Free vibration analysis of functionally graded composite plates reinforced with linearly and nonlinearly distributed carbon nanotubes in hygrothermal environments

This article presents a novel investigation of the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under hygrothermal environments. It explores both uniform and non-uniform (functionally graded) distributions of CNTs across the plate thickness for the first time. The effective material properties of the CNTRC, considering temperature and moisture dependence, are determined using the extended rule of mixture. First-order shear deformation theory (FSDT) is employed to derive the governing equations incorporating hygro-elastic and thermo-elastic relations. These equations are solved using the finite element method. A validation study verifies the accuracy of the employed approaches. Subsequently, a comprehensive parametric study investigates the influence of plate geometry (length-to-width and width-to-thickness ratios), CNTs volume fraction, boundary conditions, linear and non-linear CNTs distributions, and hygrothermal environments on the free vibration behavior of polymeric nanocomposite plates reinforced with CNTs fillers is conducted. The results reveal that the increase in temperature and moisture leads to a decrease in the effective stiffness of the FG-CNTRC plates.