A polynomial approach to the analysis of guided waves in anisotropic cylinders of infinite length

We present a polynomial approach for determining the guided waves in homogeneous infinitely long cylinders utilizing elastic materials of cylindrical anisotropy. The formulation is based on linear three-dimensional elasticity. The displacement components, expanded in a series of Legendre polynomials and trigonometric functions, are introduced into the equations of motion along with position-dependent elastic constants with the advantage that the solution of the wave equation is reduced to an eigenvalue problem. Normalized frequencies are calculated for cubic and orthotropic cylinders. Results are compared with those published earlier in order to check up the accuracy and range of applicability of the proposed approach. The developed software proves to be very efficient to retrieve the guided waves of any nature and the modes of all orders. Potential applications of the approach for studying radially inhomogeneous cylinders are suggested and conceptual and computational advantages are described.