Forced Vibration Analysis of Composite Beams Reinforced by Carbon Nanotubes.

Ömer Civalek,Şeref D Akbaş,Shahriar Dastjerdi,Bekir Akgöz

doi:10.3390/nano11030571

Abstract

This paper presents forced vibration analysis of a simply supported beam made of carbon nanotube-reinforced composite material subjected to a harmonic point load at the midpoint of beam. The composite beam is made of a polymeric matrix and reinforced the single-walled carbon nanotubes with their various distributions. In the beam kinematics, the first-order shear deformation beam theory was used. The governing equations of problem were derived by using the Lagrange procedure. In the solution of the problem, the Ritz method was used, and algebraic polynomials were employed with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method was applied in the time history. In the numerical examples, the effects of carbon nanotube volume fraction, aspect ratio, and dynamic parameters on the forced vibration response of carbon nanotube-reinforced composite beams are investigated. In addition, some comparison studies were performed, with special results of published papers to validate the using formulations.

Highlights

Composite material refers to any solid that consists of more than one component, in which they are in separate phases
Free vibration analysis of functionally graded single-walled carbon nanotubes (CNTs) reinforced aluminum alloy beam was performed by Selmi and Bisharat [19]
Yas and Heshmati [22] investigated the vibrational characteristics of FG-carbon nanotube-reinforced composite (CNTRC) beams reinforced by randomly oriented CNTs subjected to a moving load, based on Bernoulli–Euler and Timoshenko beam theories by finite element method

Summary

Introduction

Composite material refers to any solid that consists of more than one component, in which they are in separate phases. Some studies on the bending, buckling, and vibration responses of carbon nanotube-reinforced composite (CNTRC) beams are mentioned below. Free vibration analysis of functionally graded single-walled CNTs reinforced aluminum alloy beam was performed by Selmi and Bisharat [19] Ke et al [21] surveyed the nonlinear free vibration response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams on the basis of first-order shear deformation beam theory with von Kármán geometric nonlinearity assumption. Yas and Heshmati [22] investigated the vibrational characteristics of FG-CNTRC beams reinforced by randomly oriented CNTs subjected to a moving load, based on Bernoulli–Euler and Timoshenko beam theories by finite element method. Mayandi and Jeyaraj [33] investigated the static and dynamic behaviors of FG-CNTRC beams subjected to various non-uniform thermal loads by employing the finite element method. A detailed parametric study wasand carried out to peruse the CNTs volume volume fraction, slenderness ratio, dynamic parameters oninfluences the forcedofvibration refraction, slenderness sponse of CNTRC beam.ratio, and dynamic parameters on the forced vibration response of CNTRC beam

Theory and Formulation

Numerical Results

Conclusions