Polynomial method applied to acoustic waves in inhomogeneous cylinders

We present a numerical method for calculating the waves in inhomogeneous cylinders utilizing elastic materials of cylindrical anisotropy. The formulation is based on linear three dimensional elasticity using an analytic form for the displacement field. We have developed the required formulas to apply it to cylinders in which the inhomogeneity in the elastic moduli and density is a function of the radial coordinate giving rise to functionally graded material (FGM) cylinders. The method incorporates the stress-free boundary conditions directly in the equations of motion by assuming position-dependent elastic constants and mass density. The technique is applied to analyze several inhomogeneous cylinders made up of a mixture of ceramic and metal and results are compared with those published earlier. The agreement is very good for both thin and thick cylinders which clearly illustrates the effectiveness of using the presented method to numerically model guided waves in inhomogeneous cylinders.