Free Vibration Analysis of Functionally Graded Beam with Linearly Varying Thickness

Abstract

The present study investigates the free vibration analysis of functionally graded material (FGM) beam which is rectangular in cross section with linearly varying thickness along its axis with the help of finite element formulation. This formulation of finite element is developed based on the Timoshenko beam theory which we called as first-order shear deformation theory. In the present analysis of the beam with linearly varying thickness, the beam element has five nodes and thirteen degrees of freedom. Properties of the material used in this beam element are varying continuously according to the power law along the thickness direction. Governing equations used for the formulation of present work are derived from Lagrange’s equations. The natural frequency of beam is calculated using different boundary conditions, exponents of power law, depth to span ratios, and tapered ratios. The present beam element is accurately demonstrated by comparing the results with the available data of publications for constant thickness and for variable thickness, and some results are new and can be further considered for future researches.