Wave Propagation in Finite Rods of Viscoelastic Material

Abstract

The paper is concerned in the main with a Maxwellmaterial, which corresponds to a model having a spring and dashpot in series. The equation for longitudinal wave propagation in rods is shown to be equivalent to the telegraph equation, and solutions of transient wave problems are treated briefly in the Appendix using the Laplace transform technique. Impact on a semi‐infinite rod is considered in detail in the report. A method of superposition of images is discussed to use this solution to solve boundary value problems for finite rods. The resulting stress distributions are discussed and contrasted with those for an elastic rod. The natural grouping of problems is discussed according to the relative magnitude of the duration of interest, the relaxation time, and the wave traverse time. The influence of the idealization involved in the Maxwell model is briefly touched upon.