Elastic Wave Propagation In Graded Materials

With a wide application of Functionally Graded Materials in engineering, the nondestructive test of Functionally Graded Materials becomes more and more important. The theoretical basis of ultrasonic nondestructive test, studies of the elastic wave propagation in the materials have drawn more and more attentions. The elastic wave propagation along the gradient direction in Functionally Graded Materials is studied systematically in this paper, which can provide theoretical guidance for the design and non-destructive test of Functionally Graded Materials.The origin and development status of Functionally Graded Materials are firstly stated in this paper, then the research status of elastic waves propagation problem in homogeneous medium, non-homogeneous medium and Functionally Graded Materials are summarized.The standard differential equation with varied coefficient is established and solved for the one-dimensional longitudinal wave and shear wave propagation problem in the Functionally Graded Materials. The analytical solutions of displacement in functionally graded materials are obtained. The elastic modulus and density changes of Functionally Graded Materials vary in exponential form and parabola, and they are respectively taken as examples to calculate and analyze.The curves of one-dimensional longitudinal wave and shear wave velocity and amplitude in the Functionally Graded Materials are obtained, and the general properties of the one-dimensional longitudinal wave and shear wave propagation are analyzed. The material and geometrical parameters effects on wave velocity, wave amplitude, cut-off frequency are analyzed.The elastic wave propagation is studied by consistent mass, lumped mass and mixing quality of the finite element discrete model. The dispersion, cut-off frequency and spurious oscillation phenomenon of elastic wave in homogeneous model and discrete model and the links between these phenomena are analyzed. Taking one dimension rod as example, the propagation of wave in a uniform rod and the gradient rod is simulated, and they are compared combining with analytical solutions.