A nonlocal beam theory for bending, buckling, and vibration of nanobeams

International Journal of Engineering Science

Volumn 52, Issue , 2012, Pages 56-64

  Thai, Huu Tai ^a  

^a Hanyang University   (South Korea)

Author keywords

Bending; Buckling; Nanobeam; Nonlocal beam theory; Vibration

Indexed keywords

ANALYTICAL SOLUTIONS; BEAM THEORIES; BUCKLING LOADS; CONSTITUTIVE RELATIONS; EULER BERNOULLI BEAM THEORY; HAMILTON'S PRINCIPLE; NANOBEAM; NONLOCAL; QUADRATIC VARIATIONS; SHEAR CORRECTION FACTORS; SIMPLY SUPPORTED BEAMS; SMALL SCALE; STRESS RESULTANTS; VIBRATION;

BENDING (DEFORMATION); BENDING (FORMING); BUCKLING; ELASTICITY; EULER EQUATIONS; NANOWIRES; SHEAR FLOW; STRUCTURAL DESIGN;

VIBRATION ANALYSIS;

EID: 84855896366     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2011.11.011     Document Type: Article

References (39)

1. R. Ansari, and S. Sahmani Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories International Journal of Engineering Science 49 2011 1244 1255
2. B. Arash, and R. Ansari Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain Physica E 42 2010 2058 2064
3. B. Arash, and Q. Wang A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphines Computational Materials Science 51 2012 303 313
4. M. Asghari, M.H. Kahrobaiyan, and M.T. Ahmadian A nonlinear Timoshenko beam formulation based on the modified couple stress theory International Journal of Engineering Science 48 2010 1749 1761
5. M. Aydogdu Vibration of multi-walled carbon nanotubes by generalized shear deformation theory International Journal of Engineering and Science 50 2008 837 844 (Pubitemid 351417858)
6. M. Aydogdu A general nonlocal beam theory: Its application to nanobeam bending buckling and vibration Physica E 41 2009 1651 1655
7. M. Aydogdu Axial vibration of the nanorods with the nonlocal continuum rod model Physica E 41 2009 861 864
8. A. Benzair, A. Tounsi, A. Besseghier, H. Heireche, N. Moulay, and L. Boumia The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory Journal of Physics D: Applied Physics 41 2008 225404
9. O. Civalek, and C. Demir Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory Applied Mathematical Modelling 35 2011 2053 2067
10. A.C. Eringen Nonlocal polar elastic continua International Journal of Engineering Science 10 1972 1 16
11. A.C. Eringen On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves Journal of Applied Physics 54 1983 4703 4710 (Pubitemid 14450262)
12. A.C. Eringen, and D.G.B. Edelen On nonlocal elasticity International Journal of Engineering Science 10 1972 233 248
13. A.R. Hadjesfandiari, and G.F. Dargush Couple stress theory for solids International Journal of Solids and Structures 48 2011 2496 2510
14. S. Iijima Helical microtubules of graphitic carbon Nature 354 1991 56 58 (Pubitemid 21896780)
15. M. Janghorban, and A. Zare Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method Physica E 43 2011 1602 1604
16. D. Kumar, C. Heinrich, and A.M. Waas Buckling analysis of carbon nanotubes modeled using nonlocal continuum theories Journal of Applied Physics 103 2008 073521
17. H.M. Ma, X.L. Gao, and J.N. Reddy A microstructure-dependent Timoshenko beam model based on a modified couple stress theory Journal of Mechanics Physics and Solids 56 2008 3379 3391
18. T. Murmu, and S.C. Pradhan Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM Physica E 41 2009 1232 1239
19. T. Murmu, and S.C. Pradhan Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory Computational Materials Science 46 2009 854 859
20. W.D. Nix, and H. Gao Indentation size effects in crystalline materials: A law for strain gradient plasticity Journal of the Mechanics and Physics of Solids 46 1998 411 425 (Pubitemid 128394207)
21. J.N. Reddy Energy Principles and Variational Methods in Applied Mechanics 2002 John Wiley & Sons Inc
22. J.N. Reddy Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates International Journal of Engineering Science 48 2010 1507 1518
23. J.N. Reddy Microstructure-dependent couple stress theories of functionally graded beams Journal of the Mechanics and Physics of Solids 59 2011 2382 2399
24. J.N. Reddy Nonlocal theories for buckling bending and vibration of beams International Journal of Engineering Science 45 2007 288 307 (Pubitemid 47094801)
25. J.N. Reddy, and S.D. Pang Nonlocal continuum theories of beams for the analysis of carbon nanotubes Journal of Applied Physics 103 2008 023511
26. C.M.C. Roque, A.J.M. Ferreira, and J.N. Reddy Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method International Journal of Engineering Science 49 2011 976 984
27. S. Sahmani, and R. Ansari Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions Journal of Mechanics, Science and Technology 25 2011 2365 2375
28. V. Senthilkumar Buckling analysis of a single-walled Carbon nanotube with nonlocal continuum elasticity by using differential transform method Advanced in Science Letters 3 2010 337 340
29. V. Senthilkumar, S.C. Pradhan, and G. Prathap Buckling analysis of Carbon nanotube based on nonlocal Timoshenko beam theory using differential transform method Advanced in Science Letters 3 2010 415 421
30. Q. Wang Wave propagation in carbon nanotubes via nonlocal continuum mechanics Journal of Applied Physics 98 2005 124301
31. C.M. Wang, S. Kitipornchai, C.W. Lim, and M. Eisenberger Beam bending solutions based on nonlocal Timoshenko beam theory Journal of Engineering Mechanics 134 2008 475 481 (Pubitemid 351699502)
32. Q. Wang, and K.M. Liew Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures Physics Letters A 363 2007 236 242
33. Q. Wang, and V.K. Varadan Vibration of carbon nanotubes studied using nonlocal continuum mechanics Smart Materials and Structures 15 2006 659 666
34. Q. Wang, V.K. Varadan, and S.T. Quek Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models Physics Letters A 357 2006 130 135 (Pubitemid 44037244)
35. Q. Wang, and C.M. Wang The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes Nanotechnology 18 2007 075702
36. C.M. Wang, Y.Y. Zhang, and X.Q. He Vibration of nonlocal Timoshenko beams Nanatechnology 18 2007 105401
37. C.M. Wang, Y.Y. Zhang, S.S. Ramesh, and S. Kitipornchai Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory Journal of Physics D: Applications and Physics 39 2006 3904 3909 (Pubitemid 44261950)
38. Y.Q. Zhang, G.R. Liu, and X.Y. Xie Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity Physics Reviews B 71 2005 195404
39. Y.Y. Zhang, C.M. Wang, W.H. Duan, Y. Xiang, and Z. Zong Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes Nanotechnology 20 2009 395707