Free vibration analysis of cracked composite plates reinforced with CNTs using extended finite element method (XFEM)

Abstract

In this article, the free vibration behavior of cracked nanocomposite plates was investigated using the extended finite element method (XFEM), with a focus on examining the impact of different distribution patterns (UD, FG-X, FG-A, and FG-O) in the functionally graded (FG) carbon nanotube composite (FG-CNTRC) plate. The FG material properties are assumed to vary through the thickness direction according to different distributions. The governing equations are based on the first-order shear deformation plate theory (FSDT), and the nanocomposite plates are composed of a polymer matrix and the FG-CNTRC. The novelty of this article lies in studying the free vibration behavior of the CNTRC plate, considering all distribution patterns, using XFEM. The effective elastic modulus is computed using the modified Halpin Tsai model, while mass density and Poisson’s ratio are determined by employing the rule of mixture. A parametric study is conducted to investigate the effect of the crack length, crack position, width/thickness ratios, volume fraction, and power law index (Pin) of nanofillers on the natural frequencies of the CNTRC plate, offering valuable insights for different distribution patterns under various boundary conditions. The results demonstrate that the XFEM's accuracy and efficiency as a tool for the free vibration analysis of cracked nanocomposite plates.