One-dimensional wave propagation in a functionally graded elastic medium

In this study the one-dimensional wave propagation in a functionally graded elastic slab is considered. It is assumed that the stiffness and density of the medium vary continuously in thickness direction and it is initially at rest and stress-free. The slab is subjected to a pressure pulse on one surface and a vanishing stress or displacement condition on the other. The solution is obtained in wave summation form. Propagation of a rectangular pressure pulse in a graded medium that consists of either nickel/zirconia or aluminum/silicon carbide is studied as examples. It is shown that there is considerable wave distortion in time and the distortion is much more pronounced in slabs with fixed/free boundary conditions. A simple approximate expression giving the peak stress is developed. Also it is demonstrated that the energy balance principle may be used as a convergence criterion in the calculation of stresses.