On the dynamic behavior of plates made of porous advanced materials reinforced with carbon nanotubes using a p-version of finite element method

A p-version finite element method (p-FEM) based on First-Order Shear Deformation Theory (FSDT) is utilized to investigate the dynamic behavior of functionally graded porous sandwich plates reinforced with carbon nanotubes (FG-CNTR). The plate comprises three layers, with the core layer as FG-CNTR, accounting for several types (Uniform, FG-X, and FG-O distributions). Both the bottom and top surfaces consist of a porous, functionally graded material (FGM) employing five different porosity models (Perfect, Imperfect I, …, V). The obtained numerical results have converged and are compared with published data to demonstrate the validity and accuracy of the present formulation. For the response under dynamic conditions, the solution obtained from the p-version of FEM using the mode superposition method is compared with a novel developed analytical solution used Classical Plate Theory (CPT). The effects of various parameters, including the carbon nanotube distribution pattern, porosity model, CNT volume fraction, geometric characteristics, mechanical load, volume fraction exponent, damping coefficient, and boundary conditions, are illustrated and analyzed in depth. These findings provide important guidance for the efficient design and optimization of FGM structures in various engineering applications.