Dynamics of a functionally graded material axial bar: Spectral element modeling and analysis

Functionally graded material (FGM) bars in axial motion (hereafter called “FGM axial bars”) have great potential for applications in many engineering fields. Therefore, it is important to develop a reliable mathematical model that can provide very accurate dynamic and wave propagation characteristics in FGM axial bars, especially at high frequencies. As an extension of our previous work, we present a spectral element model for a modified FGM axial bar model wherein nonuniform lateral contraction in the thickness direction is taken into account. We assume that material properties of the modified FGM axial bar model vary in the radial direction according to the power law. The performance of the proposed spectral element model is validated through comparison with solutions from a conventional finite element model, and with the results from the previous FGM axial bar model. In addition, the effects of lateral contraction on the dynamic and wave propagation characteristics in example FGM axial bars are numerically investigated.