Thermo-resonance analysis of an excited graphene sheet using a new approach

Abstract

Forced vibration of graphene nanoplate based on a refined plate theory in conjunction with higher-order nonlocal strain gradient theory in the thermal environment has been investigated. Regarding the higher-order nonlocal strain gradient theory, both stress nonlocality and size-dependent effects are taken into account, so the equilibrium equations which are governing on the graphene sheet have been formulated by the theory. The extracted equations will be solved by a closed-form approach by which maximum dynamic deflection has been obtained while all the edges are considered as simple boundaries. To approve the results of the plate theory, several available well-known references have been compared. Finally, after determining the accuracy of the equations, different parameters have been examined for showing the behavior of the nanoplate exposed to a transverse dynamic harmonic load.

Keywords

• Forced vibration; A refined plate theory; Higher-order nonlocal strain gradient theory; Dynamic deflections

References

1. Taghioskoui, M., Trends in graphene research. Materials Today, 12, 34–37, 2009.
2. Park, S., Ruoff, R. S., Chemical methods for the production of graphenes. Nature Nanotechnoly, 4, 217-224, 2009.
3. An, X., Yu, J. C., Graphene-based photocatalytic composites. Royal Society of Chemistry Advances, 1, 1426–1434, 2011.
4. Xiang, Q., Yu, J., Jaroniec, M., Graphene-based semiconductor photocatalysts. Chemical Society Reviews, 41, 782–796, 2012.
5. Esmaeili, A., Entezari, M. H., Facile and fast synthesis of graphene oxide nanosheets via bath ultrasonic Irradiation. Journal of Colloid and Interface Science, 432, 19-25, 2014.
6. Ebrahimi, F., Barati, M. R., Damping vibration analysis of graphene sheets on viscoelastic medium incorporating hygro-thermal effects employing nonlocal strain gradient theory. Composite Structures, 185, 241-253, 2018.
7. Radic, N., Jeremić, D., Thermal buckling of double-layered graphene sheets embedded in an elastic medium with various boundary conditions using a nonlocal new first-order shear deformation theory. Composites Part B: Engineering, 97, 201–215, 2016.
8. Malikan, M., Jabbarzadeh, M., Sh. Dastjerdi, Non-linear Static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum. Microsystem Technologies, 23, 2973-2991, 2017.

9. Malikan, M., Buckling analysis of a micro composite plate with nano coating based on the modified couple stress theory. Journal of Applied and Computational Mechanics, 4, 1–15, 2018.
10. Malikan, M., Analytical predictions for the buckling of a nanoplate subjected to nonuniform compression based on the four-variable plate theory. Journal of Applied and Computational Mechanics, 3, 218–228, 2017.
11. Shahsavari, D., Karami, B., Mansouri, S., Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories. European Journal of Mechanics / A Solids, 67, 200-214, 2018.
12. Farajpour, A., Haeri Yazdi, M. R., Rastgoo, A., Mohammadi, M., A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mechanica, 227, 1849–1867, 2016.
13. Zhang, L. W., Zhang, Y., Liew, K. M., Vibration analysis of quadrilateral graphene sheets subjected to an inplane magnetic field based on nonlocal elasticity theory. Composites Part B: Engineering, 118, 96-103, 2017.
14. Feng, C., Kitipornchai, S., Yang, J., Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs). Engineering Structures, 140, 110–119, 2017.
15. Gholami, R., Ansari, R., Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates. Engineering Structures, 156, 197–209, 2018.
16. Civalek, O., The determination of frequencies of laminated conical shells via the discrete singular convolution method. Journal of Mechanics of Materials and Structures, 1, 163-182, 2006.
17. Shen, J., Wang, H., Zheng, Sh., Size-dependent pull-in analysis of a composite laminated micro-beam actuated by electrostatic and piezoelectric forces: Generalized differential quadrature method. International Journal of Mechanical Sciences, 135, 353-361, 2018.
18. Gürses, M., Civalek, O., Korkmaz, A., Ersoy H. Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory. International journal for numerical methods in engineering, 79, 290-313, 2009.
19. Civalek, O., Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches. Composites Part B: Engineering, 50, 171–179, 2013.
20. Baltacıoglu, A. K., Akgoz, B., Civalek, O., Nonlinear static response of laminated composite plates by discrete singular convolution method. Composite Structures, 93, 153–161, 2010.
21. Civalek, O., Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory. Journal of Composite Materials, 42, 2853-2867, 2008.
22. Baltacıoglu, A. K., Civalek, O., Akgoz, B., Demir, F., Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution. International Journal of Pressure Vessels and Piping, 88, 290-300, 2011.
23. Shahba, A., Attarnejada, R., Hajilar, S. Free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams. Shock and Vibration, 18, 683–696, 2011.
24. Civalek, O., Demir, C., Buckling and bending analyses of cantilever carbon nanotubes using the Euler Bernoulli beam theory based on non-local continuum model. Asian Journal of Civil Engineering, 12, 651-661, 2011.
25. Akgöz, B., Civalek, O., Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories. Journal of Computational and Theoretical Nanoscience, 8, 1821-1827, 2011.
26. Civalek, O., Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method. Composites Part B: Engineering, 111, 45-59, 2017.
27. Malikan, M., Electroelastic biaxial compression of nanoplates considering piezoelectric effects, Journal of Polymer Science and Engineering, (2018), http://dx.doi.org/10.24294/jpse.v0i0.558
28. Malikan, M., Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory. Applied Mathematical Modelling, 48, 196–207, 2017.
29. Malikan, M., Tornabene, F., Dimitri, R., Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals. Materials Research Express, 5, 095006, 2018.
30. Malikan, M., Electro-thermal buckling of elastically supported double-layered piezoelectric nanoplates affected by an external electric voltage. Multidiscipline Modeling in Materials and Structures, (2018), https://doi.org/10.1108/MMMS-01-2018-0010.
31. Golmakani, M. E., Malikan, M., Sadraee Far, M. N., Majidi, H. R., Bending and buckling formulation of graphene sheets based on nonlocal simple first order shear deformation theory. Materials Research Express, 5, 065010, 2018.
32. Malikan, M., Temperature influences on shear stability a nanosize plate with piezoelectricity effect. Multidiscipline modeling in materials and structures, 14, 125-142, 2018.
33. Wan, J., Chen, W. J., Li, X. P., Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory. Archive of Applied Mechanics, 83, 431–444, 2013.
34. Mercan, K., Civalek, O., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix. Composite Structures, 143, 300–309, 2016.
35. Demir, C., Mercan K, Civalek, O. Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel. Composites Part B: Engineering, 94, 1-10, 2016.
36. Mercan, K., Civalek, O., Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ. Composites Part B: Engineering, 114, 34-45, 2017.
37. Jouneghani, F. Z., Dimitri, R., Bacciocchi, M., Tornabene, F., Free vibration analysis of functionally graded porous doubly-curved shells based on the first-order shear deformation theory. Applied Sciences, 7, 1-20, 2017.
38. Nejati, M., Dimitri, R., Tornabene, F., Yas, M. H., Thermal buckling of nanocomposite stiffened cylindrical shells reinforced by Functionally Graded Wavy Carbon Nano-Tubes with temperature-dependent properties. Applied Sciences, 7, 1-24, 2017.
39. Kiani, Y., Dimitri, R., Tornabene, F., Free vibration study of composite conical panels reinforced with FG-CNTs. Engineering Structures, 172, 472-482, 2018.
40. Kiani, Y., Dimitri, R., Tornabene, F., Free Vibration of FG-CNT Reinforced Composite Skew Cylindrical Shells using Chebyshev-Ritz Formulation. Composites Part B: Engineering, 147, 169-177, 2018.
41. Jouneghani, F. Z., Dimitri, R., Tornabene, F., Structural response of porous FG nanobeams under hygro-thermo-mechanical loadings. Composites Part B: Engineering, 152, 71-78, 2018.
42. Fantuzzi, N., Tornabene, F., Bacciocchi, M., Dimitri, R., Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates. Composites Part B: Engineering, 115, 384–408, 2017.
43. Nejati, M., Asanjarani, A., Dimitri, R., Tornabene, F., Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes. International Journal of Mechanical Sciences, 130, 383–398, 2017.
44. Tornabene, F., Fantuzzi, N., Bacciocchi, M., Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes. Composites Part B: Engineering, 115, 449–476, 2017. Tornabene, F., Bacciocchi, M., Fantuzzi, N., Reddy, J. N., Multiscale approach for three-Phase CNT/Polymer/Fiber laminated nanocomposite structures. Polymer Composite, In Press, DOI: 10.1002/pc.24520.
45. She, G. L., Yuan, F. G., Ren, Y. R., Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory. Applied Mathematical Modelling, 47, 340-357, 2017.
46. She, G. L., Yuan, F. G., Ren, Y. R., Liu, H. B., Xiao, W. Sh., Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory. Composite Structures, 203, 614-623, 2018.
47. She, G. L., Yuan, F. G., Ren, Y. R., On wave propagation of porous nanotubes. International Journal of Engineering Science, 130, 62-74, 2018.
48. She, G. L., Ren, Y. R., Yuan, F. G., Xiao, W. S., On vibrations of porous nanotubes. International Journal of Engineering Science, 125, 23-35, 2018.
49. She, G. L., Ren, Y. R., Xiao, W. S., Liu, H. B., Study on thermal buckling and post-buckling behaviors of fgm tubes resting on elastic foundations. Structural Engineering & Mechanics, 66, 729-736, 2018.
50. She, G. L., Yuan, F. G., Ren, Y. R., Xiao, W. S., On buckling and post-buckling behavior of nanotubes. International Journal of Engineering Science, 121, 130-142, 2017.
51. Malikan, M., Nguyen, V. B., Tornabene, F., Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory. Materials Research Express, 5, 075031, 2018.
52. Malikan, M., Dimitri, R., Tornabene, F., Transient response of oscillated carbon nanotubes with an internal and external damping. Composites Part B: Engineering, 158, 198-205, 2019.
53. Malikan, M., Nguyen, V. B., A novel one variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on the Eringen's nonlocal differential law. World Journal of Engineering, 2018. https://doi.org/10.1108/WJE-11-2017-0357
54. Malikan, M., Nguyen, V. B., Tornabene, F., Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory. Engineering Science and Technology, an International Journal, 21, 778-786, 2018.
55. Malikan, M., Dimitri, R., Tornabene, F., Effect of sinusoidal corrugated geometries on the vibrational response of viscoelastic nanoplates. Applied Sciences, 8, 1432, 2018.
56. Malikan, M., On the buckling response of axially pressurized nanotubes based on a novel nonlocal beam theory. Journal of Applied and Computational Mechanics, (2018), DOI: 10.22055/JACM.2018.25507.1274
57. Malikan, M., Nguyen, V. B., Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory. Physica E: Low-dimensional Systems and Nanostructures, 102, 8-28, 2018.
58. Malikan, M., Dastjerdi, Sh., Analytical buckling of FG nanobeams on the basis of a new one variable first-order shear deformation beam theory. International Journal of Engineering & Applied Sciences, 10, 21-34, 2018.
59. Malikan, M., Sadraee Far, M. N., Differential quadrature method for dynamic buckling of graphene sheet coupled by a viscoelastic medium using neperian frequency based on nonlocal elasticity theory. Journal of Applied and Computational Mechanics. 4, 147-160, 2018.
60. Golmakani, M. E., Rezatalab, J., Nonuniform biaxial buckling of orthotropic Nano plates embedded in an elastic medium based on nonlocal Mindlin plate theory. Composite Structures, 119, 238-250, 2015.
61. Golmakani, M. E., Sadraee Far, M. N., Buckling analysis of biaxially compressed double‑layered graphene sheets with various boundary conditions based on nonlocal elasticity theory. Microsystem Technologies, 23, 2145-2161, 2017.
62. Ansari, R., Sahmani, S., Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations. Applied Mathematical Modelling, 37, 7338–51, 2013.