Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method

Composite Structures

Volumn 93, Issue 2, 2011, Pages 774-779

  Pradhan, S C ^a   Kumar, A ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Differential quadrature method; Nonlocal elasticity theory; Orthotropic graphene sheet; Vibration

Indexed keywords

CONSTITUTIVE RELATIONS; DIFFERENTIAL QUADRATURE METHODS; ELASTIC THEORY; GOVERNING DIFFERENTIAL EQUATIONS; GRAPHENE SHEETS; MATERIAL PROPERTY; NONDIMENSIONAL; NONLOCAL; NONLOCAL ELASTICITY; NONLOCAL ELASTICITY THEORY; NONLOCAL THEORY; ORTHOTROPIC GRAPHENE SHEET; SINGLE-LAYERED GRAPHENE SHEETS; SMALL SCALE; VIBRATION; VIBRATION FREQUENCY;

BOUNDARY CONDITIONS; DIFFERENTIATION (CALCULUS); ELASTICITY; EQUATIONS OF MOTION; VIBRATION ANALYSIS;

GRAPHENE;

EID: 79951517665     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2010.08.004     Document Type: Article

References (37)

1. Ball P. Roll up for the revolution. Nature (London) 2001, 414:142-144.
2. Baughman R.H., Zakhidov A.A., de Heer W.A. Carbon nanotubes - the route toward applications. Science 2002, 297:787-792.
3. Bodily B.H., Sun C.T. Structural and equivalent continuum properties of single-walled carbon nanotubes. Int J Mater Prod Technol 2003, 18(4/5/6):381-397.
4. Li C., Chou T.W. A structural mechanics approach for the analysis of carbon nanotubes. Int J Solids Struct 2003, 40:2487-2499.
5. Li C., Chou T.W. Single-walled nanotubes as ultrahigh frequency nanomechanical oscillators. Phys Rev B 2003, 68:073405.
6. Pradhan SC, Phadikar JK. Nonlinear analysis of carbon nano tubes. In: Proceedings of fifth international conference on smart materials, structures and systems. Bangalore: Indian Institute of Science; 24-26 July, 2008 [paper ID 19].
7. Wang C.M., Tan V.B.C., Zhang Y.Y. Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes. J Sound Vib 2006, 294:1060-1072.
8. Wang Q., Vardan V.K. Characteristics of carbon nanotubes. Int J Solids Struct 2005, 43:254-265.
9. Fu Y.M., Hong J.W., Wang X.Q. Analysis of nonlinear vibration for embedded carbon nanotubes. J Sound Vib 2006, 296:746-756.
10. Wang Q., Zhou G.Y., Lin K.C. Scale effect on wave propagation of double walled carbon nanotubes. Int J Solids Struct 2006, 43:6071-6084.
11. Tserpes K.I., Papanikos P. Continuum modeling of carbon nanotube-based super-structures. Compos Struct 2009, 91(2):131-137.
12. Wang Q., Varadan V.K. Vibration of carbon nanotubes studied using nonlocal continuum mechanics. Smart Mater Struct 2006, 15:659-666.
13. Yoon J., Ru C.Q., Mioduchowski A. Vibration of embedded multiwall carbon nanotubes. Compos Sci Technol 2003, 63:1533-1542.
14. Ru C.Q. Column buckling of multiwalled carbon nanotubes with interlayer radial displacements. Phys Rev B 2000, 62:16962-16967.
15. Li C., Chou T.W. Elastic moduli of multi-walled carbon nanotubes and the effect of van der Waals forces. Compos Sci Technol 2003, 11:1517-1524.
16. Lu P., Lee H.P., Lu C., Zhang P.Q. Application of nonlocal beam models for carbon nanotubes. Int J Solids Struct 2007, 44:5289-5300.
17. Gibson R.F., Ayorinde O.E., Wen Yuan-Feng Vibration of carbon nanotubes and there composites: a review. Compos Sci Technol 2007, 67:1-28.
18. Eringen A.C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 1983, 54:4703-4710.
19. Eringen A.C. Nonlocal continuum field theories 2002, Springer-Verlag, New York.
20. Reddy J.N. Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci 2007, 45:288-307.
21. Luo X., Chung D.D.L. Vibration damping using flexible graphite. Carbon 2000, 38:1510-1512.
22. Zhang L., Huang H. Young's moduli of ZnO nanoplates: ab initio determinations. Appl Phys Lett 2006, 89:183111.
23. He X.Q., Kitipornchai S., Liew K.M. Resonance analysis of multi-layered graphene sheets used as nanoscale resonators. Nanotechnology 2005, 16:2086-2091.
24. Kitipornchai S., He X.Q., Liew K.M. Continuum model for the vibration of multilayered graphene sheets. Phys Rev B 2005, 72:075443.
25. Jomehzadeh E., Saidi A.R. Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates. Compos Struct 2010, 93(2):1015-1020.
26. Behfar K., Naghdabadi R. Nanoscale vibrational analysis of a multi-layered grapheme sheet embedded in an elastic medium. Compos Sci Technol 2005, 7-8:1159-1164.
27. Reddy JN, Mechanics of laminated composite plates, theory and analysis, Boca Raton (FL): Chemical Rubber Company; 1997.
28. Shu C. Differential quadrature and its application in engineering 2000, Springer, Berlin.
29. Murmu T., Pradhan S.C. Buckling analysis of a single-walled carbon nanotubes embedded in an elastic medium based on nonlocal continuum mechanics. Physica E 2009, 41:1232-1239.
30. Pradhan S.C., Phadikar J.K. Nonlocal elasticity theory for vibration of nanoplates. J Sound Vib 2009, 325:206-223.
31. Aydogdu M. Axial vibration of the nanorods with nonlocal continuum rod model. Physica E 2009, 41:861-864.
32. Wang Q., Wang C.M. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology 2007, 18:075702.
33. Pradhan S.C. Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory. Phys Lett A 2009, 373:4182-4188.
34. Liew K.M., He X.Q., Kitipornchai S. Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix. Acta Mater 2006, 54:4229-4236.
35. Pradhan S.C., Murmu T. Small scale effect on vibration analysis of single-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory. J Appl Phys 2009, 105:124306.
36. Murmu T., Pradhan S.C. Vibration analysis of nanoplates under uniaxial pretressed conditions via nonlocal elasticity. J Appl Phys 2009, 106:104301.
37. Pradhan S.C., Phadikar J.K. Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models. Phys Lett A 2009, 373:1062-1069.