Skip to main content
SpringerLink
Log in

On the buckling behavior of piezoelectric nanobeams: An exact solution

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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.

    Article  Google Scholar 

  2. 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.

    Article  MathSciNet  Google Scholar 

  3. 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.

    Article  Google Scholar 

  4. 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.

    Article  Google Scholar 

  5. 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.

    Article  Google Scholar 

  6. 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.

    Article  Google Scholar 

  7. 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.

    Article  MathSciNet  Google Scholar 

  8. 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.

    Google Scholar 

  9. 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.

    Article  Google Scholar 

  10. T. Murmu and S. Adhikari, Nonlocal frequency analysis of nanoscale biosensors, Sensors and Actuators A: Physical, 173 (1) (2012) 41–48.

    Article  Google Scholar 

  11. J. Pei, F. Tian and T. Thundat, Glucose biosensor based on the microcantilever, Analytical Chemistry, 76 (2) (2004) 292–297.

    Article  Google Scholar 

  12. 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.

    Article  Google Scholar 

  13. 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.

    Article  Google Scholar 

  14. 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.

    Google Scholar 

  15. 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.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45 (2) (2007) 288–307.

    Article  MATH  Google Scholar 

  17. 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.

    Article  Google Scholar 

  18. 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.

    Article  MathSciNet  Google Scholar 

  19. A. C. Eringen and D. G. B. Edelen, On nonlocal elasticity, International Journal of Engineering Science, 10 (3) (1972) 233–248.

    Article  MathSciNet  MATH  Google Scholar 

  20. 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.

    Article  Google Scholar 

  21. A. C. Eringen, Nonlocal continuum field theories, Springer, New York (2002).

    MATH  Google Scholar 

  22. A. C. Eringen, Nonlocal continuum mechanics based on distributions, International Journal of Engineering Science, 44 (3) (2006) 141–147.

    Article  MathSciNet  MATH  Google Scholar 

  23. 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.

    Article  Google Scholar 

  24. 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.

    Article  Google Scholar 

  25. 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.

    Article  Google Scholar 

  26. 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.

    Article  Google Scholar 

  27. 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.

    Article  Google Scholar 

  28. I. Lee and J. Lee, Measurement uncertainties in resonant characteristics of MEMS resonators, Journal of Mechanical Science and Technology, 27 (2) (2013) 491–500.

    Article  Google Scholar 

  29. 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.

    Article  MathSciNet  Google Scholar 

  30. Z. L. Wang and J. Song, Piezoelectric nanogenerators based on zinc oxide nanowire arrays, Science, 312 (5771) (2006) 242–246.

    Article  Google Scholar 

  31. X. Wang, J. Song, J. Liu and Z. L. Wang, Direct-current nanogenerator driven by ultrasonic waves, Science, 316 (5821) (2007) 102–105.

    Article  Google Scholar 

  32. 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.

    Google Scholar 

  33. 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.

    Google Scholar 

  34. Z. Yan and L. Jiang, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects, Nanotechnology, 22 (24) (2011) 245703.

    Google Scholar 

  35. 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.

    Google Scholar 

  36. 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.

    Article  Google Scholar 

  37. Q. Wang, On buckling of column structures with a pair of piezoelectric layers, Engineering Structures, 24 (2) (2002) 199–205.

    Article  Google Scholar 

  38. 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.

    Article  Google Scholar 

  39. 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.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Smart Material and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran

    Ali Akbar Jandaghian & Omid Rahmani

Authors
  1. Ali Akbar Jandaghian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Omid Rahmani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Omid Rahmani.

Additional information

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-015-0716-7

Keywords

Search

Navigation