Dynamic Buckling of Embedded Laminated Nanocomposite Plates Based on Sinusoidal Shear Deformation Theory

Document Type : Research Paper


1 Faculty of Engineering, Ayatollah Boroujerdi University, Boroujerd, Iran

2 Department of mechanical engineering, Imam hossein University, Tehran, Iran


In this study, the dynamic buckling of the embedded laminated nanocomposite plates is investigated. The plates are reinforced with the single-walled carbon nanotubes (SWCNTs), and the Mori-Tanaka model is applied to obtain the equivalent material properties of them. Based on the sinusoidal shear deformation theory (SSDT), the motion equations are derived using the energy method and Hamilton's principle. The Navier’s method is used in conjunction with the Bolotin's method for obtaining the dynamic instability region (DIR) of the structure. The effects of different parameters such as the volume percentage of SWCNTs, the number and orientation angle of the layers, the elastic medium, and the geometrical parameters of the plates are shown on DIR of the structure. Results indicate that by increasing the volume percentage of SWCNTs the resonance frequency increases, and DIR shifts to right. Moreover, it is found that the present results are in good agreement with the previous researches.


[1] Matsunag, H., “Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory”, Composite Structures, Vol. 48, pp. 231-244, 2000.
[2] Kim, T.W. and Kim, J.H., “Nonlinear vibration of viscoelastic laminated composite plates”, International Journal of Solids and Structures, Vol. 39, pp. 2857–2870, 2002.
[3] Malekzadeh, P., Fiouz, A.R. and Razi, H., “Three-dimensional dynamic analysis of laminated composite plates sujected to moving load”, Composite Structures, Vol. 90, pp. 105–114, 2009.
[4] Dinis, L.M.J.S., Natal Jorge, R.M. and Belinha, J., “Static and dynamic analysis of laminated plates based on an unconstrained third order theory and using a radial point interpolator meshless method”, Computers and Structures, Vol. 89, pp. 1771–1784, 2011.
[5] Honda, Sh., Kumagai, T., Tomihashi, K. and Narita, Y., “Frequency maximization of laminated sandwich plates under general boundary conditions using layerwise optimization method with refined zigzag theory”, Journal of Sound and Vibration, Vol. 332, pp. 6451–6462, 2013.
[6] Sahoo, R. and Singh, B.N., “A new shear deformation theory for the static analysis of laminated composite and sandwich plates”, International Journal of Mechanical Sciences, Vol. 75, pp. 324–336, 2013.
[7] Heydari, M.M., Kolahchi, R., Heydari, M. and Abbasi, A., “Exact solution for transverse bending analysis of embedded laminated Mindlin plate”, Structural Engineering and Mechanics, Vol. 49(5), pp. 661–672, 2014.
[8] Saidi, H., Tounsi, A. and Bousahla, A.A., “A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations”, Geomechanics and Engineering, Vol. 11, pp. 289-307, 2016. 
[9] Awrejcewicz, J., Kurpa, L. and Mazur, O., “Dynamical instability of laminated plates with external cutout”, International Journal of Non-Linear Mechanics, Vol. 81, pp. 103–114, 2016.
[10] Liang, K., “Koiter–Newton analysis of thick and thin laminated composite plates using a robust shell element”, Composite Structures, Vol. 161, pp. 530-539, 2017.
[11] Thai, H.T. and Kim, S.E., “A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates”, Composite Structures, Vol. 99, pp. 172-178, 2013.
[12] Reddy, J.N., “A Simple Higher Order Theory for Laminated Composite Plates”, Journal of Applied Mechanics, Vol. 51, pp. 745–752, 1984.
[13] Shi, D.L.and Feng, X.Q., “The Effect of Nanotube Waviness and Agglomeration on the elastic Property of Carbon Nanotube-Reinforced Composties”, Journal of Engineering Materials and Technology, Vol. 126, pp. 250-270, 2004.
[14] Kolahchi, R., Safari, M. and Esmailpour, M., “Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium”, Composite Structures, Vol. 150, pp. 255-265, 2016.
[15] Akhavan, H., Hosseini Hashemi, Sh., Rokni Damavandi Taher, H., Alibeigloo, A. and Vahabi,  Sh., “Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis”, Computational Material and Science, Vol. 44, pp. 968–978, 2009.
[16] Phung-Van, P., De Lorenzis, L., Thai, Ch.H., Abdel-Wahab, M. and Nguyen-Xuan, H., “Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements”, Computational Material and Science, Vol. 96, pp. 495–505, 2015.
[17] Putcha, N.S. and Reddy, J.N., “Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory”, Journal of Sound and Vibration, Vol. 104, pp. 285–300, 1986.