Surface effect on free vibration behavior of circular graphene sheet with an eccentric hole

Document Type : Research Article

Authors

Department of Mechanical Engineering, College of Engineering, Qom University of Technology, Qom, Iran

Abstract

In this article, an analytical method is used to study surface and geometrical defect effects on free vibrations behavior of circular nanoplates. Due to production process and constrains conditions, nanoplates may be opposed to structural defect. Some of the defects can be modelled as an eccentric hole. Gurtin-Murdoch and thin plate theories are employed to model the eccentric circular nanoplate. In order to solve equation of motion, separation of variables method as well as additional theorem for the regular and modified of first and second kinds of Bessel functions are used. To validate the approach, present results are compared to those obtained by literature. Both of symmetric and antisymmetric vibration modes are analyzed. Some mode shapes are illustrated to make the better physical sense. Finally, effects of various geometrical and material properties on natural frequencies of the nanoplates are investigated. Also, effects of various boundary conditions as free, clamped and simply supported on the natural frequencies are investigated using a wide range of results. Results show that surface effects and eccentric circular defect play an important role in vibrational behavior of an eccentric circular nanoplate. It is observed that the free boundary condition has no more effect on the fundamental natural frequency.

Keywords

Main Subjects

References

[1] S.R. Asemi, A. Farajpour, Decoupling the nonlocal elasticity equations for thermo-mechanical vibration of circular graphene sheets including surface effects, Physica E: Low-dimensional Systems and Nanostructures, 60(2014) 80-90.
[2] R. Ansari, R. Gholami, M.F. Shojaei, V. Mohammadi, S.Sahmani, Surface stress effect on the pull-in instability of circular nanoplates, Acta Astronautica, 102 (2014) 140-150.
[3] R. Ansari, R. Gholami, M.F. Shojaei, V. Mohammadi, S.Sahmani, Surface stress effect on the vibrational response of circular nanoplates with various edge supports, Journal of Applied Mechanics, 80(2) (2013) 021021.
[4] R. Ansari, R. Gholami, M.F. Shojaei, V. Mohammadi, S. Sahmani, Surface stress effect on the vibrational response of circular nanoplates with various edge supports, Journal of Applied Mechanics, 80(2) (2013) 021021.
[5] C.M. Wang, W.H. Duan, Free vibration of nanorings/ arches based on nonlocal elasticity, Journal of Applied Physics, 104(1) (2008) 014303.
[6] A. Assadi, Size dependent forced vibration of nanoplates with consideration of surface effects, Applied Mathematical Modelling, 37(5) (2013) 3575-3588.
[7] A. Assadi, B. Farshi, Vibration characteristics of circular nanoplates, Journal of Applied Physics, 108(7) (2010) 074312.
[8] B. Farshi, A. Assadi, A. Alinia-Ziazi, Frequency analysis of nanotubes with consideration of surface effects,Applied Physics Letters, 96(9) (2010) 093105.
[9] S.C. Pradhan, T. Murmu, Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics,Computational materials science, 47(1) (2009) 268-274.
[10] K. Behfar, R. Naghdabadi, Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium, Composites science and technology,65(7) (2005) 1159-1164.
[11] M. Bedroud, H.S. Hosseini, R. Nazemnezhad,Axisymmetric/asymmetric buckling of circular/annular nanoplates via nonlocal elasticity, Modares Mechanical Engineering, 13(5) (2013) 144-152.
[12] R. Nazemnezhad, S. Hosseini-Hashemi, M. Kermajani,S. Amirabdollahian, Exact solutions for free vibration of lévy-type rectangular nanoplates via nonlocal third-order plate theory, Modares Mechanical Engineering, 14(7)(2014) 122-130.
[13] A. Farajpour, M. Dehghany, A.R. Shahidi, Surface and nonlocal effects on the axisymmetric buckling of circular graphene sheets in thermal environment, Composites Part B: Engineering, 50 (2013) 333-343.
[14] M.R.K. Ravari, S. Talebi, A.R. Shahidi, Analysis of the buckling of rectangular nanoplates by use of finitedifference method, Meccanica, 49(6) (2014) 1443-1455.
[15] E. Jomehzadeh, A.R. Saidi, Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates, Composite Structures, 93(2)(2011) 1015-1020.
[16] A. Farajpour, M. Mohammadi, A.R. Shahidi, M.Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, 43(10) (2011) 1820-1825.
[17] M. Mohammadi, M. Goodarzi, M. Ghayour, A.Farajpour, Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B: Engineering, 51(2013) 121-129.
[18] M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B:Engineering, 45(1) (2013) 32-42.
[19] B. Gheshlaghi, S.M. Hasheminejad, Size dependent damping in axisymmetric vibrations of circularm nanoplates, Thin Solid Films, 537 (2013) 212-216.
[20] E. Mahmoudinezhad, R. Ansari, Vibration analysis of  circular and square single-layered graphene sheets: Anaccurate spring mass model, Physica E: Low-dimensional Systems and Nanostructures, 47 (2013) 12-16.
[21] M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces, Archive for rational mechanics and analysis, 57(4) (1975) 291-323.
[22] G.N. Watson, A treatise on the theory of Bessel functions, Cambridge university press, 1995.
 
 
Amirkabir Journal of Mechanical Engineering
Volume 49, Issue 2
August 2017
Pages 299-308

Files

Share

How to cite

Statistics