Reflection of Nonlinear Acoustic Waves from the Mechanically Free Surface of an Unconsolidated Granular Medium

Abstract

SummaryThe problem of the nonlinear reflection of acoustic waves from a mechanically free surface of an unconsolidated granular layer under gravity is solved analytically using the successive approximations method. The theory revealed specific dependencies of the characteristics of the generated acoustic harmonics of longitudinal and shear waves on frequency and the thickness of the granular layer, which are related to a power-law gravity-induced depth stratification of linear and nonlinear mechanical properties of the granular layer. The developed theory could be useful for the analysis of the acoustic experiments directed to the investigation of fundamental mechanical properties of unconsolidated granular media near the jamming transition taking place at zero confining pressure.

Ultrafast optical detection of coherent acoustic phonons emission driven by superdiffusive hot electrons

“…The numerical simulation of the transient reflectivity shown in Fig. 3(c) has been carried out following the established photoelastic model of the detection process [29,30,35,36] where the measured transient reflectivity is ∆R/2R = Re(∆r/r), with : ∆r/r = 2ik 0 u(0)…”

Temporal and spatial tracking of ultrafast light-induced strain and polarization modulation in a ferroelectric thin film

“…3, A and B). This abrupt signal change corresponds to the arrival of coherent longitudinal acoustic phonons at the BiFeO 3 -substrate interface (35)(36)(37)(38). Thanks to a small acoustic reflection coefficient (see note S3), this acoustic mode is largely transferred into the substrate.…”

Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity

“…This order of magnitude is insufficient to open the intergrain contacts in the granular crystal, which are estimated to be statically preloaded in our experiments in average by the strain of η 0 ∝ 10 −5 . This estimate is done for the Hertzian contacts, for which η 0 ≈ K −2/3 (a/2) −4/3 N 2/3 0 , where K ≡ (4/3)[E/(1 − ν 2 )] denotes the effective modulus [29,33]. Thus, the observation of 3/2 power law in our nonlinear acoustic experiments in three-dimensional granular crystal demonstrates that, in ordered granular assemblies, similarly to the documented observations for disordered granular media (see [24] and the reference therein), there is an important fraction of weak contacts, which are statically preloaded much weaker than in average.…”

“…In three-dimensional noncohesive granular media, the translational symmetry is actually always naturally broken along the direction of the gravity field, because the static loading on the contacts between the beads and, as a consequence, their rigidities, increase along the gravity direction [33]. It has been earlier demonstrated that this gravity-induced inhomogeneity of the elastic properties in the vertical direction induces acoustic waves guided along the mechanically free surface of the granular assemblies [34][35][36] and in subsurface channels [37].…”