An Exact Elastodynamic Solution for Func-tionally Graded Thick-Walled Cylinders Subjected to Dynamic Pressures

In the present paper, an exact solution for transient response of an infinitely long functionally graded thick-walled cylinder subjected to dynamic pressures at the boundary surfaces is presented for arbitrary initial conditions. The cylinder is assumed to have a plane-strain condition and the dynamic pressures are assumed to be imposed uniformly and axisymmetrically on the boundary surfaces. Material properties of the cylinder are assumed to vary through the thickness according to a power law function. In contrast to many previous researches, the FGM cylinder is not divided into isotropic sub-cylinders. A solution approach associated with the expansion of the transient wave functions in terms of a series of the Eigen functions is employed. The dynamic radial displacement expression is divided into quasi-static and dynamic parts and for each part, an analytical solution is presented. By this method, radial displacement and stress distributions in the functionally graded thick-walled cylinders are obtained for various values of the exponent of the power law function, various radius ratios, and various dynamic loads. Finally, advantages of the proposed method are discussed.