Acoustic wave propagation in functionally graded materials cylindrically: Polynomial approach

A new approach is presented to determine the guided waves in hollow FGM cylinders made up of macroscopically inhomogeneous composite materials. The materials properties, elastic coefficients and mass density, are assumed to vary in the direction of the thickness according to a known radial variation law. The equations of motion are solved numerically by expanding each displacement component using Legendre polynomials and trigonometric functions. Dispersion curves of the guided waves for longitudinal, torsional and flexural modes are calculated and presented. Mechanical displacements, normal stresses and power flow distributions are presented for certain specific modes. This approach could be of use in waveguiding engineering, in non-destructive evaluation to predict which modes could be of interest either in non-destructive testing of FGM structures or, by means of a numerical inversion algorithm, to determine through-thickness gradients in material parameters.