Polynomial modeling of acoustic guided wave propagation in homogeneous cylinder of infinite length

In this paper, we present a polynomial approach for determining the acoustic guided waves in homogeneous infinitely long cylinders using elastic materials of cylindrical anisotropy. The formulation is based on linear three-dimensional elasticity using an analytic form for the displacement field. The approach incorporates the stress-free boundary conditions directly into the equations of motion which are solved numerically by expanding each displacement component using Legendre polynomials and trigonometric functions. The problem is then reduced for anisotropic homogeneous structures to a tractable eigenvalue problem allowing the dispersion curves and associated profiles to be easily calculated. Numerical results of the guided waves for axisymmetric and flexural modes are presented and compared with those published earlier in order to check up the accuracy and range of applicability of the approach. The developed software proves to be very efficient to retrieve the guided waves of any nature and the modes of all orders. The computational advantages of the approach are described.