Journal of Computational Applied Mechanics

Application of Halpin-Tsai Method in Modelling and Size-dependent Vibration Analysis of CNTs/fiber/polymer Composite Microplates.

Document Type : Research Paper

Authors

Faculty of Mechanical Engineering, University of Kashan, Kashan , Islamic Republic of Iran

Abstract

In the present study, modelling and vibration analysis of Carbon nanotubes/ fiber/ polymer composite microplates are investigated. The governing equations of the Carbon nanotubes/ fiber/ polymer composite microplates are derived based on first order shear deformation plate theory, rather than other plate theories, due to accuracy and simplicity of polynomial functions. The modified couple stress theory is employed because of its capability to interpret the size effect. Halpin-Tsai model is utilized to evaluate the material properties of two-phase composite consisted of uniformly distributed and randomly oriented Carbon nanotubes through the epoxy resin matrix. Afterwards, the structural properties of carbon nanotubes reinforced polymer matrix, which is assumed as a new matrix, and then, reinforced with E-Glass fiber, they are calculated by fiber micromechanics approach. Employing Hamilton’s principle, the equations of motion are obtained and solved by Hybrid analytical numerical method. The influences of various parameters such as the weight percentage of single-walled carbon nanotube, aspect ratio, and size effect on the vibration characteristics of microplate are discussed in details. Results indicate that the stability of Carbon nanotubes/fiber/polymer composite microplates can be improved by adding appropriate values of Carbon nanotubes. In addition, increase in the frequencies is more pronounced in the case of microplates reinforced with SWCNT compared with MWCNT. These findings can be used in design and manufacturing of marine vessels and aircrafts.

Keywords

Main Subjects

[1]     Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson J.W. (1994). Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia, 42(2): 475–487.
[2]     Stolken, J.S. and Evans, A.G. (1998). A microbend test method for measuring the plasticity length scale, Acta Materialia, 46(14): 5109–5115.
[3]     Chong, A.C.M., Yang, F., Lam, D.C.C. and Tong, P. (2001). Torsion and bending of micron-scaled structures, Journal of Materials Research, 16(4): 1052–1058.
[4]     Koiter, W.T. (1964). Couple stresses in the theory of elasticity, I and II, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series, B 67: 17–44.
[5]     Eringen, A.C. (1972)., Nonlocal polar elastic continua, International Journal of Engineering Science 10(1): 1–16.
[6]     Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003). Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51(8): 1477–1508.
[7]     Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002). Couple stress based strain gradient theory for elasticity,  International Journal of Solids and Structures, 39(10): 2731–2743.
[8]     Tsiatas G.C. (2009). A new Kirchhoff plate model based on a modified couple stress theory, International Journal of Solids and Structures, 46(13): 2757–2764.
[9]     Yin, L., Qian, Q., Wang, L. and Xia, W. (2010). Vibration analysis of microscale plates based on modified couple stress theory, Acta Mechanica Solid a Sinica, 23(5): 386–393.
[10]  Jomehzadeh, E., Noori, H.R. and Saidi, A.R. (2011). The size-dependent vibration analysis of micro plates based on a modified couple stress theory, Physica E: Low-dimensional Systems and Nanostructures, 43(4), 877–883.
[11]  Asghari, M. (2012). Geometrically nonlinear micro-plate formulation based on the modified couple stress theory, International Journal of Engineering Science, 51: 292–309.
[12]  Sahmani, S. and Ansari, R. (2013). On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory, Composite Structures, 95: 430–442.
[13]  Mohammadimehr, M., Mohandes, M. and Moradi, M. (2014). Size dependent effect on the buckling and vibration analysis of double bonded nanocomposite piezoelectric plate rein- forced by BNNT based on modified couple stress theory, Journal of Vibration and Control, doi: 10.1177/1077546314544513.
[14]  Kim, M., Park, Y.B., Okoli, O.I. and Zhang, C. (2009). Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites, Composites Science and Technology, 69(3-4): 335-342.
[15]  Bhardwaj, G., Upadhyay, A.K., Pandey, R. and Shukla, K.K. (2013). Non-linear flexural and dynamic response of CNT reinforced laminated composite plates, Composites Part B: Engineering, 45(1): 89-100.
[16]  Reddy, J.N. (2004). Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, FL, Second Edition.
[17]  GhorbanpourArani, A. and Haghparast, E. (2015). Size-dependent vibration of axially moving viscoelastic microplates based on sinusoidal shear deformation theory, International Journal of Applied Mechanics.
[18]  Ghorbanpour Arani, A., Khoddami Maraghi, Z. and Khani Arani, H. (2015). Orthotropic patterns of Pasternak foundation in smart vibration analysis of magnetostrictive nanoplate, Journal of Mechanical Engineering Science, doi: 10.1177/0954406215579929.
[19]  Rafiee, M., He, X.Q., Mareishi, S. and Liew, K.M. (2014). Modeling and stress analysis of smart CNTs/fiber/polymer multiscale composite plates, International Journal of Applied Mechanics, 6(3): 1450025-1450048.
[20]  M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco pasternak foundation, Journal of Solid Mechanics, Vol. 6, pp. 98-121, 2014.
[21] Ke, LL., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012). Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory, Journal of Sound and Vibration, 331: 94–106
Journal of Computational Applied Mechanics
Volume 47, Issue 1
June 2016
Pages 45-52
  • Receive Date: 26 January 2016
  • Revise Date: 24 February 2016
  • Accept Date: 04 April 2016