Higher-Order Theories for the Free Vibration Analysis of Doubly Curved Shells Made of Nanostructured Materials

Recent advances in various engineering fields require the study of materials at the nanoscale and mesoscale levels. Functionally graded carbon nanotubes (FG-CNTs) are nonhomogeneous materials characterized by a nanostructure consisting of one or more layers of carbon atoms. This study presents an efficient numerical solution, based on continuum mechanics, for investigating the dynamic behavior of FG-CNTs nanocomposite shells. The formulation is based on higher-order theories and adopts the equivalent single layer (ESL) approach to express the displacement field variable. The generalized differential quadrature (GDQ) method is used for the numerical implementation of the fundamental equations of the problem. The proposed model predicts accurately the influence of the CNT molecular configuration on the dynamic response of doubly curved structures taking into account the chiral indexes, the bond molecular forces, and the presence of curvatures. Furthermore, an effective homogenization technique is presented to evaluate the mechanical properties of hybrid polymeric matrices of a composite layer containing FG-CNTs. This approach also accounts for the agglomeration effects within the nanocomposite. Extensive numerical examples are provided to compare the mode frequencies and mode shapes of structures with different materials and curvatures with respect to refined three-dimensional finite element-based solutions. The results show a very good agreement between different approaches, such that the present formulation can be considered as a valid alternative to more commonly used numerical methods, providing very accurate results with significantly reduced computational effort.