Propagation of a large amplitude longitudinal wave in a semi-infinite elastic rod

A general solution is given to the problem of large amplitude wave propagation in a semi-infinite elastic thin rod. The solution is obtained by the method of characteristics. An explicit form of the solution is given in the case where an end velocity, which is a step function of time, is prescribed. More general types of end velocity can be accommodated provided that the variation with time is monotonically increasing; otherwise shocks will form and the present solution is no longer valid.