Propagation of axisymmetric transients in a Rod

The propagation of axisymmetric transients in a rod, governed by the Mindlin-McNiven theory, is treated by the method of wave-front expansion. The transients are due to impulsive-end loading specified in the form of stress, strain, velocity, or acceleration boundary conditions. The analysis is based on the concept of a wave as a carrier of discontinuities in the field variable and its derivatives. These discontinuities are determined from a set of recurrence relations, which are in turn generated using time-harmonic asymptotic series solutions to the equations of motion. Discontinuities of all orders are determined and the transient solution obtained as a series expansion behind the wave front. The entire solution procedure has been programmed and requires a minimum of input data. Numerical examples are presented to illustrate the method and the results are discussed. Distortion of the transient waves is clearly seen from the results where axial force, strain, velocity, and acceleration responses are presented.