst., Int. J., 20(5), 573-581. https://doi.org/10.12989/sss.2017.20.5.573
- Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., Int. J., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699
- Bui, T.Q., Doan, D.H., Van Do, T., Hirose, S. and Duc, N.D. (2016), "High frequency modes meshfree analysis of Reissner-Mindlin plates", J. Sci. Adv. Mater. Devices, 1, 400-412. https://doi:10.1016/j.jsamd.2016.08.005
- Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Technol., 77, 419-428. https://doi: 10.1016/j.ast.2018.03.020
- Duc, N.D. and Cong, P.H. (2015), "Nonlinear vibration of thick FGM plates on elastic foundation subjected to thermal and mechanical loads using the first-order shear deformation plate theory", Cogent Eng., 2(1), 1045222. https://doi: 10.1080/23311916.2015.1045222
- Duc, N.D. and Quan, T.Q. (2014), "Transient responses of functionally graded double curved shallow shells with temperature-dependent material properties in thermal environment", Eur. J. Mech. - A/Solids, 47, 101-123. https://doi: 10.1016/j.euromechsol.2014.03.002
- Duc, N.D. and Thang, P.T. (2014), "Nonlinear buckling of imperfect eccentrically stiffened metal-ceramic-metal S-FGM thin circular cylindrical shells with temperature-dependent properties in thermal environments", Int. J. Mech. Sci., 81, 17-25. https://doi: 10.1016/j.ijmecsci.2014.01.016
- Duc, N.D. and Tung, H.V. (2010), "Mechanical and thermal postbuckling of shear-deformable FGM plates with temperature-dependent properties", Mech. Compos. Mater., 46, 461-476. https://doi: 10.1007/s11029-010-9163-9
- Duc, N.D., Cong, P.H., Anh, V.M., Quang, V.D., Tran, P., Tuan, N.D. and Thinh, N.H. (2015), "Mechanical and thermal stability of eccentrically stiffened functionally graded conical shell panels resting on elastic foundations and in thermal environment", Compos. Struct., 132, 597-609. https://doi:10.1016/j.compstruct.2015.05.072
- Duc, N.D., Nguyen, P.D. and Khoa, N.D. (2017a), "Nonlinear dynamic analysis and vibration of eccentrically stiffened S-FGM elliptical cylindrical shells surrounded on elastic foundations in thermal environments", Thin-Wall. Struct., 117, 178-189. https://doi:10.1016/j.tws.2017.04.013
- Duc, N.D., Khoa, N.D. and Thiem, H.T. (2017b), "Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy's third-order shear deformation shell theory", Mech. Adv. Mater. Struct., 25, 1156-1167. https://doi:10.1080/15376494.2017.1341581
- Ebrahimi, F. and Barati, M.R. (2016), "An exact solution for buckling analysis of embedded piezo-electro-magnetically actuated nanoscale beams", Adv. Nano Res., Int. J., 4(2), 65-84. http://doi.org/10.12989/anr.2016.4.2.065
- Ebrahimi, F., Daman, M. and Jafari, A. (2017), "Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment", Smart Struct. Syst., Int. J., 20(6), 709-728. https://doi.org/10.12989/sss.2017.20.6.709
- Ebrahimi, F., Nouraei, M., Dabbagh, A. and Civalek, O. (2019a), "Buckling analysis of graphene oxide powder-reinforced nanocomposite beams subjected to non-uniform magnetic field", Struct. Eng. Mech., Int. J., 71(5), 351-361. https://doi.org/10.12989/sem.2019.71.4.351
- Ebrahimi, F., Karimiasl, M. and Mahesh, V. (2019b), "Vibration analysis of magneto-flexo-electrically actuated porous rotary nanobeams considering thermal effects via nonlocal strain gradient elasticity theory", Adv. Nano Res., Int. J., 7(4), 223-231. https://doi.org/10.12989/anr.2019.7.4.223
- Fu, J.Y., Zhu, W., Li, N. and Cross, L.E. (2006), "Experimental studies of the converse flexoelectric effect induced by inhomogeneous electric field in a barium strontium titanate composition", J. Appl. Phys., 100(2), 024112. https://doi.org/10.1063/1.2219990
- Guerroudj, H.Z., Yeghnem, R., Kaci, A., Zaoui, F.Z., Benyoucef, S. and Tounsi, A. (2018), "Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory", Smart Struct. Syst., Int. J., 22(1), 121-132. https://doi.org/10.12989/sss.2018.22.1.121
- Hosseini-Hashemi, S., Kermajani, M. and Nazemnezhad, R. (2015), "An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory", Eur. J. Mech., A/Solids, 51, 29-43. https://doi.org/10.1016/j.euromechsol.2014.11.005
- Hu, S. and Shen, S. (2010), "Variational principles and governing equations in nano-dielectrics with the flexoelectric effect", Sci. China Phys. Mech. Astron., 53(8), 1497-1504. https://doi.org/10.1007/s11433-010-4039-5
- Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92(3), 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024
- Khoa, N.D., Thiem, H.T. and Duc, N.D. (2017), "Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal-ceramic-metal layers in thermal environment using Reddy's third-order shear deformation shell theory", Mech. Adv. Mater. Struct., 26, 248-259. https://doi:10.1080/15376494.2017.1341583
- Kiran, M.C. and Kattimani, S.C. (2018), "Free vibration and static analysis of functionally graded skew magneto-electro-elastic plate", Smart Struct. Syst., Int. J., 21(4), 493-519. https://doi.org/10.12989/sss.2018.21.4.493
- Lao, C.S., Kuang, Q., Wang, Z.L., Park, M.C. and Deng, Y. (2007), "Polymer functionalized piezoelectric-FET as humidity/chemical nanosensors", Appl. Phys. Lett., 90(26), 2-4. https://doi.org/10.1063/1.2748097
- Liu, C., Hu, S. and Shen, S. (2012), "Effect of flexoelectricity on electrostatic potential in a bent piezoelectric nanowire", Smart Mater. Struct., 21(11), 115024. https://doi.org/10.1088/0964-1726/21/11/115024
- Liu, C., Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2013), "Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory", Compos. Struct., 106, 167-174. https://doi.org/10.1016/j.compstruct.2013.05.031
- Ma, W. and Cross, L.E. (2001), "Observation of the flexoelectric effect in relaxor Pb(Mg1/3Nb2/3)O3 ceramics", Appl. Phys. Lett., 78(19), 2920-2921. https://doi.org/10.1063/1.1356444
- Ma, W. and Cross, L.E. (2002), "Flexoelectric polarization of barium strontium titanate in the paraelectric state", Appl. Phys. Lett., 81(18), 3440-3442. https://doi.org/10.1063/1.1518559
- Ma, W. and Cross, L.E. (2006), "Flexoelectricity of barium titanate", Appl. Phys. Lett., 88(23), 2004-2007. https://doi.org/10.1063/1.2211309
- Mahesh, V., Kattimani, S., Harursampath, D. and Trung, N.T. (2019), "Coupled evaluation of the free vibration characteristics of magneto-electro-elastic skew plates in hygrothermal environment", Smart Struct. Syst., Int. J., 24(2), 267-292. https://doi.org/10.12989/sss.2019.24.2.267
- Maranganti, R., Sharma, N.D. and Sharma, P. (2006), "Electromechanical coupling in nonpiezoelectric materials due to nanoscale nonlocal size effects: Green's function solutions and embedded inclusions", Phys. Rev. B - Condens Matt. Mater. Phys., 74(1), 1-14. https://doi.org/10.1103/PhysRevB.74.014110
- Mashkevich, V.S. (1957), "Electrical, optical and elastic properties of diamond type crystals", Sov. Phys. JETP, 5(4), 707-713.
- Mehrabadi, S.J., Aragh, B.S., Khoshkhahesh, V. and Taherpour, A. (2012), "Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight single-walled carbon nanotubes", Compos. Part B: Eng., 43(4), 2031-2040. https://doi.org/10.1016/j.compositesb.2012.01.067
- Mindlin, R.D. (1968), "Polarization gradient in elastic dielectrics", Int. J. Solids Struct., 4(6), 637-642. https://doi.org/10.1016/0020-7683(68)90079-6
- Minh, P.P. and Duc, N.D. (2019), "The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory", Compos. Part B: Eng., 175, 107086. https://doi:10.1016/j.compositesb.2019.107086
- Nguyen, T.D., Mao, S., Yeh, Y.-W., Purohit, P.K. and McAlpine, M.C. (2013), "Nanoscale Flexoelectricity", Adv. Mater., 25(7), 946-974. https://doi.org/10.1002/adma.201203852
- Rahmani, O., Hosseini, S.A.H., Ghoytasi, I. and Golmohammadi, H. (2018), "Free vibration of deep curved FG nano-beam based on modified couple stress theory", Steel Compos. Struct., Int. J., 26(5), 607-620. https://doi.org/10.12989/scs.2018.26.5.607
- Robinson, C.R., White, K.W. and Sharma, P. (2012), "Elucidating the mechanism for indentation size-effect in dielectrics", Appl. Phys. Lett., 101(12), 122901. https://doi.org/10.1063/1.4753799
- Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A. and Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., Int. J., 33(6), 805-822. https://doi.org/10.12989/scs.2019.33.6.805
- Sharma, N.D., Maranganti, R. and Sharma, P. (2007), "On the possibility of piezoelectric nanocomposites without using piezoelectric materials", J. Mech. Phys. Solids, 55(11), 2328-2350. https://doi.org/10.1016/j.jmps.2007.03.016
- Sharma, N.D., Landis, C.M. and Sharma, P. (2010), "Piezoelectric thin-film super-lattices without using piezoelectric materials", J. Appl. Phys., 108(2), 024304. https://doi.org/10.1063/1.3443404
- Shen, S. and Hu, S. (2010), "A theory of flexoelectricity with surface effect for elastic dielectrics", J. Mech. Phys. Solids, 58(5), 665-677. https://doi.org/10.1016/j.jmps.2010.03.001
- Shu, L., Wei, X., Pang, T., Yao, X. and Wang, C. (2011), "Symmetry of flexoelectric coefficients in crystalline medium", J. Appl. Phys., 110(10), 104106. https://doi.org/10.1063/1.3662196
- Tagantsev, A.K. (1986), "Piezoelectricity and flexoelectricity in crystalline dielectrics", Phys. Rev. B, 34(8), 5883-5889. https://doi.org/10.1103/PhysRevB.34.5883
- Tagantsev, A.K. and Gerra, G. (2006), "Interface-induced phenomena in polarization response of ferroelectric thin films", J. Appl. Phys., 100(5), 051607. https://doi.org/10.1063/1.2337009
- Tanner, S.M., Gray, J.M., Rogers, C.T., Bertness, K.A. and Sanford, N.A. (2007), "High-Q GaN nanowire resonators and oscillators", Appl. Phys. Lett., 91(20), 203117. https://doi.org/10.1063/1.2815747
- Van Thu, P. and Duc, N.D. (2016), "Non-linear dynamic response and vibration of an imperfect three-phase laminated nanocomposite cylindrical panel resting on elastic foundations in thermal environments", Sci. Eng. Compos. Mater., 24. https://doi.org/10.1515/secm-2015-0467
- Wang, Z.L. (2006), "Piezoelectric Nanogenerators Based on Zinc Oxide Nanowire Arrays", Science, 312(5771), 242-246. https://doi.org/10.1126/science.1124005
- Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation", Appl. Mathe. Model., 39(18), 5459-5472. https://doi.org/10.1016/j.apm.2014.12.058
- Yang, X.D., Chen, L.Q. and Zu, J.W. (2011), "Vibrations and stability of an axially moving rectangular composite plate", J. Appl. Mech., 78(1), 011018-011029. https://doi.org/10.1115/1.4002002
- Yang, W., Liang, X. and Shen, S. (2015), "Electromechanical responses of piezoelectric nanoplates with flexoelectricity", Acta Mechanica, 226(9), 3097-3110. https://doi.org/10.1007/s00707-015-1373-8
- Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., Int. J., 21(1), 15-21. https://doi.org/10.12989/sss.2018.21.1.015
- Yudin, P.V. and Tagantsev, A.K. (2013), "Fundamentals of flexoelectricity in solids", Nanotechnology, 24(43), 432001. https://doi.org/10.1088/0957-4484/24/43/432001
- Zhang, Z. and Jiang, L. (2014), "Size effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity", J. Appl. Phys., 116(13), 134308. https://doi.org/10.1063/1.4897367
- Zhang, Z., Yan, Z. and Jiang, L. (2014), "Flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nanoplate", J. Appl. Phys., 116(1), 014307. https://doi.org/10.1063/1.4886315
- Zhang, S., Xu, M., Liu, K. and Shen, S. (2015), "A flexoelectricity effect-based sensor for direct torque measurement", J. Phys. D: Appl. Phys., 48(48), 485502. https://doi.org/10.1088/0022-3727/48/48/485502
- Zhao, M., Qian, C., Lee, S.W.R., Tong, P., Suemasu, H. and Zhang, T.Y. (2007), "Electro-elastic analysis of piezoelectric laminated plates", Adv. Compos. Mater., 16(1), 63-81. https://doi.org/10.1163/156855107779755273
- Zenkour, A.M. (2015), "A comparative study for bending of cross-ply laminated plates resting on elastic foundations", Smart Struct. Syst, Int. J., 15(6), 1562-1582. https://doi.org/10.12989/sss.2015.15.6.1569
- Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010
- Zubko, P., Catalan, G. and Tagantsev, A.K. (2013), "Flexoelectric effect in solids", Annual Rev. Mater. Res., 43(1), 387-421. https://doi.org/10.1146/annurev-matsci-071312-121634
피인용 문헌
- Computer modeling for frequency performance of viscoelastic magneto-electro-elastic annular micro/nanosystem via adaptive tuned deep learning neural network optimization vol.11, pp.2, 2020, https://doi.org/10.12989/anr.2021.11.2.203
- Thermomechanical Buckling Analysis of the E&P-FGM Beams Integrated by Nanocomposite Supports Immersed in a Hygrothermal Environment vol.26, pp.21, 2020, https://doi.org/10.3390/molecules26216594