In this study, the free vibration behavior of composite panels with double curvature consisting of three phases of polymer, glass fibers and carbon nanotubes has been investigated. To accurately model the effect of shear deformation in thick layers, the higher-order shear deformation theory of Reddy (HSDT) was used. The governing equations were derived using the Hamilton principle and then solved using the Navier analytical method suitable for simply supported edges. Based on the classification of the mid-surface curvature, four types of panels including cylindrical, spherical, saddle and flat plate were investigated. Next, by extracting the stiffness matrix and effective mass relations, the problem was formulated as an eigenvalue problem and the natural frequencies were calculated. The obtained results show that the presence of carbon nanotubes increases the stiffness and consequently the natural frequencies. Also, comparison between different panels shows that spherical panels have the highest natural frequencies due to the presence of curvature in two directions, followed by cylindrical, saddle and flat panels, respectively. Comparison of the results with previous researches also shows good agreement, which confirms the validity of the presented analytical model.
Zhang et al. (Wed,) studied this question.