Finite Element Model for Free Vibration Analyses of FG-CNT Reinforced Composite Beams using Refined Shear Deformation Theories

Abstract

Abstract The present article deals with the free vibration of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams employing various refined deformation theories and validates the accuracy and feasibility of these proposed theories. The theories involved are the first order shear deformation theory (FSDT) and other refined theories involving additional higher order terms. Carbon nanotubes (CNTs) are assumed to be oriented along the axis of the beam. Uniform and three types of different functionally graded (FG) distributions of CNTs through the thickness of the beam are considered. The rule of mixture is used to describe the effective material properties of the beams. The governing equations are derived using Hamilton’s principle and solved using the finite element method (FEM). A FEM code is compiled in MATLAB considering a C 0 finite element. The influences of different key parameters such as CNT volume fraction, distribution type of CNTs, boundary conditions and slenderness ratio on the natural frequencies of FG-CNTRC beams are investigated. It can be concluded that the above-mentioned parameters have significant influence on the free vibration of the beam and the accuracy of the proposed refined theories is good.