Wave propagation in non-homogeneous thin elastic rods subjected to time dependent stress impact

The problem of wave propagation in a non-homogeneous elastic rod subjected to time dependent stress impact is considered. Similarity transformations are applied to the equation of motion of the rod and its boundary condition. Along with the similarity characteristic relationship on the moving front these are used to obtain the similarity representation as a boundary value problem. A closed form solution of the similarity representation is obtained and, in addition, restrictions on the parameters and relations among them are also obtained. Results for the stress distribution in the rod at a specific time are graphically represented in non-dimensional co-ordinates.