Experimental evidence of Non-linear dissipation using Acoustic Micro-Lapses

Abstract

Non-linear material behaviour is observed experimentally in a laboratory using a new method called Acoustic Micro-Lapses (AML). In this approach, the shooting of two waves is synchronised in a way that the second wave (TW) is to sense the fluctuations in material stiffness induced by the first (PW). The tests include four samples; twenty trials are performed for each sample by increasing time-delays between the waves. The recorded waves are decoupled and compared to determine spectral differences by computing a quantity proportional to the energy difference as function of the increasing time delay (E^m_Δt). For a tight sandstone and aluminium samples, the random behaviour of E^m_Δt implies that TW finds the same equilibrium conditions as PW. The Lucite and the Berea sandstone depict distinct maxima, implying that TW sensed the transitory perturbations induced by PW. Therefore, it is inferred that PW and TW must propagate with different phase speeds. To assess the previous results, quasi-static modelling is performed using two time delayed step functions. The corresponding creep compliance shows a strong discontinuity when the second step is applied, implying the existence of two unrelaxed moduli. This supports the lab data in that the two waves must have different dispersion relations such that they propagate with different speeds.