Spectral Element Model for an FGM bar in Axial Vibration

초록

As the functionally graded materials (FGM) bars which vibrate in axial or longitudinal direction have great potential for applications in diverse engineering fields, developing a reliable mathematical model that provides very reliable vibration and wave characteristics of a FGM axial bar, especially at high frequencies, has been an important research issue during last decades. Thus, as an extension of the previous works (Hong et al. 2014, Hong and Lee 2015) on three-layered FGM axial bars (hereafter called FGM bars), an approximate spectral element model is proposed for a FGM bar model in which axial and radial displacements in the radial direction are treated more realistic by representing the inner FGM layer by multiple sub-layers. The accuracy and performance of the proposed enhanced spectral element model is evaluated by comparison with the solutions obtained by using the commercial finite element package ANSYS. The proposed spectral element model is also evaluated by comparison with the author’s previous spectral element model. In addition, the effects of Poisson’s ratio on the dynamics and wave characteristics in example FGM bars are numerically investigated. Based on the numerical results obtained in this study, the following conclusions are made: (1) To accurately predict the natural frequencies and frequency response functions up to a high frequency, we recommend the present SEM, instead of the SEM by Hong and Lee (2015). (2) To accurately predict the dynamic responses at near the excitation point, the inner FGM layer must be represented by multiple sub-layers, rather than representing it as a single layer as done by Hong and Lee (2015). (3) The dynamic responses or wave propagations at a distance sufficiently far from the excitation point can be well predicted by using the SEM by Hong and Lee (2015.