Abstract
This paper investigates buckling response of higher-order shear deformable nanobeams made of functionally graded piezoelectric (FGP) materials embedded in an elastic foundation. Material properties of FGP nanobeam change continuously in thickness direction based on power-law model. To capture small size effects, Eringen’s nonlocal elasticity theory is adopted. Employing Hamilton’s principle, the nonlocal governing equations of FGP nanobeams embedded in elastic foundation are obtained. To predict buckling behavior of embedded FGP nanobeams, the Navier-type analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on the buckling loads of size-dependent FGP nanobeams.
Similar content being viewed by others
References
Ebrahimi F, Rastgo A (2008) An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory. Thin-Walled Struct 46(12):1402–1408
Atmane HA, Tounsi A, Meftah SA, Belhadj HA (2010) Free vibration behavior of exponential functionally graded beams with varying cross-section. J Vib Control 17(2):311–318
Şimşek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des 240(4):697–705
Alshorbagy AE, Eltaher MA, Mahmoud FF (2011) Free vibration characteristics of a functionally graded beam by finite element method. Appl Math Model 35(1):412–425
Asghari M, Rahaeifard M, Kahrobaiyan MH, Ahmadian MT (2011) The modified couple stress functionally graded Timoshenko beam formulation. Mater Des 32(3):1435–1443
Thai HT, Vo TP (2012) Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. Int J Mech Sci 62(1):57–66
Ebrahimi F, Zia M (2015) Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities. Acta Astronaut 116:117–125
Barati MR, Zenkour AM, Shahverdi H (2016) Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory. Compos Struct 141:203–212
Şimşek M, Yurtcu HH (2013) Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos Struct 97:378–386
Eltaher MA, Emam SA, Mahmoud FF (2013) Static and stability analysis of nonlocal functionally graded nanobeams. Compos Struct 96:82–88
Sharabiani PA, Yazdi MRH (2013) Nonlinear free vibrations of functionally graded nanobeams with surface effects. Compos B Eng 45(1):581–586
Uymaz B (2013) Forced vibration analysis of functionally graded beams using nonlocal elasticity. Compos Struct 105:227–239
Rahmani O, Pedram O (2014) Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory. Int J Eng Sci 77:55–70
Nazemnezhad R, Hosseini-Hashemi S (2014) Nonlocal nonlinear free vibration of functionally graded nanobeams. Compos Struct 110:192–199
Ebrahimi F et al (2015) Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams. J Mech Sci Technol 29(3):1207–1215
Ebrahimi F, Salari E (2015) Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method. Compos B Eng 79:156–169
Ebrahimi F, Salari E (2015) A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position. CMES Comput Model Eng Sci 105(2):151–181
Ansari R, Pourashraf T, Gholami R (2015) An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory. Thin-Walled Struct 93:169–176
Rahmani O, Jandaghian AA (2015) Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory. Appl Phys A 119(3):1019–1032
Zemri A, Houari MSA, Bousahla AA, Tounsi A (2015) A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory. Struct Eng Mech 54(4):693–710
Zeighampour H, Beni YT (2015) Free vibration analysis of axially functionally graded nanobeam with radius varies along the length based on strain gradient theory. Appl Math Model 39(18):5354–5369
Shi ZF, Chen Y (2004) Functionally graded piezoelectric cantilever beam under load. Arch Appl Mech 74(3–4):237–247
Doroushi A, Eslami MR, Komeili A (2011) Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory. J Intell Mater Syst Struct 22(3):231–243
Kiani Y et al (2011) Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams. Int J Mech Mater Des 7(3):185–197
Komijani M, Kiani Y, Esfahani SE, Eslami MR (2013) Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams. Compos Struct 98:143–152
Lezgy-Nazargah M, Vidal P, Polit O (2013) An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams. Compos Struct 104:71–84
Shegokar NL, Lal A (2014) Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties. Meccanica 49(5):1039–1068
Ansari R, Ashrafi MA, Hosseinzadeh S (2014) Vibration characteristics of piezoelectric microbeams based on the modified couple stress theory. Shock Vib 2014:12
Sahmani S, Bahrami M (2015) Size-dependent dynamic stability analysis of microbeams actuated by piezoelectric voltage based on strain gradient elasticity theory. J Mech Sci Technol 29(1):325–333
Eringen AC, Edelen DGB (1972) On nonlocal elasticity. Int J Eng Sci 10(3):233–248
Eringen AC (1972) Nonlocal polar elastic continua. Int J Eng Sci 10(1):1–16
Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–4710
Ke LL, Liu C, Wang YS (2015) Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions. Physica E 66:93–106
Ebrahimi F, Barati MR (2015) A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams. Arab J Sci Eng 40:1–12
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Marcelo A. Savi.
Rights and permissions
About this article
Cite this article
Ebrahimi, F., Barati, M.R. Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium. J Braz. Soc. Mech. Sci. Eng. 39, 937–952 (2017). https://doi.org/10.1007/s40430-016-0551-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40430-016-0551-5