Theory And Numerical Study On One Dimensional Elastic Wave Propagation In Functionally Graded Materials

Functionally graded material is a new kind of composite material, just developed andresearched in the last decade, which is a special non-uniform material, having a goodapplication performance. With the wide development and application of this material in allwalks of life, more and more scholars in various fields pay attention on its mechanicalproperties and elastic wave characteristics, the studies for functionally graded materialplay an important theoretical significance on engineering design. In this paper, onedimensional elastic wave propagation law in functionally graded materials was studiedsystematically, which not only can provide a theoretical basis for ultrasonic nondestructivetesting, but also provide theoretical guidance for the design and improvement offunctionally graded materials.Currently, most of the scholars analyze the structural fluctuations in functionallygraded materials using the numerical methods. But in this paper we studied the onedimensional elastic wave (shear wave and longitudinal wave) propagation law infunctionally graded materials by WKBJ approximation theory, and obtained thedisplacement analytic solution of functionally graded materials. Taking materialparameters (elastic modulus or shear modulus or mass density) of the functionally gradedmaterials which change parabolic and exponentially for example, the propagationvelocity,wave amplitude curves and cutoff frequency of one dimensional elastic wavewere obtained by calculation and the influence of material parameters and geometricparameters on them was analyzed.In this paper, one dimensional longitudinal wave propagation in functionally gradedmaterials was simulated using the finite element analysis software ABAQUS. Through thedata of numerical simulations, the displacement wave amplitude curves are found out, andthe results are consistent with related theories. To change the material parameters offunctionally graded materials and the wave frequency, we find the influence law of theseparameters on the wave amplitude. This method can provide a numerical method for thestudy of other elastic wave propagation in functionally graded materials.