Document Type : Original Article

Authors

Department of Mechanical Engineering, University of Shahrekord, Iran

Abstract

In this paper, the free vibration of defective nanographene is investigated using Molecular Dynamics Simulation (MD) and Differential Quadrature Method (DQM). The equations of motions and the related boundary conditions are derived based on the differential constitutive relations in conjunction with the classical plate theory via Hamilton’s principle. Then, DQM is used to investigate free vibration of the nanographene with various boundary conditions. At first, in order to determine natural frequencies more realistically, nanographene mechanical properties are determined using MD simulations. The effects of defects are investigated by analyzing pristine and defective nanographenes containing Stone Wales, vacancy, and Adatom defects. According to the results, the non-dimensional fundamental natural frequency parameter converges to the analytical value for N=10×10. Results indicate that graphene with CCCC boundary conditions has the maximum natural frequency. The minimum value corresponds to the graphene with SSSS boundary conditions. In addition, Non-dimensional fundamental frequency parameter of the nanoplate increases with increasing nanoplate aspect ratio. Finally, defects reduce density, position ratio and elastic moduli of nanographene, which causes a decrease in natural frequency. Stone Wales and vacancy defects decrease nanographene natural frequencies by about 8 and 25 percent, respectively.

Keywords

  • Eringen, A. C., On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves, Journal of applied physics, 54, No. 9, 1983, pp. 4703-4710.
  • Aydogdu, M., Arda, M., Torsional Vibration Analysis of Double Walled Carbon Nanotubes Using Nonlocal Elasticity, International Journal of Mechanics and Materials in Design, 12, No. 1, 2016, pp. 71-84.
  • Saffari, P. R., Fakhraie, M., and Roudbari, M. A., Nonlinear Vibration of Fluid Conveying Cantilever Nanotube Resting on Visco-Pasternak Foundation Using Non-Local Strain Gradient Theory, Micro & Nano Letters, 15, No. 3, 2020, pp. 181-186.
  • Yayli, M. Ö., Free Vibration Analysis of a Single-Walled Carbon Nanotube Embedded in an Elastic Matrix under Rotational Restraints, Micro & Nano Letters, 13, No. 2, 2018, pp. 202-206.
  • Chang, W. J., Lee, H. L., Vibration Analysis of Viscoelastic Carbon Nanotubes, Micro & Nano Letters, 7, No. 12, 2012, pp. 1308-1312.
  • Yayli, M. Ö., On the Axial Vibration of Carbon Nanotubes with Different Boundary Conditions, Micro & Nano Letters, 9, No. 11, 2014, pp. 807-811.
  • Sobamowo, G., Nonlinear Vibration Analysis of Single-Walled Carbon Nanotube Conveying Fluid in Slip Boundary Conditions Using Variational Iterative Method, Journal of Applied and Computational Mechanics, 2, No. 4, 2016, pp. 208-221.
  • Ghobanpour Arani, A., Rastgoo, A., Ghorbanpour Arani, A., and Zarei, M. S., Nonlocal Vibration of Y-Swcnt Conveying Fluid Considering a General Nonlocal Elastic Medium, Journal of Solid Mechanics, 8, No. 2, 2016, pp. 232-246.
  • Hosseini–Hashemi, S., Fakher, M., and Nazemnezhad, R., Surface Effects on Free Vibration Analysis of Nanobeams Using Nonlocal Elasticity: A Comparison between Euler-Bernoulli and Timoshenko, Journal of Solid Mechanics, 5, No. 3, 2013, pp. 290-304.
  • Rajabi, K., Hosseini Hashemi, S. and Nezamabadi, A., Size-Dependent Forced Vibration Analysis of Three Nonlocal Strain Gradient Beam Models with Surface Effects Subjected to Moving Harmonic Loads, Journal of Solid Mechanics, 11, No. 1, 2019, pp. 39-59.
  • Refaeinejad, V., Rahmani, O., and Hosseini, S., An Analytical Solution for Bending, Buckling, and Free Vibration of Fg Nanobeam Lying on Winkler-Pasternak Elastic Foundation Using Different Nonlocal Higher Order Shear Deformation Beam Theories, Scientia Iranica, 24, No. 3, 2017, pp. 1635-1653.
  • Ebrahimi, F., Shaghaghi, G. R., Vibration Analysis of an Initially Pre-Stressed Rotating Carbon Nanotube Employing Differential Transform Method, ADMT Journal, 8, No. 4, 2015 pp. 1-12.
  • Mahmoudpour, E., Nonlinear Vibration Analysis of Fg Nano-Beams in Thermal Environment and Resting on Nonlinear Foundation Based on Nonlocal and Strain-Inertia Gradient Theory, ADMT Journal, 11, No. 3, 2018, pp. 11-24.
  • Nazemizadeh, M., Bakhtiari-Nejad, F., and Shahriari, B., Vibration Sensitivity Analysis of Nano-Mechanical Piezo-Laminated Beams with Consideration of Size Effects, ADMT Journal, 13, No. 4, 2020, pp. 57-68.
  • Liew, K., Zhang, Y., and Zhang, L., Nonlocal Elasticity Theory for Graphene Modeling and Simulation: Prospects and Challenges, Journal of modeling in Mechanics and Materials, 1, No. 1, 2017, pp. 1-11.
  • Shahsavari, D., Karami, B., and Li, L., Damped Vibration of a Graphene Sheet Using a Higher-Order Nonlocal Strain-Gradient Kirchhoff Plate Model, Comptes Rendus Mécanique, 346, No. 12, 2018, pp. 1216-1232.
  • Farajpour, M. R., Rastgoo, A., Farajpour, A., and Mohammadi, M., Vibration of Piezoelectric Nanofilm-Based Electromechanical Sensors Via Higher-Order Non-Local Strain Gradient Theory, Micro & Nano Letters, 11, No. 6, 2016, pp. 302-307.
  • Zhang, L., Zhang, Y., and Liew, K., Vibration Analysis of Quadrilateral Graphene Sheets Subjected to an in-Plane Magnetic Field Based on Nonlocal Elasticity Theory, Composites Part B: Engineering, 118, 2017, pp. 96-103.
  • Ahmad Pour, M., Golmakani, M., and Malikan, M., Thermal Buckling Analysis of Circular Bilayer Graphene Sheets Resting on an Elastic Matrix Based on Nonlocal Continuum Mechanics, Journal of Applied and Computational Mechanics, Vol. 74, 2019, pp. 1-9.
  • Mohammadi, M., Farajpour, A., Goodarzi, M., and Heydarshenas, R., Levy Type Solution for Nonlocal Thermo-Mechanical Vibration of Orthotropic Mono-Layer Graphene Sheet Embedded in an Elastic Medium, Journal of Solid Mechanics, 5, No. 2, 2013, pp. 116-132.
  • Jalali, M. H., Shahriari, B., Zargar, O., Baghani, M., and Baniassadi, M., Free Vibration Analysis of Rotating Functionally Graded Annular Disc of Variable Thickness Using Generalized Differential Quadrature Method, Scientia Iranica, Vol. 25, No. 2, 2018, pp. 728-740.
  • Shaat, M., Abdelkefi, A., New Insights on the Applicability of Eringen’s Nonlocal Theory, International Journal of Mechanical Sciences, 121, 2017, pp. 67-75.
  • Wu, W., Yin, J., Xie, W., Zhang, W., Wu, B., Jiang, Y., Zhang, P., and Ding, Y., Effect of Vacancy Distribution on the Relaxation Properties of Graphene: A Molecular Dynamics Study, Micro & Nano Letters, 10, No. 12, 2015, pp. 693-695.
  • Aghadavoudi, F., Golestanian, H., and Tadi Beni, Y., Investigating the Effects of Cnt Aspect Ratio and Agglomeration on Elastic Constants of Crosslinked Polymer Nanocomposite Using Multiscale Modeling, Polymer Composites, Vol. 20, No. 14, 2017, pp. 1-12.
  • Mohammadzadeh Honarvar, F., Pourabbas, B., Salami Hosseini, M., Kharazi, M., and Erfan-Niya, H., Molecular Dynamics Simulation: The Effect of Graphene on the Mechanical Properties of Epoxy Based Photoresist: Su8, Scientia Iranica, 25, No. 3, 2018, pp. 1879-1890.
  • Aghadavoudi, F., Golestanian, H., and Beni, Y. T., Investigation of CNT Defects on Mechanical Behavior of Cross linked Epoxy based Nanocomposites by Molecular Dynamics, Int J Adv Design Manuf Technol, Vol. 9, No. 1, 2016. pp. 137-146.
  • Pradhan, S., Phadikar, J., Nonlocal Elasticity Theory for Vibration of Nanoplates, Journal of Sound and Vibration, 325, No. 1-2, 2009, pp. 206-223.
  • Fereidoon, A., Aleaghaee, S., and Taraghi, I., Mechanical Properties of Hybrid Graphene/Tio2 (Rutile) Nanocomposite: A Molecular Dynamics Simulation, Computational Materials Science, 102, No. 1, 2015, pp. 220-227.
  • Golestanian, H., Khodadadi, A., Haghighi, M., and Aghadavoudi, F., Molecular Dynamics Simulation of Functional and Hybrid Epoxy Based Nanocomposites, Mechanics of Advanced Composite Structures‎, Vol. 7, No. 2, 2020, pp. 233-243.
  • Karami, G., Malekzadeh, P., Application of a New Differential Quadrature Methodology for Free Vibration Analysis of Plates, International Journal for Numerical Methods in Engineering, 56, No. 6, 2003, pp. 847-868.
  • Frank, I., Tanenbaum, D. M., van der Zande, A. M., and McEuen, P. L., Mechanical Properties of Suspended Graphene Sheets, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena, 25, No. 6, 2007, pp. 2558-2561.
  • Neek-Amal, M., Peeters, F., Linear Reduction of Stiffness and Vibration Frequencies in Defected Circular Monolayer Graphene, Physical review B, 81, No. 23, 2010, pp. 235-243.