Free vibration analysis of a functionally graded viscoelastic supported beam

Abstract

In this study, the resonance frequency behavior of a functionally graded beam under viscoelastic boundary conditions is investigated. Nondimensional frequency parameters of the beam are analyzed using the finite element method. The system of equations of motion is derived by using Lagrange's equations under the assumption of Euler-Bernoulli beam theory. The material properties of the beam are assumed to vary through thickness according to the power-law distribution. Different boundary conditions are attained by applying various stiffness and damping coefficients to viscoelastic support elements. The model is validated by comparing the results with a previous study. The effects of various material distribution and boundary conditions are discussed in detail.