A nonlocal curved beam model based on a modified couple stress theory

International Journal of Structural Stability and Dynamics

Volumn 11, Issue 3, 2011, Pages 495-512

  Liu, Y P ^a   Reddy, J N ^b  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b Texas AandM University   (United States)

Author keywords

classical curved beam theory; couple stress theory; free vibration; Hamilton's principle; natural frequency; simply supported beam; size effect; Timoshenko curved beam

Indexed keywords

COUPLE STRESS THEORY; CURVED BEAM THEORY; CURVED BEAMS; FREE VIBRATION; HAMILTON'S PRINCIPLE; SIMPLY SUPPORTED BEAMS; SIZE EFFECT;

NATURAL FREQUENCIES; POISSON RATIO; ROTATION; SIZE DETERMINATION;

CURVED BEAMS AND GIRDERS;

EID: 79956208718     PISSN: 02194554     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219455411004233     Document Type: Article

References (32)

1. X. Li, B. Bhushan, K. Takashima, C.-W. Baek and Y.-K. Kim, Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques, Ultramicroscopy 97 (2003) 481-494. (Pubitemid 36683321)
2. J. Pei, F. Tian and T. Thundat, Glucose biosensor based on the microcantilever, Analytical Chemistry 76 (2004) 292-297. (Pubitemid 38090764)
3. D. C. C. Lam, F. Yang, A. C. M. Chong, J. Wang and P. Tong, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51 (2003) 1477-1508.
4. A. W. McFarland and J. S. Colton, Role of material microstructure in plate sti® ness with relevance to microcantilever sensors, Journal of Micromechanics Microengineering 15 (2005) 1060-1067. (Pubitemid 41237440)
5. 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 the Mechanics and Physics of Solids 56 (2008) 3379-3391.
6. A. Anthoine, E® ect of couple-stresses on the elastic bending of beams, International Journal of Solids and Structures 37 (2000) 1003-1018. (Pubitemid 30509380)
7. W. T. Koiter, Couple-stresses in the theory of elasticity: I and II, Proceedings of the Koninklijke Nederlands Akademie Van Wetenschappen B67 (1964) 17-44.
8. S. Papargyri-Beskou, K. G. Tsepoura, D. Polyzos and D. E. Beskos, Bending and stability analysis of gradient elastic beams, International Jouranl Solids and Structures 40 (2003) 385-400. (Pubitemid 36122318)
9. I. Vardoulakis and J. Sulem, Bifurcation Analysis in Geomechanics (Blackie/Chapman and Hall, London, 1995).
10. I. Vardoulakis and A. E. Giannakopoulos, An example of double forces taken from structural analysis, International Journal of Solids and Structures 43 (2006) 4047-4062. (Pubitemid 43815308)
11. A. E. Giannakopoulos and K. Stamoulis, Structural analysis of gradient elastic components, International Journal of Solids and Structures 44 (2007) 3440-3451. (Pubitemid 46400676)
12. J. Peddieson, G. R. Buchanan and R. P. McNitt, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science 41 (2003) 305-312.
13. C. M. Wang, Y. Y. Zhang, S. S. Ramesh and S. Kitipornchai, Buckling analysis of microand nano-rods/tubes based on nonlocal Timoshenko beam theory, Journal of Physics D Applied Physics 39 (2006) 3904-3909. (Pubitemid 44261950)
14. 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)
15. J. N. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 45 (2007) 288-307. (Pubitemid 47094801)
16. J. V. Araujo dos Santos and J. N. Reddy, Vibration of Timoshenko beams using nonclassical elasticity theories, Shock and Vibration, to appear.
17. J. F. C. Yang and R. S. Lakes, Experimental study of micropolar and couple stress elasticity in compact bone in bending, Journal of Biomechanics 15 (1982) 91-98. (Pubitemid 12188350)
18. R. Maranganti and P. Sharma, A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir) relevance for nanotechnologies, Journal of the Mechanics and Physics of Solids 55 (2007) 1823-1852. (Pubitemid 47021162)
19. S. K. Park and X.-L. Gao, Bernoulli-Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16 (2006) 2355-2359. (Pubitemid 44679456)
20. F. Yang, A. C. M. Chong, D. C. C. Lam and P. Tong, Couple-stress-based strain gradient theory for elasticity, International Journal of Solids and Structures 39 (2002) 2731-2743. (Pubitemid 34617098)
21. S. K. Park and X.-L. Gao, Variational formulation of a modified couple stress theory and its application to a simple shear problem, Zeitschrift f€ur Angewandte Mathematik Physik 59 (2008) 904-917.
22. R. D. Mindlin, In°uence of couple-stresses on stress concentrations, Experimental Mechanics 3 (1963) 1-7.
23. J. N. Reddy, Energy Principles and Variational Methods in Applied Mechanics (Second Edition) (Wiley, New York, 2002).
24. J. N. Reddy, Theory and Analysis of Elastic Plates and Shells (Second Edition) (Taylor & Francis, Philadelphia, 2007).
25. T. Kaneko, On Timoshenko's correction for shear in vibrating beams, Journal of Physics D Applied Physics 8 (1975) 1927-1936.
26. N. G. Stephen and M. Levinson, A second order beam theory, Journal of Sound and Vibration 67 (1979) 293-305.
27. J. J. Jensen, On the shear coefficient in Timoshenko's beam theory, Journal of Sound and Vibration 87 (1983) 621-635. (Pubitemid 13546152)
28. C. M. Wang, Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions, ASCE Journal of Engineering Mechanics 121 (1995) 763-765.
29. J. R. Hutchinson, Shear coe±cients for Timoshenko beam theory, ASME Journal of Applied Mechanics 68 (2001) 87-92. (Pubitemid 33716354)
30. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (Third Edition) (McGraw-Hill, New York, 1970).
31. J. N. Reddy, An Introduction to Continuum Mechanics (Cambridge University Press, New York, 2008).
32. C. E. Maneschy, Y. Miyano, M. Shimbo and T. C. Woo, Residual-stress analysis of an epoxy plate subjected to rapid cooling on both surfaces, Experimental Mechanics 26 (1986) 306-312. (Pubitemid 17512330)