Boundary characteristic orthogonal polynomials are used as shape functions in the Rayleigh-Ritz method to investigate vibration and buckling of nanobeams embedded in an elastic medium. The present formulation is based on the nonlocal Euler-Bernoulli beam theory. The eigen value equation is developed for the buckling and vibration analyses. The orthogonal property of these polynomials makes the computation easier with less computational effort. It is observed that the frequency and critical buckling load parameters are dependent on the temperature, elastic medium, small scale coefficient, and length-to-diameter ratio. These observations are useful in the mechanical design of devices that use carbon nanotubes.
Corresponding Authors:
S Chakraverty
E-mail: snechak@gmail.com
Cite this article:
S Chakraverty, Laxmi Behera Vibration and buckling analyses of nanobeams embedded in an elastic medium 2015 Chin. Phys. B 24 097305
[1] Tan Y and Wang Y G 2013 Chin. Phys. Lett.30 117901 [2] Tan Y and Wang Y G 2013 Chin. Phys. Lett.30 047901 [3] Tan Y and Wang Y G 2013 Chin. Phys. Lett.30 017902 [4] Tan Y and Wang Y G 2013 Chin. Phys. Lett.30 017901 [5] Wang W H, Wang W Z and Xu H X 2011 Chin. Phys. Lett.28 078103 [6] Jia W L, Zhao L, Hou L, Ji W L, Shi W and Qu G H 2014 Acta Phys. Sin.63 077201 (in Chinese) [7] Wang Y L, Su K H, Yan H X and Wang X 2014 Acta Phys. Sin.63 046101 (in Chinese) [8] Lei D, Menggen Q Q G, Zhang H L and Zhi Y B 2013 Acta Phys. Sin.62 248502 (in Chinese) [9] Li M Y, Yu M, Su Q, Liu X Q, Xie E Q and Zhang X Q 2012 Acta Phys. Sin. 61 236101 (in Chinese) [10] Wang Y L, Su K H, Wang X and Liu Y 2011 Acta Phys. Sin.60 098111 (in Chinese) [11] Shao Z F, Yang Y Q, Liu S T and Wang Q 2014 Chin. Phys. B23 096105 [12] Shao Z F, Yang Y Q, Liu S T and Wang Q 2014 Chin. Phys. B23 096102 [13] He C X, Jian Y, Qi X Y and Xue J K 2014 Chin. Phys. B23 025202 [14] Han Z D, Li X Y, Yang Z, Liu R P, Liu S D and Zhang Y 2012 Chin. Phys. B21 118102 [15] Ren Y, Ma W J, Zeng Q S, Li J Z, Dong H B and Zhou We Y 2012 Chin. Phys. B21 098103 [16] Iijima S 1991 Nature354 56 [17] Ruud J A, Jervis T R and Spaepan F 1994 J. Appl. Phys.75 4969 [18] Eringen A C 1972 International Journal of Engineering Science10 1 [19] Peddieson J, Buchanan G R and McNitt R P 2003 International Journal of Engineering Science41 305 [20] Xu M 2006 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science462 2977 [21] Wang C M, Zhang Y Y and He X Q 2007 Nanotechnology18 105401 [22] Wang C, Zhang Y, Ramesh S S and Kitipornchai S 2006 J. Phys. D: Appl. Phys.39 3904 [23] Reddy J 2007 International Journal of Engineering Science45 288 [24] Aydogdu M 2009 Physica E41 1651 [25] Ghannadpour S, Mohammadi B and Fazilati J 2013 Composite Structures96 584 [26] Ansari R, Sahmani S and Rouhi H 2011 a Phys. Lett. A375 1255 [27] Maachou M, Zidour M, Baghdadi H, Ziane N and Tounsi A 2011 Solid State Commun.151 1467 [28] Zidour M, Benrahou K H, Semmah A, Naceri M, Belhadj H A, Bakhti K and Tounsi A 2012 Computational Materials Science51 252 [29] Benzair A, Tounsi A, Besseghier A, Heireche H, Moulay N and Boumia L 2008 J. Phys. D: Appl. Phys.41 225404 [30] Wang L, Ni Q, Li M and Qian Q 2008 Physica E40 3179 [31] Zhang Y, Liu X and Liu G 2007 Nanotechnology18 445701 [32] Murmu T and Pradhan S 2009 Computational Materials Science46 854 [33] Murmu T and Pradhan S 2009 Physica E41 1232 [34] Narendar S and Gopalakrishnan S 2011 Physica E43 1185 [35] Ansari R, Gholami R and Darabi M 2011 Journal of Thermal Stresses34 1271 [36] Murmu T and Pradhan S 2010 Computational Materials Science47 721 [37] Tounsi A, Semmah A and Bousahla A A 2013 Journal of Nanomechanics and Micromechanics3 37 [38] Bhat R 1991 Journal of Sound and Vibration149 170 [39] Singh B and Chakraverty S 1992 Journal of Sound and Vibration152 149 [40] Singh B and Chakraverty S 1994 Communications in Numerical Methods in Engineering10 1027 [41] Singh B and Chakraverty S 1994 Journal of Sound and Vibration173 157 [42] Singh B and Chakraverty S 1994 c Journal of Sound and Vibration173 289 [43] Behera L and Chakraverty S 2014 Meccanica49 51 [44] Amirian B, Hosseini-Ara R and Moosavi H 2012 Archives of Mechanics64 581 [45] Li M and Zheng H 2013 Research Journal of Applied Sciences Engineering and Technology5 2729
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