An Exact Elastodynamic Solution forFunctionally Graded Thick-Walled CylindersSubjected to Dynamic Pressures

In the present paper, an exact solutionfor transient response ofan infinitely long functionally graded thick-walled cylinder subjectedto dynamic pressures at the boundary surfaces is presentedfor arbitrary initial conditions. The cylinder is assumedto have a plane-strain condition and the dynamic pressures areassumed to be imposed uniformly and axisymmetrically on theboundary surfaces, Material properties of the cylinder are assumedto vary through the thickness according to a power lawfunction. In contrast to many previous researches, the FGMcylinderis not divided into isotropic sub-cylinders. A solution approachassociated with the expansion of the transient waveunctions in terms ofa series ofthe Eigen functions is employedThe dynamic radial displacement expression is divided into quasi-static and dynamic parts andfor each part, all analytical solutionis presented By this method, radial displacement andstress distributions in the functionally graded thick-walled cylindersare obtained for various values of the exponent of thepower law/unction, various radius ratios, and various dynamicloads. Finally, advantages of the proposed method are discussed