Free vibration analysis of FG porous, multilayer thick plates reinforced with carbon nanotubes using element free Galerkin method in the framework of Carrera unified formulation

The present study conducts a free vibration analysis of functionally graded (FG) multilayer thick porous plates reinforced with carbon nanotubes within the framework of the Carrera Unified Formulation (CUF). The material properties, including CNT weight fraction and porosity, exhibit a layer-wise gradual variation through the thickness of the plate. The Element-Free Galerkin (EFG) method is employed to obtain the natural frequencies of FG CNT/polymer-reinforced porous multilayer thick plates. A modified Halpin-Tsai micromechanical model and the rule of mixtures are used to predict the effective properties of porous materials reinforced with CNTs. The obtained results are compared with other higher deformation theories, and they demonstrate the accuracy and efficiency of the proposed EFG-CUF method. Finally, a parametric study is conducted to show the effect of key parameters, including CNT weight fraction, porosity, number of layers, layer arrangement, thickness-to width, and width-to-length ratios on the natural frequencies of the plate.