Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T06:41:11.144Z Has data issue: false hasContentIssue false
  • English
  • Français

Buckling Analysis of Double-Layer Piezoelectric Nanoplates Surrounded by Elastic Foundations and Thermal Environments Considering Nonlocal and Surface Energy Models

Published online by Cambridge University Press:  28 June 2017

S. Rafieian ,
M. Hashemian  and
M. Pirmoradian
S. Rafieian
Affiliation:
Department of Mechanical EngineeringKhomeinishahr BranchIslamic Azad UniversityKhomeinishahr, Iran
M. Hashemian*
Affiliation:
Department of Mechanical EngineeringKhomeinishahr BranchIslamic Azad UniversityKhomeinishahr, Iran
M. Pirmoradian
Affiliation:
Department of Mechanical EngineeringKhomeinishahr BranchIslamic Azad UniversityKhomeinishahr, Iran
*
*Corresponding author ([email protected])
Get access

Abstract

This study investigated the effects of considering surface and nonlocal energy parameters on the buckling analysis of double piezoelectric nanoplate (DPNP) embedded in elastic foundations and thermal environments. Both in-phase and out-of-phase modes of buckling and various boundary conditions are studied and compared with each other. The governing equations were derived by drawing on the principle of virtual work and then solved by employing the finite difference method. Finite difference solution was validated using Navier's method and journal references. A parametric study was also launched in order to investigate the effects of the external electric voltage, nonlocal parameters, different boundary conditions, elastic foundations and thermal environments on the surface effect of DPNP buckling. The obtained numerical results showed that the influence of surface stress on in-phase and out-of-phase modes of buckling of the DPNP was enhanced by augmenting the nonlocal parameters and external electric voltage; on the other hand, it was found to be decreased by increasing elastic foundations and temperature changes. In addition, the value of surface stress effects for the in-phase mode was higher than that of the out-of-phase one.

Keywords

Double piezoelectric nanoplateBucklingSurface energy effectNonlocal theory
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 483 - 494
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Tanner, S. M., Gray, J. M., Rogers, C.T., Bertness, K. A. and Sanford, N. A., “High-Q GaN Nanowire Resonators and Oscillators,” Applied Physics Letters, 91, pp. 203117–203119 (2007).Google Scholar
2. Lao, C. S., Kuang, Q., Wang, Z. L., Park, M. C. and Deng, Y., “Polymer Functionalized Piezoelectric-FET as Humidity/Chemical Nanosensors,” Applied Physics Letters, 90, pp. 262107–262109 (2007).Google Scholar
3. Fei, P. et al., “Piezoelectric Potential Gated Field-Effect Transistor Based on a Free-Standing ZnO Wire,” Nano Letters, 9, pp. 3435–3439 (2009).Google Scholar
4. Park, K. I. et al., “Piezoelectric BaTiO3 Thin Film Nanogenerator on Plastic Substrates,” Nano Letters, 10, pp. 4939–4943 (2010).Google Scholar
5. Qi, Y. et al., “Enhanced Piezoelectricity and Stretch Ability in Energy Harvesting Devices Fabricated from Buckled PZT Ribbons,” Nano Letters, 11, pp. 1331–1336 (2011).Google Scholar
6. Chen, C. Q., Shi, Y., Zhang, Y. S., Zhu, J. and Yan, Y. J., “Size Dependence of Young's Modulus in ZnO Nanowires,” Physic Review Letters, 96, pp. 075505–075508 (2006).Google Scholar
7. Stan, G., Ciobanu, C. V., arthangal, P. M. P. and Cook, R. F., “Diameter-Dependent Radial and Tangential Elastic Moduli of ZnO Nanowires,” Nano Letters, 7, pp. 3691–3697 (2007).Google Scholar
8. Chu, H. M., Li, W. L. and Hu, S. Y., “Effects of Couple Stresses on Pure Squeeze EHL Motion of Circular Contacts,” Journal of Mechanics, 22, pp. 77–84 (2006)Google Scholar
9. Shahriari, B. and Shirvani, S., “Small-Scale Effects on the Buckling of Skew Nanoplates Based on Non-Local Elasticity and Second-Order Strain Gradient Theory,” Journal of Mechanics, DOI: 10.1017/jmech.2017.16 (2017).Google Scholar
10. Wang, Y. G., Lin, W. H., Zhou, C. L. and Liu, R. X., “Thermal Postbuckling and Free Vibration of Extensible Microscale Beams Based on Modified Couple Stress Theory,” Journal of Mechanics, 31, pp. 37–46 (2015).Google Scholar
11. Eringen, A. C. and Edelen, D. G. B., “On Nonlocal Elasticity,” International Journal of Engineering Science, 10, pp. 233–248 (1972).Google Scholar
12. Eringen, A. C., “On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves,” Journal of Applied Physics, 54, pp. 4703–4710 (1983).Google Scholar
13. Shokrani, M. H., Karimi, M., Tehrani, M. S. and Mirdamadi, H. R., “Buckling Analysis of Double-Orthotropic Nnanoplates Embedded in Elastic Media Based on Non-Local Two-Variable Refined Plate Theory Using the GDQ Method,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38, pp. 2589–2606 (2016).Google Scholar
14. Radic, N., Jeremic, D., Trifkovic, S. and Milutinovic, M., “Buckling Analysis of Double-Orthotropic Nanoplates Embedded in Pasternak Elastic Medium Using Nonlocal Elasticity Theory,” Composites Part B: Engineering, 61, pp. 162–171 (2014).Google Scholar
15. Karimi, M., Mirdamadi, H. R. and Shahidi, A. R., “Shear Vibration and Buckling of Double-Layer Orthotropic Nanoplates Based on RPT Resting on Elastic Foundations by DQM Including Surface Effects,” Microsystem Technologies, 23, pp. 765–797 (2017).Google Scholar
16. Murmu, T., Sienz, J., Adhikari, S. and Arnold, C., “Nonlocal Buckling of Double-Nanoplate-Systems under Biaxial Compression,” Composites Part B: Engineering, 44, pp. 84–94 (2013).Google Scholar
17. Karimi, M. and Shahidi, A. R., “Finite Difference Method for Biaxial and Uniaxial Buckling of Rectangular Silver Nanoplates Resting on Elastic Foundations in Thermal Environments Based on Surface Stress and Nonlocal Elasticity Theories,” Journal of Solid Mechanics, 8, pp. 719–733 (2016).Google Scholar
18. Sobhy, M., “Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions,” Journal of Mechanics, 30, pp. 443–453 (2014).Google Scholar
19. Karimi, M. and Shahidi, A. R., “Nonlocal, Refined Plate, and Surface Effects Theories Used to Analyze Free Vibration of Magnetoelectroelastic Nanoplates under Thermo-Mechanical and Shear Loadings,” Applied Physics A, DOI: 10.1007/s00339-017-0828-2 (2017)Google Scholar
20. Gurtin, M. E. and Murdoch, A. I., “Surface Stress in Solids,” International Journal of Solids and Structures, 14, pp. 431–440 (1978).Google Scholar
21. Assadi, A. and Farshi, B., “Vibration Characteristics of Circular Nanoplates,” Journal of Applied Physics, 108, pp. 074312–074316 (2010).Google Scholar
22. Assadi, A. and Farshi, B., “Size Dependent Stability Analysis of Circular Ultrathin Films in Elastic Medium with Consideration of Surface Energies,” Physica E, 43, pp. 1111–1117 (2011).Google Scholar
23. Assadi, A., Farshi, B. and Alinia-Ziazi, A., “Size Dependent Dynamic Analysis of Nanoplates,” Journal of Applied Physics, 107, pp. 124310–124313 (2010).Google Scholar
24. Karimi, M., Shokrani, M. H. and Shahidi, A. R., “Size-Dependent Free Vibration Analysis of Rectangular Nanoplates with the Consideration of Surface Effects Using Finite Difference Method,” Journal of Applied and Computational Mechanics, 1, pp. 122–133 (2015).Google Scholar
25. Yan, Z. and Jiang, L. Y., “Surface Effects on the Vibration and Buckling of Piezoelectric Nanoplates,” Europhysics Letters, 99, pp. 27007–27013 (2012).Google Scholar
26. Yan, Z. and Jiang, L. Y., “Vibration and Buckling Analysis of a Piezoelectric Nanoplate Considering Surface Effects and In-Plane Constraints,” Proceedings of the Royal Society of London A, 468, pp. 3458–3475 (2012).Google Scholar
27. Yan, Z. and Jiang, L. Y., “Surface Effects on the Electroelastic Responses of a Thin Piezoelectric Plate with Nanoscale Thickness,” Journal of Physics D: Applied Physics, 45, pp. 255401–255409 (2012).Google Scholar
28. Zhang, J., Wang, C. and Chen, W., “Surface and Piezoelectric Effects on the Buckling of Piezoelectric Nanofilms Due to Mechanical Loads,” Meccanica, 49, pp. 181–189 (2014).Google Scholar
29. Zhang, J., Wang, C. and Adhikari, S., “Surface Effect on the Buckling of Piezoelectric Nanofilms,” Journal of Physics D: Applied Physics, 45, pp. 285301–285308 (2012).Google Scholar
30. Karimi, M., Mirdamadi, H. R. and Shahidi, A. R., “Positive and Negative Surface Effects on the Buckling and Vibration of Rectangular Nanoplates under Biaxial and Shear In-Plane Loadings Based on Nonlocal Elasticity Theory,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, pp. 1391–1404 (2017).Google Scholar
31. Karimi, M., Haddad, H. A. and Shahidi, A. R., “Combining Surface Effects and Non-Local Two Variable Refined Plate Theories on the Shear/Biaxial Buckling and Vibration of Silver Nanoplates,” Micro and Nano Letters, 10, pp. 276–281 (2015).Google Scholar
32. Karimi, M. and Shahidi, A. R., “Finite Difference Method for Sixth Order Derivatives of Differential Equations in Buckling of Nanoplates Due to Coupled Surface Energy and Non-Local Elasticity Theories,” International Journal of Nano Dimension, 6, pp. 525–538 (2015).Google Scholar
33. Wang, K. F. and Wang, B. L., “Combining Effects of Surface Energy and Non-Local Elasticity on the Buckling of Nanoplates,” Micro and Nano Letters, 6, pp. 941–943 (2011).Google Scholar
34. Wang, K. F. and Wang, B. L., “Vibration of Nanoscale Plates with Surface Energy via Nonlocal Elasticity,” Physica E, 44, pp. 448–453 (2011).Google Scholar
35. Asemi, S. R. and Farajpour, A., “Vibration Characteristics of Double-Piezoelectric-Nanoplate-Systems,” Micro and Nano Letters, 9, pp. 280–285 (2014).Google Scholar
36. Asemi, S. R. and Farajpour, A., “Thermo-Electro- Mechanical Vibration of Coupled Piezoelectric-Nanoplate Systems under Non-Uniform Voltage Distribution Embedded in Pasternak Elastic Medium,” Current Applied Physics, 14, pp. 814–832 (2014).Google Scholar
37. Asemi, S. R., Farajpour, A., Asemi, H. R. and Mohammadi, M., “Influence of Initial Stress on the Vibration of Double-Piezoelectric-Nanoplate Systems with Various Boundary Conditions Using DQM,” Physica E, 63, pp. 169–179 (2014).Google Scholar
38. Karimi, M., Shahidi, A. R. and Ziaei-Rad, S., “Surface Layer and Nonlocal Parameter Effects on the In-Phase and Out-of-Phase Natural Frequencies of a Double-Layer Piezoelectric Nanoplate under Thermo-Electro-Mechanical Loadings,” Microsystem Technologies, DOI: 10.1007/s00542-017-3395-8 (2017).Google Scholar