Dynamics and waves characteristics of the FGM axial bars by using spectral element method

The functionally graded material bars in axial or longitudinal motions (simply FGM axial bars) have a great potential for the applications in many engineering fields. Thus it is essential to develop a reliable computational model which has the capability to accurately predict the dynamics and waves in the FGM axial bars, especially at the high frequency regime. Thus this paper presents a spectral element model for the FGM axial bars whose material properties vary in the radial direction according to the power law. The spectral element model is formulated from the governing equations of motion in the frequency domain by using the variational method. The radial contraction is taken into account in the spectral element model by adopting the Mindlin-Herrmann rod theory. The accuracy of the present spectral element model is verified first in due course by comparing with the solutions obtained by the conventional finite element model. The dynamics and wave characteristics of the FGM axial bars are then numerically investigated.