Functionally Graded Material Axial Bars: Spectral Element Analysis

초록

The functionally graded material (FGM) bars subject to axial motions (hereafter called "FGM axial bars") have a great potential for applications in diverse engineering fields. Accordingly it is very important to develop a reliable and accurate dynamic model that can provide satisfactory dynamic and wave propagation characteristics in FGM axial bars, especially at high frequencies. This study is an extension of our previous work (Hong et al. 2014). In this study, we present a spectral element model for a modified FGM axial bar model wherein the effects of non-uniform contractions in the radial direction (simply, radial contraction) are taken into account. It is assumed 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 then evaluated through the comparison with the solutions obtained by the conventional finite element model and with the results by the previous FGM axial bar model (Hong et al. 2014). In addition, the effects of the non-uniform radial contraction on the dynamics and wave propagation characteristics in some example FGM axial bars are numerically investigated. From numerical results obtained in this study, the following conclusions are made: (1) The proposed spectral element model has the capability to provide very accurate high frequency characteristics of the dynamics and waves in an FGM axial bar by employing a very small number of finite elements compared to the standard FEM. (2) Compared to the spectral element model developed in the previous work (Hong et al. 2014) wherein the radial contraction was assumed to be constant in the cross-section of a FGM axial bar, the present spectral element model can successfully capture the high frequency characteristics of the radial contraction waves propagating in the FGM axial bars. (3) The region in which the radial contraction waves are propagating depends on the excitation freq