Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T09:55:23.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermo-Electro-Mechanical Vibration Characteristics of Graphene/Piezoelectric/Graphene Sandwich Nanobeams

Published online by Cambridge University Press:  25 September 2017

N. Kammoun ,
H. Jrad ,
S. Bouaziz ,
M. B. Amar ,
M. Soula  and
M. Haddar
N. Kammoun
Affiliation:
Mechanics, Modelling and Production Laboratory (LA2MP)Mechanic DepartmentNational School of Engineers of SfaxUniversity of SfaxSfax, Tunisia
H. Jrad*
Affiliation:
Mechanics, Modelling and Production Laboratory (LA2MP)Mechanic DepartmentNational School of Engineers of SfaxUniversity of SfaxSfax, Tunisia
S. Bouaziz
Affiliation:
Mechanics, Modelling and Production Laboratory (LA2MP)Mechanic DepartmentNational School of Engineers of SfaxUniversity of SfaxSfax, Tunisia
M. B. Amar
Affiliation:
Laboratoire des Sciences des Procédés et des Matériaux (LSPM)CentreNnational de la Recherche Scientifique (CNRS)Université Paris 13Sorbonne Paris CitéVilletaneuse, France
M. Soula
Affiliation:
Applied Mechanics and Engineering Laboratory (LMAI-ENIT)National School of Engineers of TunisUniversity of Tunis El ManarTunis, Tunisia
M. Haddar
Affiliation:
Mechanics, Modelling and Production Laboratory (LA2MP)Mechanic DepartmentNational School of Engineers of SfaxUniversity of SfaxSfax, Tunisia
*
*Corresponding author ([email protected])
Get access

Abstract

This paper reports an investigation on thermo-electro-mechanical vibration of graphene/piezoelectric graphene/piezoelectric/graphene sandwich nanobeams. Based on the nonlocal elasticity theory, Timoshenko beam theory and Hamilton's principles, the governing equations are developed and solved using generalized differential quadrature (GDQ) method. The effects of the nonlocal parameter, external electrical voltage, temperature change and axial force on vibration of graphene/piezoelectric/graphene sandwich nanobeams are examined. The performance and the accuracy of the presented model are highlighted through numerical examples with different boundary conditions. This study reports that the nonlocal parameter and thermo-electro-mechanical loadings have important effect on the natural frequencies and the deflection mode shapes of the graphene/piezoelectric/graphene sandwich nanobeam. The present work can serve as guideline for the design of a nanoscale graphene/piezoelectric/graphene beams based electromechanical resonator sensors.

Keywords

Smart materialsScale effectNonlocal elasticityThermo-electro-mechanical loadings
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 1 , February 2019 , pp. 65 - 79
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2019 

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. Novoselov, K. S. et al., “Electric Field Effect in Atomically Thin Carbon Films,” Science, 306, pp. 666–669 (2004).Google Scholar
2. Sung, C. S. and Jia, L. T., “Characterizing Thermal and Mechanical Properties of Graphene/Epoxy Nanocomposites,” Composites: Part B, 56, pp. 691–697 (2014).Google Scholar
3. Li, D., Müller, M. B., Gilje, S., Kaner, R. B. and Wallace, G. G., “Processable Aqueous Dispersions of Graphene Nanosheets,” Nature Nanotechnology, 3, pp. 101–105 (2008).Google Scholar
4. Nazemnezhad, R., “Nonlocal Timoshenko Beam Model for Considering Shear Effect of Van Der Waals Interactions on Free Vibration of Multilayer Graphene Nanoribbons,” Composite Structures, 133, pp. 522–528 (2015).Google Scholar
5. Li, F. M. and Lyu, X. X., “Active Vibration Control of Lattice Sandwich Beams Using the Piezoelectric Actuator/Sensor Pairs,” Composites Part B: Engineering, 67, pp. 571–578 (2014).Google Scholar
6. Wang, Y. Z., Li, F. M. and Kishimoto, K., “Thermal Effects on Vibration Properties of Double Layered Nanoplates at Small Scales,” Composites Part B: Engineering, 42, pp. 1311–1317 (2011).Google Scholar
7. 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, 203117 (2007).Google Scholar
8. Li, H. B. and Wang, X., “Nonlinear Dynamic Characteristics of Graphene/Piezoelectric Laminated Films in Sensing Moving Loads,” Sensors and Actuators A: Physical, 238, pp. 80–94 (2016).Google Scholar
9. Li, H. B., “Nonlinear Frequency Shift Behavior of Graphene–Elastic–Piezoelectric Laminated Films as a Nano-Mass Detector,” International Journal of Solids and Structures, 84, pp. 17–26 (2016).Google Scholar
10. Shin, K. Y., Hong, J. Y. and Jang, J., “Flexible and Transparent Graphene Films as Acoustic Actuator Electrodes Using Inkjet Printing,” Chemical Communications, 47, pp. 8527–8529 (2011).Google Scholar
11. Xu, S. C. et al., “Flexible and Transparent Graphene-Based Loudspeakers,” Applied Physics Letters, 102, 151902 (2013).Google Scholar
12. Zeng, Y., Zhao, Y. and Jiang, Y., “Investigate the Interface Structure and Growth Mechanism of High Quality ZnO Films Grown on Multilayer Graphene Layers,” Applied Surface Science, 301, pp. 391–395 (2014).Google Scholar
13. Bauer, S., Pittrof, A., Tsuchiya, H. and Schmuki, P., “Size-Effects in TiO2 Nanotubes: Diameter Dependent Anatase/Rutile Stabilization,” Electrochemistry Communications, 13, pp. 538–541 (2011).Google Scholar
14. Peddieson, J., Buchanan, G. R. and McNitt, R. P., “Application of Nonlocal Continuum Models to Nanotechnology,” International Journal of Engineering Science, 41, pp. 305–312 (2003).Google Scholar
15. Eringen, A. C., “Nonlocal Polar Elastic Continua,” International Journal of Engineering Science, 10, pp. 1–16 (1972).Google Scholar
16. Mindlin, R. D., “Influence of Couple-Stresses on Stress Concentrations,” Experimental Mechanics, 3, pp. 1–7 (1963).Google Scholar
17. Koiter, W. T., “Couple-Stresses in the Theory of Elasticity: I and II, Koninklijke Nederlandse Akademie van Wetenschappen,” Royal Netherlands Academy of Arts and Sciences, 67, pp. 17–44 (1964).Google Scholar
18. Toupin, R. A., “Theories of Elasticity with Couple-Stress,” Archive for Rational Mechanics and Analysis, 17, pp. 85–112 (1964).Google Scholar
19. Mindlin, R. D., “Second Gradient of Strain and Surface-Tension in Linear Elasticity,” International Journal of Solids and Structures, 1, pp. 217–238 (1965).Google Scholar
20. Lam, D. C. C., Yang, F., Chong, A. C. M., Wang, J. and Tong, P., “Experiments and Theory in Strain Gradient Elasticity,” Journal of Mechanics and Physics of Solids, 51, pp. 1477–1508 (2003).Google Scholar
21. Lim, C. W., “On the Truth of Nanoscale for Nanobeams Based on Nonlocal Elastic Stress Field Theory: Equilibrium, Governing Equation and Static Deflection,” Applied Mathematics and Mechanics, 1, pp. 37–54 (2010).Google Scholar
22. He, X., Wang, J., Liu, B. and Liew, K., “Analysis of Nonlinear Forced Vibration of Multi-Layered Graphene Sheets,” Computational Materials Science, 61, pp. 194–199 (2012).Google Scholar
23. Ansari, R., Arash, B. and Rouhi, H., “Vibration Characteristics of Embedded Multi-Layered Graphene Sheets with Different Boundary Conditions via Nonlocal Elasticity,” Composite Structures, 93, pp. 2419–2429 (2011).Google Scholar
24. Li, H. B., Li, Y. D., Wang, X. and Huang, X., “Nonlinear Vibration Characteristics of Graphene/Piezoelectric Sandwich Films under Electric Loading Based on Nonlocal Elastic Theory,” Journal of Sound and Vibration, 358, pp. 285–300 (2015).Google Scholar
25. Nazemnezhad, R. and Hosseini, H. S., “Free Vibration Analysis of Multi-Layer Graphene Nanoribbons Incorporating Interlayer Shear Effect via Molecular Dynamics Simulations and Nonlocal Elasticity,” Physics Letters A, 378, pp. 3225–3232 (2014).Google Scholar
26. Nazemnezhad, R., “Nonlocal Timoshenko Beam Model for Considering Shear Effect of van Der Waals Interactions on Free Vibration of Multilayer Graphene Nanoribbons,” Composites Structures, 133, pp. 522–528 (2015).Google Scholar
27. Ke, L. L. and Wangn, Y. S., “Thermoelectric-Mechanical Vibration of Piezoelectric Nanobeams Based on the Nonlocal Theory,” Smart Materials and Structures, DOI:10.1088/0964-1726/21/2/025018 (2012).Google Scholar
28. Mohammad, R., Jie, Y. and Sritawa, K., “Large Amplitude Vibration of Carbon Nanotube Reinforced Functionally Graded Composite Beams with Piezoelectric Layers,” Composite Structures, 96, pp. 716–725 (2013).Google Scholar
29. Wang, Y. Q., Huang, X. B. and Li, J., “Hydroelastic Dynamic Analysis of Axially Moving Plates in Continuous Hot-Dip Galvanizing Process,” International Journal of Mechanical Sciences, 110, pp. 201–216 (2016).Google Scholar
30. Wang, Y. Q. and Zu, J. W., “Instability of Viscoelastic Plates with Longitudinally Variable Speed and Immersed in Ideal Liquid,” International Journal of Applied Mechanics, DOI: 10.1142/S1758825117500053 (2017).Google Scholar
31. Wang, Y. Q. and Zu, J. W., “Nonlinear Steady-State Responses of Longitudinally Travelling Functionally Graded Material Plates in Contact with Liquid,” Composite Structures, 164, pp. 130–144 (2017).Google Scholar
32. Wang, Y. Q. and Zu, J. W., “Nonlinear Dynamic Thermoelastic Response of Rectangular FGM Plates with Longitudinal Velocity,” Composites Part B: Engineering, 117, pp. 74–88 (2017).Google Scholar
33. Wang, Y. Q. and Zu, J. W., “Analytical Analysis for Vibration of Longitudinally Moving Plate Submerged in Infinite Liquid Domain,” Applied Mathematics and Mechanics, 38, pp. 625–646 (2017).Google Scholar
34. Wang, Y. Q., Xue, S. W., Huang, X. B. and Du, W., “Vibrations of Axially Moving Vertical Rectangular Plates in Contact with Fluid,” International Journal of Structural Stability and Dynamics, 16, 1450092 (2016).Google Scholar
35. Wang, Y., Du, W., Huang, X. and Xue, S., “Study on the Dynamic Behavior of Axially Moving Rectangular Plates Partially Submersed in Fluid,” Acta Mechanica Solida Sinica, 28, pp. 706–721 (2015).Google Scholar
36. Zhang, Y. Q., Liu, G. R. and Han, X., “Transverse Vibrations of Double-Walled Carbon Nanotubes under Compressive Axial Load,” Physics Letters, 340, pp. 258–66 (2005).Google Scholar
37. Zhou, Z. G. and Wang, B., “The Scattering of Harmonic Elastic Anti-Plane Shear Waves by a Griffith Crack in a Piezoelectric Material Plane by Using the Non-Local Theory,” International Journal of Engineering Science, 40, pp. 303–317 (2002).Google Scholar
38. Zhou, Z. G., Du, S. Y. and Wu, L. Z., “Investigation of Anti-Plane Shear Behavior of a Griffith Permeable Crack in Functionally Graded Piezoelectric Materials by Use of the Non-Local Theory,” Composites Structures, 78, pp. 575–583 (2007).Google Scholar
39. Eringen, A. C., “On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves,” Journal of Applied Physics, 54, 4703 (1983).Google Scholar
40. Eringen, A. C., Nonlocal Continuum Field Theories, Springer-Verlag, New York (2002).Google Scholar
41. Karlicic, D., Kozic, P. and Pavlovic, R., “Nonlocal Vibration and Stability of Multiple-Nanobeam System Coupled by Winkler Elastic Medium,” Applied Mathematical Modeling, pp. 1–16 (2015).Google Scholar
42. Wang, Q., “Wave Propagation in Carbon Nanotubes via Nonlocal Continuum Mechanics,” Journal of Applied Physics, 98, 12430 (2005).Google Scholar
43. Farajpour, A., Mohammadi, M., Shahidi, A. R. and Mahzoon, M., “Axisymmetric Buckling of the Circular Graphene Sheets with the Nonlocal Continuum Plate Model,” Physica E, 43, pp. 1820–1825 (2011).Google Scholar
44. Shkel, A. M., “Type I and Type II Micromachined Vibratory Gyroscopes,” Proceedings of IEEE/ION PLANS 2006, San Diego, CA, pp. 586–593 (2006).Google Scholar
45. Ansari, R., Faraji, O. M., Gholami, R. and Sadeghi, F., “Thermo-Electro-Mechanical Vibration of Postbuckled Piezoelectric Timoshenko Nanobeams Based on the Nonlocal Elasticity Theory,” Composites Part B, 89, pp. 316–327 (2016).Google Scholar