Buckling and Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Beam Under Axial Load

Abstract

Buckling and vibration analysis of cantilever functionally graded (FG) beam that reinforced with carbon nanotube (CNT) is the purpose of this paper. The beam is graded in the thickness direction, and compressive axial force impressed the beam. The volume fractions of randomly oriented agglomerated single-walled CNTs (SWCNTs) are assumed to be graded in the thickness direction. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced FG-beam, a two-parameter micromechanics model of agglomeration is employed. In this paper, an equivalent continuum model based on the Eshelby–Mori–Tanaka approach is obtained. The stability and motion equations are based on the two-dimensional elasticity theory and Hamilton’s principle. The generalized differential quadrature method (GDQM) that has high accuracy is used to discretize the equations of stability and motion and to implement the boundary conditions. To study the accuracy of the present analysis, a compression is carried out with a known data. Convergence rate, the influence of graded agglomerated CNTs, and the effect of axial forces exerted on the beam, on the natural frequencies of reinforced beam by randomly oriented agglomerated CNTs are investigated.