Geometrical Dimensional Effect on Natural Frequency of Single Layer Graphene in Armchair Configuration

Harshad Patel (Manufacturing Engineering Department, Central Institute of Petrochemicals Engineering & Technology, Ahmedabad, Gujarat, India)

Article ID: 3831



Graphene has remarkable strength, such as yield strength and elasticconstant. The dynamic behaviour of graphene sheet is affected bygeometrical variation in atomic arrangement. This paper introducedgraphene with armchair atomic structure for estimating fundamental naturalfrequencies. The presented analysis can be useful for the possible highfrequency nanomechanical resonator systems. The analytical formulation,based on classical plate theory and continuum solid modelling based finiteelement method have been performed for estimation of fundamental naturalfrequencies of single layer graphene sheet (SGLS) with different boundaryconditions. The free edge and clamped edge boundary conditions have beenconsidered. For simplifying analytical formulations, Blevins approach fordynamic solution has been adopted and for validating analytical results.The finite element analysis of SLGS has been performed using ANSYSsoftware. The effect of variation in geometrical parameters in terms ofwidth and length of SLGS has been analysed for realization of ultra-highfrequency based nanomechanical resonator systems


Single layer graphene sheet (SLGS) ;Size variation ;Fundamental natural frequency ;Finite element analysis

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[1] S. Iijima // Nature 354 (6348) (1991) 56.

[2] K. Esumi, M. Ishigami, A. Nakajima, K. Sawada, H. Honda // Carbon 34 (1996) 279.

[3] F. Scarpa, S. Adhikari, A. Srikantha Phani // Nanotechnology 20(6) (2009) 065709.

[4] K. Tanaka, H. Aoki, H. Ago, T. Yamabe, K. Okahara // Carbon 35 (1997) 121.

[5] M. Kim, H.S. An, W.-J. Lee, J. Jung // Electronic Materials Letters 9(4) (2013) 517.

[6] M. Mazar Atabaki, R. Kovacevic // Electronic Materials Letters 9(2) (2013) 133.

[7] W.G. Lee, E. Kim, J. Jung // Electronic Materials Letters 8(6) (2012) 609.

[8] C. Berger, Z. Song, T. Li, X. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, W.A. de Heer // The Journal of Physical Chemistry B 108(52) (2004) 19912.

[9] J.S. Bunch, A.M. Van Der Zande, S.S. Verbridge, I.W. Frank, D.M. Tanenbaum, J.M. Parpia, H.G. Craighead, P.L. McEuen // Science 315 (2007) 490.

[10] S.S. Gupta, R.C. Batra, Journal of Computational and Theoretical Nanoscience 7 (10) (2010) 2151-2164.

[11] S. Timoshenko, Theory of Plates and Shells, McGraw-Hill, Inc, London, 1940.

[12] Balandin AA, Ghosh S, Bao W, Calizon I, Teweldebrhan D, Miao F, et al. Superior thermal conductivity og single-layer graphene. Nano Lett 2008;8(3):902-7.

[13] Zhu Y, Murali S, Cai W, Li , Suk JW, Potts JR, et al. Graphene and graphene oxide: synthesis, properties, and application. Adc Mater 2010;22(35):3906-24.

[14] Jena, Subrat & Chakraverty, S.. (2019). Dynamic Analysis of Single-Layered Graphene Nano-Ribbons (SLGNRs) with Variable Cross-Section Resting on Elastic Foundation. Curved and Layered Structures. 6. 132-145. 10.1515/cls-2019-0011.

[15] Ren Wei Jiang, Zhi Bin Shen, Guo Jin Tang, Vibration analysis of a single-layered graphene sheetbased mass sensor using the Galerkin strip distributed transfer function method, 2016.

[16] A. Sakhaee-Pour, M.T. Ahmadian, A. Vafai // Solid State Communications 145 (2008) 168.

[17] Laura, P.A.A.; Pombo, J. L.; Susemihl, E.A. A note on the vibration of a clamped free beam with a mass at the free end. J. Sound Vib. 1974, 37, 161-168.

[18] Natsuki, Toshiaki. (2015). Theoretical Analysis of Vibration Frequency of Graphene Sheets Used as Nanomechanical Mass Sensor. Electronics. 4. 723- 738. 10.3390/electronics4040723.

[19] Samaei, A.T. & Aliha, M.R.M. & Mirsayar, M.M.. (2015). Frequency analysis of a graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics. 22. 125-135.

[20] Ekinci, K.L.; Huang, X.M.H.; Roukes, M.L. Ultrasensitive nanoelectromechanical mass detection.Appl. Phys. Lett. 2004, 84, 4469-4471.

[21] Geim, A.K. Graphene: status and prospects. Science 2009, 324, 1530-1534.

[22] Rakesh Prabhu T., Tarapada Roy, National Institute Of Technology ROURKELA,2010.Finite element modelling of multiwall carbon nanotube.

[23] Steven J. Koester ,Ultra-smooth Graphene Nanoribbon Formation Using Templated,Etching.

[24] Blevins, R. Formula for Natural Frequency and Mode Shape; Krieger; Hellerup, Denmark, 2001.

[25] Belvins, R.D. (1984) Formulas for natural frequency and mode shape. R.E. Krieger.

[26] Rakesh Prabhu T., Tarapada Roy, “Finite element modeling of multiwalled carbon nanotube”. National Institute of Technology Rourkela,2010.

[27] Zenkour, Ashraf. (2016). Vibration analysis of a single-layered graphene sheet embedded in visco-Pasternak’s medium using nonlocal elasticity theory. Journal of Vibroengineering. 18. 10.21595/ jve.2016.16585.


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