Vibration analysis of CNT reinforced functionally graded composite plates in a thermal environment based on Reddy’s higher-order shear deformation theory

Abstract This paper presents the free vibration behavior of carbon nanotube (CNT) reinforced functionally graded composite plates in a thermal environment based on Reddy’s higher-order shear deformation theory (HSDT). The element-free kp-Ritz method is used in this study. Four different types of CNT distributions are considered. The literature reveals that there is a research gap in investigating the mechanical behaviors of CNT reinforced functionally graded composite plates using Reddy’s HSDT in association with any of the mesh-free methods. To the authors’ knowledge, this paper is the first to use this approach to investigate the vibration behavior of CNT reinforced functionally graded composite plates in a thermal environment. The rule of mixture is used to estimate the resulting effective material properties. To verify the reliability of the present model, the obtained numerical results based on a conversion study have been compared with those found in the literature with evident agreement. Moreover, parametric studies have been conducted on the effects of CNT distribution, boundary conditions, plate aspect ratio, plate thickness-to-width ratio and CNT volume fraction on the non-dimensional natural frequencies. Furthermore, the effects of plate aspect ratio and plate thickness-to-width ratio on the sequence of the first six mode shapes have been investigated.