Vibration of laminated functionally graded nanocomposite structures considering the transverse shear stresses and rotary inertia

The aim of this study is to determine the fundamental frequencies of laminated double-curved nanocomposite structures considering transverse shear stresses (TSSs) and rotary inertia (RI). The basic equations of laminated double-curved structures composed of CNT patterned layers based on the Donnell type shell theory are derived within TSSs and considering RI. By applying the Galerkin technique, the fundamental equations are transformed into frequency-dependent sixth-order algebraic equations, and this equation is solved numerically to find the fundamental frequency for laminated double curved structures consisting of CNT patterned layers considering TSSs and RI. In addition, when the rotary inertia is neglected, analytical expressions for frequencies are obtained in the framework of shear deformation theory (ST) and classical theory (CT). Finally, the influences of the volume fraction, CNT patterns, array of nanocomposite layers, TSSs and RI on the fundamental frequency are examined.