Analysis of Ultrasonic Wave Dispersion in Presence of Attenuation and Second Gradient Contributions

In this study, we aim to analyze ultrasonic wave dispersion equation due to second-gradient contributions and attenuation within the framework of continuum mechanics. To analyze dispersive behavior and attenuation effects, we consider the influence both of higher-order gradient terms (second gradients) and of viscoelastic contributions of Rayleigh type. To this end, we use the extended Rayleigh-Hamilton principle to derive the governing equations of the problem. Using a wave-form solution, we establish the relationship between phase velocity and the material’s constitutive parameters, including those related to stiffness of first (standard) and of second-gradient type, and to viscosity. To validate the model, we use data available in the literature to provide a possible identification of all the material parameters. Thus, for the same identification, we observe that our model provides a good approximation of the experimentally measured trends of both the phase velocity and the attenuation vs frequency. In conclusion, this result not only confirms that our model can accurately describe both wave dispersion and attenuation in a material, as observed experimentally, but also highlights the necessity of simultaneously considering both second-gradient and viscosity parameters for a proper mechanical characterization of materials.