Abstract
In this paper, thermoelectric-mechanical buckling behavior of the piezoelectric nanobeams is investigated based on the nonlocal theory and Euler-Bernoulli beam theory. The electric potential is assumed linear through the thickness of the nanobeam and the governing equations are derived by Hamilton’s principle. The governing equations are solved analytically for different boundary conditions. The effects of the nonlocal parameter, temperature change, and external electric voltage on the critical buckling load of the piezoelectric nanobeams are discussed in detail. This study should be useful for the design of piezoelectric nanodevices.
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A. A. Jafari, A. A. Jandaghian and O. Rahmani, Transient bending analysis of a functionally graded circular plate with integrated surface piezoelectric layers, International Journal of Mechanical and Materials Engineering, 9 (1) (2014) 1–14.
A. Jandaghian, A. Jafari and O. Rahmani, Exact solution for Transient bending of a circular plate integrated with piezoelectric layers, Applied Mathematical Modelling, 37 (12) (2013) 7154–7163.
A. Jandaghian, A. Jafari and O. Rahmani, Vibrational response of functionally graded circular plate integrated with piezoelectric layers: An exact solution, Engineering Solid Mechanics, 2 (2) (2014) 119–130.
D. H. Cortes, S. K. Datta and O. M. Mukdadi, Elastic guided wave propagation in a periodic array of multilayered piezoelectric plates with finite cross-sections, Ultrasonics, 50 (3) (2010) 347–356.
M. Abdullah, M. Abdullah, M. Ramana, C. Khor, K. Ahmad, M. Mujeebu, Y. Ooi and Z. M. Ripin, Numerical and experimental investigations on effect of fan height on the performance of piezoelectric fan in microelectronic cooling, International Communications in Heat and Mass Transfer, 36 (1) (2009) 51–58.
Z. Hao and B. Liao, An analytical study on interfacial dissipation in piezoelectric rectangular block resonators with in-plane longitudinal-mode vibrations, Sensors and Actuators A: Physical, 163 (1) (2010) 401–409.
A. Lazarus, O. Thomas and J.-F. Deü, Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS, Finite Elements in Analysis and Design, 49 (1) (2012) 35–51.
S. M. Tanner, J. Gray, C. Rogers, K. Bertness and N. Sanford, High-Q GaN nanowire resonators and oscillators, Applied Physics Letters, 91 (20) (2007) 203117.
Q. Wan, Q. Li, Y. Chen, T.-H. Wang, X. He, J. Li and C. Lin, Fabrication and ethanol sensing characteristics of ZnO nanowire gas sensors, Applied Physics Letters, 84 (18) (2004) 3654–3656.
T. Murmu and S. Adhikari, Nonlocal frequency analysis of nanoscale biosensors, Sensors and Actuators A: Physical, 173 (1) (2012) 41–48.
J. Pei, F. Tian and T. Thundat, Glucose biosensor based on the microcantilever, Analytical Chemistry, 76 (2) (2004) 292–297.
Y. Fu, H. Du, W. Huang, S. Zhang and M. Hu, TiNibased thin films in MEMS applications: a review, Sensors and Actuators A: Physical, 112 (2) (2004) 395–408.
M. M. Zand and M. Ahmadian, Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects, Communications in Nonlinear Science and Numerical Simulation, 14 (4) (2009) 1664–1678.
C. Li, C. W. Lim and J. Yu, Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axial load, Smart Materials and Structures, 20 (1) (2011) 015023.
C. Li, C. W. Lim, J. Yu and Q. Zeng, Analytical solutions for vibration of simply supported nonlocal nanobeams with an axial force, International Journal of Structural Stability and Dynamics, 11 (2) (2011) 257–271.
J. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45 (2) (2007) 288–307.
A. Pirmohammadi, M. Pourseifi, O. Rahmani and S. Hoseini, Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory, Applied Physics A, 117 (3) (2014) 1547–1555.
O. Rahmani and O. Pedram, Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory, International Journal of Engineering Science, 77 (2014) 55–70.
A. C. Eringen and D. G. B. Edelen, On nonlocal elasticity, International Journal of Engineering Science, 10 (3) (1972) 233–248.
A. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54 (9) (1983) 4703–4710.
A. C. Eringen, Nonlocal continuum field theories, Springer, New York (2002).
A. C. Eringen, Nonlocal continuum mechanics based on distributions, International Journal of Engineering Science, 44 (3) (2006) 141–147.
S. Narendar, Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects, Composite Structures, 93 (12) (2011) 3093–3103.
K. Kiani, Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique, Physica E., 43 (1) (2010) 387–397.
L. Ke, Y. Xiang, J. Yang and S. Kitipornchai, Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory, Computational Materials Science, 47 (2) (2009) 409–417.
J. Yang, L. Ke and S. Kitipornchai, Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Physica E., 42 (5) (2010) 1727–1735.
H. Ali-Akbari, R. Firouz-Abadi, H. Haddadpour and M. Noorian, Shell-like instability of large diameter singlewalled carbon nanotubes conveying fluid, Journal of Mechanical Science and Technology, 26 (11) (2012) 3389–3397.
I. Lee and J. Lee, Measurement uncertainties in resonant characteristics of MEMS resonators, Journal of Mechanical Science and Technology, 27 (2) (2013) 491–500.
H. Moeenfard and M. T. Ahmadian, Analytical closed form model for static pull-in analysis in electrostatically actuated torsional micromirrors, Journal of Mechanical Science and Technology, 27 (5) (2013) 1443–1449.
Z. L. Wang and J. Song, Piezoelectric nanogenerators based on zinc oxide nanowire arrays, Science, 312 (5771) (2006) 242–246.
X. Wang, J. Song, J. Liu and Z. L. Wang, Direct-current nanogenerator driven by ultrasonic waves, Science, 316 (5821) (2007) 102–105.
W. Su, Y. Chen, C. Hsiao and L. Tu, Generation of electricity in GaN nanorods induced by piezoelectric effect, Applied Physics Letters, 90 (6) (2007) 063110.
Z. Yan and L. Jiang, Surface effects on the electromechanical coupling and bending behaviours of piezoelectric nanowires, Journal of Physics D: Applied Physics, 44 (7) (2011) 075404.
Z. Yan and L. Jiang, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects, Nanotechnology, 22 (24) (2011) 245703.
L.-L. Ke and Y.-S. Wang, Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory, Smart Materials and Structures, 21 (2) (2012) 025018.
L.-L. Ke, Y.-S. Wang and Z.-D. Wang, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory, Composite Structures, 94 (6) (2012) 2038–2047.
Q. Wang, On buckling of column structures with a pair of piezoelectric layers, Engineering Structures, 24 (2) (2002) 199–205.
C. Liu, L.-L. Ke, Y.-S. Wang, J. Yang and S. Kitipornchai, Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Composite Structures, 106 (0) (2013) 167–174.
H.-T. Thai and T. P. Vo, A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams, International Journal of Engineering Science, 54 (0) (2012) 58–66.
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Recommended by Associate Editor Nam-Su Huh
Omid Rahmani is an associated professor and director of “Smart Material and New Advanced Materials Laboratory”, who specializes in smart composite material and Nano mechanics. He has over 40 papers in the well-known journals and international conferences since 2008. Dr. Rahmani also was staying at Aalborg University, Denmark as visiting Ph.D. scholar during 2010-2011.
Ali Akbar Jandaghian received his M.S. degree from K. N. Toosi University of Technology in Tehran, Iran, in 2010. He is currently a Ph.D. student at University of Zanjan (ZNU) in Zanjan, Iran. His research interests are vibration, nanomechanics and piezoelectric materials.
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Jandaghian, A.A., Rahmani, O. On the buckling behavior of piezoelectric nanobeams: An exact solution. J Mech Sci Technol 29, 3175–3182 (2015). https://doi.org/10.1007/s12206-015-0716-7
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DOI: https://doi.org/10.1007/s12206-015-0716-7