Size Dependent Nonlinear Bending Analysis of a Flexoelectric Functionally Graded Nano-Plate Under Thermo-Electro-Mechanical Loads
Subject Areas : EngineeringA Ghobadi 1 , Y Tadi Beni 2 , H Golestanian 3
1 - Mechanical Engineering Department, Shahrekord University, Shahrekord, Iran
2 - Faculty of Engineering, Shahrekord University, Shahrekord, Iran
3 - Faculty of Engineering, Shahrekord University, Shahrekord, Iran
Keywords:
Abstract :
[1] Lao C.S., Kuang Q., Wang Z. L., Park M.C., Deng Y.L., 2007, Polymer functionalized piezoelectric-FET as humidity/chemical nanosensors, Applied Physics Letters 90: 262107.
[2] Tanner S.M., Gray J.M., Rogers C.T., Bertness K.A., Sanford N.A., 2007, High-Q GaN nanowire resonators and oscillator, Applied Physics Letters 91: 203117.
[3] Kogan S.M., 1996, Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals, Soviet Physics, Solid State 5: 2069-2070.
[4] Majdoub M.S., Sharma P., Cagin T., 2008, Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect, Physical Review B 77: 125424.
[5] Kogan S.M., 1963, Piezoelectric effect under an inhomogeneous strain and acoustic scattering of carriers in crystals, Fizika Tverdogo Tela 5: 2829-2831.
[6] Maranganti R., Sharma N.D., Sharma P., 2006, Electromechanical coupling in nonopiezoelectric materials due to nanoscale nonlocal size effects: Green’s function solutions and embedded inclusions, Physical Review B 74: 014110.
[7] Shen S.P., Hu S.L., 2010, A theory of flexoelectricity with surface effect for elastic dielectrics, Journal of the Mechanics and Physics of Solids 58: 665-677.
[8] Yan Z., Jiang L.Y., 2013, Flexoelectric effect on the electroelastic responses of bending piezoelectric nano-beams, Journal of Applied Physics 113: 194102.
[9] Yan Z., Jiang L.Y., 2013, Size-dependent bending and vibration behavior of piezoelectric nano-beams due to flexoelectricity, Journal of Physics D: Applied Physics 46: 355502.
[10] Li A., Zhou S., Qi L., Chen X., 2015, A reformulated flexoelectric theory for isotropic dielectrics, Journal of Physics D: Applied Physics 48(46): 465202.
[11] Xu Y.M., Shen H.S., Zhang C.L., 2013, Nonlocal plate model for nonlinear bending of bilayer grapheme sheets subjected to transverse loads in thermal environment, Composite Structures 98: 294-302.
[12] Chen Y., Lee J.D., Eskandarian A., 2004, Atomistic viewpoint of the applicability of microcontinuum theories, International Journal of Solids Structures 41(8): 2085-2097.
[13] Li A.Q., Zhou S.J., Zhou S.S., Wang B.L., 2014, Size-dependent analysis of a three-layer micro-beam including electromechanical coupling, Composite Structures 116: 120-127.
[14] Hadjesfandiari A.R., 2013, Size-dependent piezoelectricity, International Journal of Solids Structures 50: 2781-2791.
[15] Liang X., Shen S.P., 2013, Size-dependent piezoelectricity and elasticity due to the electric field-strain gradient coupling and strain gradient elasticity, International Applied Mechanics 5: 1350015.
[16] Hu S.L., Shen S.P., 2009, Electric field gradient theory with surface effect for nano-dielectrics, Computers, Materials and Continua 13: 63-87.
[17] Yang J.S., 1999, Equations for the extension and flexure of electroelastic plate under strong electric fields, International Journal of Solids Structures 36: 3171-3192.
[18] Liu C., Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2013, Thermo-electro mechanical vibration of piezoelectric nano-plate based on the nonlocal theory, Composite Structures 106: 167-174.
[19] Yan Z., Jiang L.Y., 2011, Electromechanical response of a curved piezoelectric nano-beam with the consideration of surface effects, Journal of Physics D: Applied Physics 44: 365301.
[20] Ke L.L., Wang Y.S., 2012, Thermoelectric-mechanical vibration of piezoelectric nano-beams based on the nonlocal theory, Smart Materials and Structures 21(2): 025018.
[21] Zhang Z., Yan Z., Jiang L., 2014, Flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nano-plate, Journal of Applied Physics 116(1):014307.
[22] Zhang Z., Jiang L., 2014, Size effects on electromechanical coupling fields of a bending piezoelectric nano-plate due to surface effects and flexoelectricity, Journal of Applied Physics 116(13): 4308.
[23] Yang W., Liang X., Shen S., 2015, Electromechanical responses of piezoelectric nano-plate with flexoelectricity, Acta Mechanica 226: 3097-3110.
[24] Yan Z., Jiang L.Y., 2012, Vibration and buckling analysis of a piezoelectric nano-plate considering surface effects and in-plane constraint, Proceedings of the Royal Society of Series A 468: 3458-3475.
[25] Yan Z., Jiang L.Y, 2013, Size-dependent bending and vibration behavior of piezoelectric nano-beams due to flexoelectricity, Journal of Physics D: Applied Physics 46: 355502.
[26] Murmua T., Sienz J., Adhikari S., Arnold C., 2013, Nonlocal buckling of double-nano-plate-systems under biaxial compression, Composites Part B 44: 84-94.
[27] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magneto electroelastic nano-plate based on nonlocal theory, Composite Structures 111: 522-529.
[28] Liang X., Hu S., Shen S., 2014, Effects of surface and flexoelectricity on a piezoelectric nano-beam, Smart Materials and Structures 23: 035020.
[29] Liang X., Shuling H., Shengping S., 2015, Size-dependent buckling and vibration behaviors of piezoelectric nanostructures due to flexoelectricity, Smart Materials and Structures 24: 105012.
[30] Yan Z., Jiang L.Y., 2015, Effect of flexoelectricity on the electroelastic fields of a hollow piezoelectric nanocylinder, Smart Materials and Structures 24: 065003.
[31] Ke L., Liu C., Wang Y.S., 2015, Free vibration of nonlocal piezoelectric nano-plate under various boundary conditions, Physica E 66: 93-106.
[32] Liu C., Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2013, Thermo-electro-mechanical vibration of piezoelectric nano-plate based on the nonlocal theory, Composite Structures 106: 167-174.
[33] Liang X., Yang W., Hu S., Shen S., 2016, Buckling and vibration of flexoelectric nanofilms subjected to mechanical loads, Journal of Physics D: Applied Physics 49: 115307.
[34] Alibeigi E., Tadi Beni Y., Mehralian F. 2018, Thermal buckling of magneto-electro- elastic piezoelectric nano-beams based on the modified couple stress theory, The European Physical Journal Plus 133: 133.
[35] Komijani M., Kiani Y., Esfahani S., Eslami M.,2 013, Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams, Composite Structures 98: 143-152.
[36] Komijani M., Reddy J., Eslami M., 2014, Nonlinear analysis of microstructure-dependent functionally graded piezoelectric material actuators, Journal of the Mechanics and Physics of Solids 63: 214-227.
[37] Xiang H.J., Shi Z., 2009, Static analysis for functionally graded piezoelectric actuators or sensors under a combined electrothermal load, European Journal of Mechanics A 28: 338-346.
[38] Yang J., Xiang H., 2007, Thermo-electro-mechanical characteristics of functionally graded piezoelectric actuators, Smart Materials and Structures 16: 784.
[39] Tadi Beni Y., 2016, A nonlinear electro-mechanical analysis of nano-beams based on the size-dependent piezoelectricity, Journal of Mechanics 33: 289-301.
[40] Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2014, Free vibration of size-dependent magneto-electro-elastic nano-plate based on the nonlocal theory, Acta Mechanica Sinica 30: 516-525.
[41] Ke L.L, Wang Y.S., Reddy J.N., 2014, Thermo-electro-mechanical vibration of size-dependent piezoelectric cylindrical nanoshells under various boundary conditions, Composite Structures 116: 626-636.
[42] Kiani Y., Taheri S., Eslami M.R., 2011, Thermal buckling of piezoelectric functionally graded material beams, Journal of Thermal Stresses 34: 835-850.
[43] Kiani Y., Rezaei M., Taheri S., Eslami M.R., 2011, Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams, International Journal of Mechanics and Materials in Design 7: 185-197.
[44] Ebrahimi F., Barati M.R., 2017, Vibration analysis of size-dependent flexoelectricnano-plates incorporating surface and thermal effects, Journal of Mechanics of Advanced Materials and Structures 25: 611-621.
[45] Ebrahimi F., Barati M.R., 2017, Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects, Nanomaterials and Nanotechnology 7(2): 1-11.
[46] Ebrahimi F., Ehyaei J., Babaei R., 2016, Thermal buckling of FGM nano-plates subjected to linear and nonlinear varing loads on Pasternak foundation, Advanced in Materials Research 5: 245-261.
[47] Ebrahimi F., Salari E., 2015, Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nano-beams, Smart Materials and Structures 24: 125007.
[48] Ebrahimi F., Barati M.R., 2016, An exact solution for buckling analysis of embedded piezo- electro-magnetically actuated nanoscale beams, Advances in Nano Research 4: 65-84.
[49] Ebrahimi F., Barati M.R., 2017, Surface effects on the vibration behavior of flexoelectric nanobeams based on nonlocal elasticity theory, The European Physical Journal Plus 132: 11320.
[50] Ebrahimi F., Barati M.R., 2016, Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size dependent graded nanoscale beams in thermal environment, International Journal of Smart and Nano Materials 7: 69-90.
[51] Tadi Beni, Y., 2016, Size-dependent analysis of piezoelectric nano-beams including electro-mechanical coupling, Mechanics Research Communications 75: 67-80.
[52] Shen S.P, Hu S.L., 2010, A theory of flexoelectricity with surface effect for elastic dielectrics, Journal of the Mechanics and Physics of Solids 58: 665-677.
[53] Eliseev E.A., Morozovska A.N., Glinchuk M.D., Blinc R., 2009, Spontaneous flexoelectric-flexomagnetic effect in nanoferroics, Physical Review B 79: 165433.
[54] Li J.U., 2004, The effective pyroelectric and thermal expansion coefficients of ferroelectric ceramics, Mechanics of Material 36: 949-958.
[55] Toupin R.A., 1956, The elastic dielectric, Rational Mechanics and Analysis 5: 849-915.
[56] Tadi Beni Y., Mehralian F., Razavi H., 2015, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Composite Structures 120: 65-78.
[57] Mehralian F., TadiBeni Y., 2016, Ansari R., Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell, Journal of Composite Structures 152: 45-61.
[58] Fei L., Zhuo X., Xiaoyong W., Xi Y., 2009, Determination of temperature dependence of piezoelectric coefficients matrix of lead zirconate titanate ceramics by quasi-static and resonance method, Journal of Physics D: Applied Physics 42: 095417.