Vibration Analysis of Functionally Graded Carbon Nanotube Reinforced Beam Structures

Abstract

This work deals with the study of vibration behavior of the Functionally Graded Timoshenko Beam that has been reinforced with Carbon Nanotubes (CNTs), which is subjected to thermal and mechanical loads. The constituent materials of the functionally graded beam are alumina as the matrix material and single walled CNTs as the reinforcement material. The volumetric fraction varies according to power law along the thickness. The temperature dependent (TD) and temperature independent (TID) material properties of the beam are determined by employing Mori-Tanaka method and extended rule of mixture along the thickness direction. Timoshenko beam theory is used to study the dynamic behavior of the beam. The finite element method is employed to discretize the model and Hamilton’s principal is used to derive the equation of motion . Vibration analysis has been carried out to study the response of Temperature dependent and independent material properties on the dynamic behavior of the beam. The results show that CNT volume fraction and Temperature dependent material properties has substantial effect on the vibration characteristic of the beam.