Effects of graded-index on guided wave propagation in a multilayer functionally graded cylinder

The study presented in this paper deals with the acoustic wave propagation modeling in a composite cylinders of infinite lengths, made of a functionally graded materials (FGM), using a semi-analytical method. The theory of three-dimensional elasticity is used to formulate this method. The effective material properties of FGM cylinders are supposed to change continuously in the radial direction accordance to the volume fraction’s power-law distribution. The displacement components developed in a series of trigonometric functions, Legendre polynomials are embedded into the motion equations using elastic constants depending on the position, and the rectangular window function, with the advantage that the wave equation’s solution is simplified to an eigenvalue/eigenvector problem. The dispersion curves in two types of FGM cylinders are calculated using a mathematical formula for longitudinal, torsional, and flexural modes. The dispersion curves with diverse graded index are depicted. These results imply that the graded-index has a major impact on the variations in material properties following the radial direction. Furthermore, the graded index has a considerable impact on the dispersion curves. The obtained numerical results are compared with those reported in theory in order to verify the efficiency and accuracy of this approach.