Guided waves in radially graded cylinders: a polynomial approach

A numerical method for calculating guided wave propagation in an infinite cylinder composed of Functionally Graded Materials (FGM) is presented in this article. An FGM is essentially an inhomogeneous material composite, made up of two or more materials chosen to obtain desirable properties for specific applications. In this study, properties of the material like Young's modulus, Poisson's ratio and mass density, are assumed to vary in the direction of the thickness according to a known radial variation law. The proposed solution makes use of Legendre polynomials and harmonic functions to expand each mechanical displacement component. It also incorporates the stress-free boundary conditions directly into the equations of motion. Normalized frequencies of the guided acoustic modes are calculated as a function of normalized thickness. Mechanical displacements, normal stresses and power flow distributions are presented for certain specific modes. The developed software is capable of dealing efficiently and accurately with a variety of homogeneous and inhomogeneous cylinders. Advantages of the proposed method and potential applications are described.