Continuous waves probing in dynamic acoustoelastic testing

Consolidated granular media display a peculiar nonlinear elastic behavior, which is normally analysed with dynamic ultrasonic testing exploiting the dependence on amplitude of different measurable quantities, such as the resonance frequency shift, the amount of harmonics generation, or the break of the superposition principle. However, dynamic testing allows measuring effects which are averaged over one (or more) cycles of the exciting perturbation. Dynamic acoustoelastic testing has been proposed to overcome this limitation and allow the determination of the real amplitude dependence of the modulus of the material. Here, we propose an implementation of the approach, in which the pulse probing waves are substituted by continuous waves. As a result, instead of measuring a time-of-flight as a function of the pump strain, we study the dependence of the resonance frequency on the strain amplitude, allowing to derive the same conclusions but with an easier to implement procedure.