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 o f the medium vary continuously in thickness direction and it is initially a t rest and stress-free. The slab is subjected to a pressure pulse on one su rface and a vanishing stress or displacement condition on the ether. The so lution is obtained in wave summation form. Propagation of a rectangular pre ssure pulse in a graded medium that consists of either nickel/zirconia or a luminum/silicon carbide is studied as examples. It is shown that there is c onsiderable wave distortion in time and the distortion is much more pronoun ced in slabs with fixed/free boundary conditions. A simple approximate expr ession giving the peak stress is developed. Also it is demonstrated that th e energy balance principle may be used as a convergence criterion in the ca lculation of stresses. (C) 1999 Academic Press.