Free vibration analysis of multi-scale hybrid nanocomposite plates with agglomerated nanoparticles

The present article is proposed to capture the influences of carbon nanotubes' agglomeration on the natural frequency behaviors of multi-scale hybrid nanocomposite plates for the first time. The constituent material, which is a hybrid nanocomposite, is consisted of both macro- and nano-scale reinforcing fibers dispersed in a polymer matrix. The equivalent material properties are seemed to be calculated coupling the Eshelby-Mori-Tanaka model with the rule of the mixture to consider the effects of carbon nanotubes inside the probably generated clusters while finding the mechanical properties of such novel hybrid nanocomposites. Furthermore, an energy-based approach is implemented to obtain the governing equations of the problem utilizing a refined higher-order plate theorem. Next, the derived equations will be solved in the framework of Galerkin's well-known analytical method to reach the fundamental frequency. It is worth mentioning that the influence of various boundary conditions is included. Once the validity of the presented results is proven, a set of numerical examples are presented to explain how each variant can affect the plate's natural frequency. Communicated by Wei-Chau Xie.