Bending and Free Vibration Analysis of Nonlocal Functionally Graded Nanocomposite Timoshenko Beam Model Rreinforced by SWBNNT Based on Modified Coupled Stress Theory

Document Type : Research Paper


Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, I. R. Iran.



In this article, the bending and free vibration analysis of functionally graded (FG) nanocomposites Timoshenko beam model reinforced by single-walled boron nitride nanotube (SWBNNT) using micro-mechanical approach embedded in an elastic medium is studied. The modified coupled stress (MCST) and nonlocal elasticity theories are developed to take into account the size-dependent effect. The mechanical properties of FG boron nitride nanotube-reinforced composites are assumed to be graded in the thickness direction and estimated through the micro-mechanical approach. The governing equations of motion are obtained using Hamilton’s principle based on Timoshenko beam theory. The Navier's type solution is implemented to solve the equations that satisfy the simply supported boundary conditions. Furthermore, the influences of the slenderness ratio, length of nanocomposite beam, material length scale parameter, nonlocal parameter, power law index, axial wave number, and Winkler and Pasternak coefficients on the natural frequency of nanocomposite beam are investigated. Also, the effect of material length scale parameter on the dimensionless deflection of FG nanocomposite beam is studied.


[1] W. Chen, C. Weiwei, K.Y. Sze, Compos. Struct. 94 (2012) 2599-2609.
[2] A.A. Mosallaie Barzoki, A. Ghorbanpour Arani, A. Kolahchi, M.R.  Mozdianfard, Appl. Math. Model. 36 (2012) 2989-2995.
[3] R. Ansari, R. Gholami, S. Sahmani, Compos. Struct. 94 (2011) 221-228.
[4] M. Simsek, T. Kocatürk, S. D. Akbas, Compos. Struct. 95 (2013) 740-747.
[5] M. Shariyat, Compos. Struct. 88 (2009) 240–252.
[6] L.L. Ke, J. Yang, S. Kitipornchai, Compos. Struct. 92 (2010) 676–683.
[7] H.J. Xiang,J. Yang, Compos. Part B.: Eng. 39 (2008) 292–303.
[8] M. Simsek, Int. J. Eng. Sci. 48 (2010) 1721–1732.
[9] A.H. Rahmati, M. Mohammadimehr, Phys. B.: Condens. Matter.440 (2014) 88-98.
[10] M.A. Eltaher, S.A. Emam, F.F. Mahmoud, Compos. Struct.96 (2013) 82-88.
[11] A. Ghorbanpour Arani, M. Hashemian, A. Loghman, M. Mohammadimehr, J. Appl. Mech. Tech. Phys.52 (2011) 815-824.
[12] B.Akgöz, Ö. Civalek, Compos. Struct. 98 (2013) 314-322.
[13] M.H. Yas, M. Heshmati, Appl. Math. Model.36 (2012) 1371–1394.
[14] Z. Khoddami, A. Ghorbanpour Arani, R. Kolahchi, S. Amir, M.R. Bagheri, Compos. Part B.: Eng. 45 (2013) 423-432.
[15] F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Int. J. Solid. Struct. 39 (2002) 27312743.
[16] R. Ansari, R. Gholami, S. Sahmani, Compos. Struct. 94 (2011) 221-228.
[17] H.M. Ma, X.L. Gao, J.N. Reddy, J. Mech. Phys. Solids 56 (2008) 3379-3391.
[18] L.L. Ke, Y.S. Wang, Compos. Struct. 93 (2011) 342-350.