Dynamics of the Functionally Graded Material Bars: Spectral Element Modeling and Analysis

초록

Recently, functionally graded materials (FGMs) have received considerable attention in diverse engineering fields and many studies have been devoted to the static and dynamic analysis of various FGM structures. In contrast to the standard finite element method (FEM), the frequency domain spectral element method (SEM) is an exact solution method that can provide extremely accurate dynamic solutions, even at very high frequencies, by employing a minimum number of DOFs to significantly reduce the computation cost [1]. However, despite the advantages of the SEM, there have been very few applications to FGM axial bars. The goals of this paper are: (1) to derive governing equations of motion for an FGM axial bar by taking into account non-uniform lateral contraction in the thickness direction; (2) to develop a spectral element model for the modified FGM axial bar model; and (3) to investigate the effects of lateral contraction on the dynamic and wave propagation characteristics in example FGM axial bars.