Free vibration, bending and buckling of a FG-CNT reinforced composite beam

Abstract

Purpose The purpose of this paper is to perform a numerical analysis on the static and dynamic behaviors of beams made up of functionally graded carbon nanotube (FG-CNT) reinforced polymer and hybrid laminated composite containing the layers of carbon reinforced polymer with CNT. Conventional fibers have higher density as compared to carbon nanotubes (CNTs), thus insertion of FG-CNT reinforced polymer layer in fiber reinforced composite (FRC) structures makes them sustainable candidate for weight critical applications. Design/methodology/approach In this context, stress and strain formulations of a multi-layer composite system is determined with the help of Timoshenko hypothesis and then the principle of virtual work is employed to derive the governing equations of motion. Herein, extended rule of mixture and conventional micromechanics relations are used to evaluate the material properties of carbon nanotube reinforced composite (CNTRC) layer and FRC layer, respectively. A generalized eigenvalue problem is formulated using finite element approach and is solved for single layer FG-CNTRC beam and multi-layer laminated hybrid composite beam by a user-interactive MATLAB code. Findings First, the natural frequencies of FG-CNTRC beam are computed and compared with previously available results as well as with Ritz approximation outcomes. Further, free vibration, bending, and buckling analysis is carried out for FG-CNTRC beam to interpret the effect of different CNT volume fraction, number of walls in nanotube, distribution profiles, boundary conditions, and beam-slenderness ratios. Originality/value A free vibration analysis of hybrid laminated composite beam with two different layer stacking sequence is performed to present the advantages of hybrid laminated beam over the conventional FRC beam.

Bending and vibration study of carbon nanotubes reinforced functionally graded smart composite beams

“…The governing equations for an element are developed taking Hamilton's Principle [3] and global equations of equilibrium are expressed as…”

“…Material properties of FGCNT reinforced beam are given in table 1. Polymethyl methacrylate is considered as matrix material and CNT is the reinforced material [3]. The values of CNT efficiency factors used in this research are as explained in table 2.…”

“…Liew et al [2] presented an overview of the properties and modelling of FG nanotube reinforced beams and other structures. Puneet et al [3] worked on free vibration study of FGCNTRC beam and concluded that increasing number of walls as in multiwall carbon nanotubes decrease the natural frequency. Zhu et al [4] examined the bending as well as free vibration behaviour of FGCNTRC plates.…”

The recent progress of functionally graded CNT reinforced composites and structures

“…Kumar and Srinivas [128] performed the bending analysis of FG-CNTRC beams using FEM. The CNT volume fraction, distribution configuration, and the slenderness ratio were found to have significant effects on the deflection.…”

Progressive deterioration of reinforced concrete structures: effect on dynamic properties of flexural members

“…The creation of a progressive damage scenario depends on the specific type of structure or a specific type of problem to be addressed. Damages due to shear loading, flexural loading and fatigue-type loading have been studied by many researchers (Prado et al ., 2016; Capozucca, 2013; Prasad and Seshu, 2010; Orakcal et al ., 2004; Yu et al ., 2017; Feng et al ., 2021; Johnson et al ., 2021; Kumar and Srinivas, 2017). Similarly, a variety of structures like reinforced concrete (RC) frames (Li et al ., 2016), pre-stressed concrete bridges (Huth et al ., 2005) and steel truss bridges (Chang and Kim, 2016) have been tested under incremental loadings to develop damage detection techniques.…”