Transient response of non-prismatic heterogeneous viscoelastic rods and identification of their material properties

Abstract

Pulse propagation in homogeneous and heterogeneous viscoelastic thin rods of a constant or variable cross-section is investigated in this work using analytical, numerical and experimental methods. Based on the elementary theory of thin rods, the model for pulse propagation in a layered non-prismatic rod is derived and solved in the Laplace domain. Using the numerical inverse Laplace transform, semi-analytical transient solutions for both homogeneous, layered and functionally graded viscoelastic prismatic or non-prismatic rods are obtained. The parameters of the generalised Zener model (GZM) are then identified by solving the problem of parametric optimisation in Matlab and utilising the transient acceleration responses measured for rods of different types and different material properties (POM-C, PC1000, PP, PVC, PET, PLA and aluminium). A great agreement between the measured signals and the responses calculated for GZM with different numbers of relaxation times was achieved. Next, the dynamic properties of selected prismatic and non-prismatic rods have been studied. The dispersion and attenuation curves for both homogeneous and layered rods are reconstructed from the measured signal using a method adopted from the literature. The obtained results are then discussed in the context of the theoretical curves resulted from the elementary rod theory and from the theory that takes into account the lateral motions of the rod.