Free Vibration and Thermal Analysis of Randomly Oriented Carbon Nano Tube Based Functionally Graded Beam

Abstract

Present work deals with the free vibration and thermal analysis of CNT based functionally graded beam using three dimensional Timoshenko beam theory. It has been assumed that the material properties of CNT based FG beam varies only along the thickness and evaluated by rule of mixture. Finite element method is used to solve governing equation with the exact shape functions. Natural frequencies are calculated and validated with available literature. The effect of variation of CNT volume fraction and boundary conditions on the natural frequency of the beam has also been studied. Further work deals with the free vibration analysis of functionally graded nano composite beams reinforced by randomly oriented straight single-walled carbon nanotubes (SWCNTs). The Eshelby–Mori–Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. Results are presented in tabular and graphical forms to show the effects of carbon nanotube orientations, slenderness ratios and boundary conditions on the dynamic behavior of the beam. Next important work is the thermal analysis of Carbon Nano Tubes based FG (FG-CNT) Timoshenko beam. Different types of temperature distributions are used to find out the thermal behavior of Timoshenko beam. However, the material property distribution is assumed to be exponential for exponential type temperature distribution, linear and power law material distribution for linear type temperature distribution. First order Shear Deformation Theory (FSDT) is implemented along with plain strain condition to formulate expressions for stresses and strains. Finally, effect of temperature distributions on Young’s modulus, total stresses and strains is evaluated numerically for given beam. Finite difference method is also applied to find out temperature distribution for power law material distribution. The effect of CNT orientation on stresses and strains has also been found out for comparison.