The free vibration analysis of laminated nanocomposite plates and shells using first-order shear deformation theory and the Generalized Differential Quadrature (GDQ) method is presented. Each layer of the laminate is modelled as a three-phase composite. An example of such composite material is given by a polymeric matrix reinforced with Carbon Nanotubes (CNTs). CNTs enhance the mechanical properties of the polymer matrix and the nanocomposite is treated as an isotropic material; a micromechanics model is used to compute the engineering constants of the isotropic hybrid material. This approach based on the Eshelby-Mori-Tanaka scheme takes into account the agglomeration of the nanoparticles in the matrix. The second step consists in combining this enriched matrix with unidirectional and oriented reinforcing fibers to obtain a fibrous composite with improved mechanical features. The overall mechanical properties of each orthotropic ply are evaluated through different micromechanics approaches. Each technique is illustrated in details and the transversely isotropic properties of the three-phase layers are completely defined. The effects of both CNTs agglomeration and the mass fraction of these particles are investigated comparing with the results obtained by various homogenization techniques.
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