Features of nonlinear wave propagation in a layer of a granular medium

Computer simulation was performed to study compression wave propagation in a granular medium in a gravity field. It is shown that in a layer with spherical granules, periodic wave structures can be formed and their parameters depend on the granule size and layer thickness. If the layer is compressed, the wave structures fail to emerge and wave attenuation is much weaker. Wave processes in a layer of granular medium with nonspherical granules were also studied. It is shown that the medium is characterized by very strong wave attenuation and by the absence of wave structure formation and is highly sensitive to its initial stress state.     

Characteristic features of elastic wave propagation in a one-dimensional model of an unconsolidated medium

The characteristic features of elastic wave propagation in a one-dimensional model of a discrete inhomogeneous unconsolidated medium are investigated. The model is represented by a linear chain of 80 uncoupled steel spheres with a diameter of 6.5 mm. Nonlinear effects that may arise in such systems are reviewed. The experimental setup is described. Results of studying the dispersion of elastic waves in the system and the dependence of the elastic wave velocity on the wave amplitude under increasing compression are presented. The results are analyzed using the Hertz contact theory.     

Waveguide propagation of sound beams in a nonlinear medium

A possibility of a waveguide propagation of sound beams in the case of compensation of the diffraction divergence by the nonlinear refraction is demonstrated theoretically. A stationary (with respect to the longitudinal coordinate) solution is obtained to the nonlinear equation for a sound beam (the Khokhlov—Zabolotskaya equation); the solution describes the characteristic bow-shaped profile of the beam and the self-localized (with respect to the transverse coordinate) distribution of the peak values of this profile. The physical and mathematical features of this phenomenon belonging to nonlinear acoustics are discussed and compared with those of the well-known analog from nonlinear optics. A scheme of an experimental realization of the waveguide propagation of acoustic beams is proposed.     

Acoustic probing of the jamming transition in an unconsolidated granular medium

Experimentally determined dispersion relations for acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing through nonaffine motion leads to a peculiar scaling of shear rigidity with pressure near the jamming transition corresponding to zero pressure.     

The propagation of an ion sound wave in the presence of a large neutral background

The case is taken of an ion wave in a single component weakly ionised plasma. Collisional effects on the ions are also included.     

Physical modeling of nonlinear sound wave propagation in oceanic waveguides of variable depth

Results of laboratory experiments aimed at studying the spatial distribution of the difference-frequency acoustic wave field in a shallow-water waveguide with a sloping bottom are presented. It is shown that, in an inhomogeneous waveguide, the direction toward the radiation maximum in the angular spectrum of the low-frequency wave continuously varies as the rib of the wedge is approached, whereas, in a homogeneous waveguide, the angular spectrum is shaped. A spatial filtering of low-frequency modes produced by a parametric radiator and reflected from the coastal wedge is experimentally realized. The results of the experiment are confirmed by numerical modeling. Problems of the physical adequacy of the experimental results obtained under actual and laboratory conditions are discussed.     

The stratification of a wave packet in a nonlinear medium

The possibility of controlled large-scale stratification of the wave impulse in the nonlinear medium is discussed. The wide class of exact analytical solutions, describing, in the bounds of the nonlinear geometrical optics, the formation of the new intensity maxima, are found. The characteristics dimensions of the oscillations of the packet are much greater than the wave length.     

Reverse wave propagation in a randomly-inhomogeneous medium

Conclusion Therefore, it has convincingly been demonstrated in this paper that the so-called RWF mirror that reverses the radiation wave front even when using a finite aperture will assure elimination of field fluctuations during propagation in media with large-scale scatterers. Both reproduction of the mean intensity distribution and suppression of the intensity fluctuations are assured here in two-pass schemes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 51–63, November, 1985.     

Interaction of a surface magnetostatic wave with an inhomogeneous granular HTSC medium

In the present paper the dispersion properties of surface magnetostatic waves (SMSWs) propagating in a stratified structure, ferrite film—high-temperature superconducting layer, have been investigated. The problem of SMSW propagation in an inhomogeneous stratified medium has been solved and the dispersion equation has been obtained. In the solution of this problem, the granular nature of the high-temperature superconducting (HTSC) medium and the exposure to a constant magnetization field have been taken into account. Upon exposure to the constant magnetic field the HTSC film becomes an inhomogeneous anisotropic medium with respect to a variable magnetic field. The nonhomogeneous wave equation describing the SMSW field in a granular HTSC medium has been solved by the method of sequential iterations. Corrections for the SMSW velocity and attenuation, calculated with the use of the exact dispersion equation, are significant in comparison with previously obtained approximate values and exceed 20 and 40%, respectively. The method of analyzing electromagnetic fields in inhomogeneous granular high-temperature media can be used to solve some other problems, where spatially inhomogeneous HTSC media are used. Tomsk State University of Control Systems and Radioelectronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 45–48, April, 1999.     

The problem of surface wave propagation in a reduced Cosserat medium

This article continues a series of publications devoted to the study of waves in the framework of the asymmetric theory of elasticity, where the deformed state of the medium is characterized by independent vectors of translation and rotation. The problem of acoustic Rayleigh wave propagation in half space is considered within a model of the reduced Cosserat medium. A general analytic solution of this problem is obtained. The analysis of this solution is compared with the corresponding solution for a classical elastic medium and full linear Cosserat medium. It is shown that the Rayleigh wave is characterized by a range of forbidden frequencies, where this wave cannot propagate. The dispersion curve consists of two branches. One of them has a cut-off frequency and cut-off wavenumber.     

Electromagnetic wave propagation in a medium with defects

The equations of the electromagnetic field in a solid with defects were obtained and an approximate wave solution was found by the Debye–Rytov method.     

A frequency domain inversion method applied to propagation models in unconsolidated granular materials

The measurement setup consists of a water filled tank within which a smaller Plexiglas tank containing a known sediment is placed. This provides a Plexiglas-sediment-Plexiglas configuration, which is then used in conjunction with transducers and a pulser-receiver for a transmission and reflection experiment. The aim of this work is to find some physical parameters of the sediment from these measurements. A general viscoelastic model that considers losses due to absorption and dispersion along the propagation of the wave through the sediments is proposed. A rational transfer function is used to model the viscoelastic modulus of the bulk sediments, and comparisons with constant Q viscoelastic modelling and Biot modelling are performed. The estimation of the model parameters is elaborated using a maximum likelihood estimator in the frequency domain.     

Experimental study of nonlinear acoustic effects in a granular medium

Results of a series of experimental studies of nonlinear acoustic effects in a granular medium are presented. Different effects observed in the experiments simultaneously testify that the nonlinearity of granular media is governed by the weakest intergrain contacts. The behavior of the observed dependences suggests that the distribution function of contact forces strongly increases in the range of forces much smaller than the mean force value, which is inaccessible for conventional experimental measuring techniques. For shear waves in a granular medium, the effects of demodulation and second harmonic generation with conversion to longitudinal waves are studied. These effects are caused by the nonlinear dilatancy of the medium, i.e., by the nonlinear law of its volume variation in the shear stress field. With the use of shear waves of different polarizations, the anisotropy of the nonlinearity of the medium is demonstrated. The observation of the cross-modulation effect shows that the nonlinearity-induced modulation components of the probe wave are much more sensitive to weak nonstationary perturbations of the medium, as compared to the linearly propagating fundamental harmonic. The nonlinear effects under study offer promise for diagnostic applications in laboratory measurements and in seismic monitoring systems.     

Stability problem in nonlinear wave propagation

An explicit expression for the excitation spectrum of the stationary solutions of a nonlinear wave equation is obtained. It is found that all branches of many-valued solutions of a nonlinear wave equation between the (2K+1,2K+2) turning points (branch points in the complex plane of the nonlinearity parameter) are unstable. Some parts of branches between the (2K,2K+1) turning points are also unstable. The instability of the latter is related to the possibility that pairs of complex conjugate eigenvalues cross the real axis in the κ plane. Zh. éksp. Teor. Fiz. 114, 1487–1499 (October 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Asymmetric wave propagation in nonlinear systems

A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, nonmirror-symmetric model described by the one-dimensional discrete nonlinear Schr?dinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. This effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Finally, numerical simulations of asymmetric wave packet transmission are presented which beautifully display the rectifying effect.     

Weak nonlinear propagation of sound in a finite exponential horn.

This article presents an approximate solution for weak nonlinear standing waves in the interior of an exponential acoustic horn. An analytical approach is chosen assuming one-dimensional plane-wave propagation in a lossless fluid within an exponential horn. The model developed for the propagation of finite-amplitude waves includes linear reflections at the throat and at the mouth of the horn, and neglects boundary layer effects. Starting from the one-dimensional continuity and momentum equations and an isentropic pressure-density relation in Eulerian coordinates, a perturbation analysis is used to obtain a hierarchy of wave equations with nonlinear source terms. Green's theorem is used to obtain a formal solution of the inhomogeneous equation which takes into account linear reflections at the ends of the horn, and the solution is applied to the nonlinear horn problem to yield the acoustic pressure for each order, first in the frequency and then in the time domain. In order to validate the model, an experimental setup for measuring fundamental and second harmonic pressures inside the horn has been developed. For an imposed throat fundamental level, good agreement is obtained between predicted and measured levels (fundamental and second harmonic) at the mouth of the horn.