Free Vibration Analysis of Variable Stiffness Composite Laminates with Flat and Folded Shapes

Document Type : Research Paper


Civil Engineering Department, Yasouj University


In this article, free vibration analysis of variable stiffness composite laminate (VSCL) plates with flat and folded shapes is studied. In order to consider the concept of variable stiffness, in each layer of these composite laminated plates, the curvilinear fibers are used instead of straight fibers. The analysis is based on a semi-analytical finite strip method which follows classical laminated plate theory (CLPT). Natural frequencies obtained through this analysis for the flat plates are in good agreement with the results obtained through other methods. Finally, the effect of the fiber orientation angle, the folding order, crank angles and boundary conditions on the Natural frequencies is demonstrated.


[1] Akhavan H., Ribeiro P., 2011, Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers, Composite Structures 93(11): 3040-3047.
[2] Gürdal Z., Tatting B.F., Wu C.K., 2008, Variable stiffness composite panels: effects of stiffness variation on the in- plane and buckling response, Composites: PartA 39: 911-922.
[3] Ribeiro P., Akhavan H., 2012, Non-linear vibrations of variable stiffness composite laminated plates, Composite Structures 94: 2424-2432.
[4] Akhavan H., Ribeiro P., Moura M.F.S.F., 2013, Large deflection and stresses in variable stiffness composite laminates with curvilinear fibres, International Journal of Mechanical Sciences 73: 14-26.
[5] Houmat A., 2013, Nonlinear free vibration of laminated composite rectangular plates with curvilinear fibers, Composite Structures 106: 211-224.
[6] Yazdani S., Ribeiro P., Rodrigues J.D., 2014, A p-version layerwise model for large deflection of composite plates with curvilinear fibers, Composite Structures 108: 181-190.
[7] Akbarzadeh A.H., Arian Nik M., Pasini D., 2014, The role of shear deformation in laminated plate with curvilinear fiber paths and embedded defects, Composite Structures 118: 217-227.
[8] Yazdani S., Ribeiro P., 2015, A layerwise p-version finite element formulation for free vibration analysis of thick composite laminates with curvilinear fibres, Composite Structures 120: 531-542.
[9] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, FL, Second Edition.
[10] Hatami S., Azhari M., Saadatpour M.M., 2007, Free vibration of moving laminated composite plates, Composite Structures 80: 609-620.
[11] Amoushahi H., Azhari M., 2013, Static analysis and buckling of viscoelastic plates by a fully discretized nonlinear finite strip method using bubble functions, Composite Structures 100: 205-217.
[12] Cheung Y.K., 1976, Finite Strip Method in Structural Analysis, Pergamon Press, Oxford, Second Edition.
[13] Whitney J.M., 1987, Structural Analysis of Laminated Anisotropic Plates, Technomic Publishing Company Inc, Pennsylvania.
[14] Chow S.T., Liew K.M., Lam K.Y., 1992, Transverse vibration of symmetrically laminated rectangular composite plates, Composite Structures 20(4): 213-226.
[15] Leissa A.W., Narita Y., 1989, Vibration studies for simply supported symmetrically laminated rectangular plates, Composite Structures 12(2): 113-132.
[16] Dai K.Y., Liu G.R., Lim K.M., Chen X.L., 2004, A mesh-free method for static and free vibration analysis of shear deformable laminated composite plates, Journal of Sound and Vibration 269: 633-652.
[17] Topal U., Uzman Ü., 2009, Frequency optimization of laminated folded composite plates, Materials and Design 30(3): 494-501.
[18] Peng L.X., Kitipornchai S., Liew K.M., 2007, Free vibration analysis of folded plate structures by the FSDT mesh-free method, Computational Mechanics 39(6): 799-814.
[19] Guha Niyogi A., Laha M.K., Sinha P.K., 1999, Finite element vibration analysis of laminated composite folded plate structures, Shock and Vibration 6(5-6): 273-283.
[20] Le-Anh L., Nguyen-Thoi T., Ho-Huu V., Dang-Trung H., Bui-Xuan T., 2015, Static and frequency optimization of folded laminated composite plates using an adjusted Differential Evolution algorithm and a smoothed triangular plate element, Composite Structures 127: 382-394.
[21] Lee S.Y., Wooh S.C., Yhim S.S., 2004, Dynamic behavior of folded composite plates analyzed by the third order plate theory, International Journal of Solids and Structures 41(7): 1879-1892.
[22] Haldar S., Sheikh A.H., 2005, Free vibration analysis of isotropic and composite folded plates using a shear flexible element, Finite Elements in Analysis and Design 42(3): 208-226.