Free vibrations of stepped axially functionally graded Timoshenko beams

Abstract

The paper studies free transverse vibrations of axially functionally graded beams with stepped changes in geometry and in material properties. The differential quadrature method with domain decomposition technique is used. The governing equations of motion are based on Timoshenko beam theory and are derived using Hamilton’s principle. Material properties are assumed to vary along the beam in an abrupt or gradual way. General boundary conditions are considered by means of translatory and rotatory springs at both external ends of the beam. Results are presented for different combinations of boundary conditions, step locations and properties of axially functionally graded materials. The effect of dynamic stiffening of beams can be observed in various situations. There are no available previous results of axially functionally graded beams with stepped changes in material properties and in cross section. This study may be helpful for a variety of potential applications in characterizing the effect of stepped changes in material properties added to changes in geometry.