A New Quadrilateral Finite Element Formulation for the Free Vibration Analysis of CNT-Reinforced Plates with Cutouts

A new quadrilateral finite element IQ4 is developed for the free vibration of carbon nanotube-reinforced composite (CNTRC) perforated plates with a central cutout. By enriching the membrane part and incorporating a projected shear technique, the IQ4 element is proposed to address the known limitations of the standard Q4 element, such as shear locking and limited consistency in the coupling of membrane-bending components. The proposed element is formulated within the FSDT-based framework and assessed through benchmark tests to verify its convergence and accuracy. The governing equations are obtained via the weak form of Hamilton’s principle. Particular attention is given to the influence of carbon nanotube volume fraction, distribution patterns, and boundary conditions on the fundamental frequency response of CNTRC plates with cutouts. In addition, a parametric study is conducted to assess the influence of cutout geometric configuration, shape, and size ratios on the vibrational response of the CNTRC plate. The numerical results demonstrate that the formulated IQ4 element provides stable and accurate estimations of natural frequencies, even in the presence of a cutout and the coupled effects of the non-uniform distribution of reinforcement through the plate thickness. The developed formulation is expected to contribute to the structural design and optimization of advanced lightweight systems, particularly in aerospace and mechanical engineering applications.