Free and Forced Vibration Analysis of Functionally Graded Beams Using Finite Element Model Based on Refined Third-Order Theory

Abstract

This work is dedicated toward the development of the finite element (FE) model based on refined third-order theory (TOT) for the dynamic analysis of functionally graded (FG) beams. Variational approach is employed to derive the governing equations as well as consistent boundary conditions. Two-noded beam element is selected for the discretization of FG beam. The variables u0 and ψ0 are interpolated using C0-continuous linear Lagrangian functions while the presence of the second derivative of the transverse deflection in the variational equation requires C1-continuity and is interpolated using C1-continuous Hermite interpolation functions. Static deflection and free vibration responses are validated from the literature, and new results have been presented for free and forced vibration of FGM beams.