Different mechanical models for the study of ultrasonic wave dispersion for mechanical characterization of construction materials

It is well known from the literature that the phase velocity of waves is directly correlated with the stiffness of the material; however, experimental practice shows that this velocity changes significantly with varying frequencies, despite the fact that the elastic modulus of the material is, by definition, a material constant. We explore the dependence on the frequency of longitudinal ultrasonic plane waves velocity in construction materials, both from experimental and modeling points of view. For the sake of simplicity, the dispersive features are modeled by considering the case of a 1D medium, and two different kinds of mechanical models capable of describing wave dispersion phenomena are employed: a non-dissipative strain-gradient elastic model, and a dissipative viscoelastic one. In both cases, by using the extended Rayleigh–Hamilton principle, we derive the governing equations for 1D bulk waves propagation; in particular, in the case of the dissipative viscoelastic model either classical linear damping or Kelvin–Voigt damping is considered. The comparison of theoretical results with experimental findings obtained by ultrasonic tests on natural (sandstone) and artificial (concrete) construction materials shows that both theoretical models can satisfactorily describe the experimental behavior. These results encourage further experimental investigations for a clear and quantitative identification of the model that can be better used for engineering purposes.