In 2000, Ludovic Menguy and Joël Gilbert generalized the Burgers equation in order to incorporate thermoviscous losses due to boundary layers on the walls.This allowed studying the nonlinear propagation in brass instruments.Later, Joël Gilbert and colleagues were involved on the study of high-level noise sources from which emerged the study of nonlinear propagation of noise in tubes.This is the subject of the present paper.The problem is solved numerically using a fractional step method together with a convexification method.This one is suited to nonlinear propagation of acoustic signals containing a large number of pre-shocks and shocks which coalesce during the propagation.Model predictions and experimental data are compared and shown to be in a good agreement.It is shown that the Gaussianity of narrowband noise at the inlet of the tube is not conserved during nonlinear propagation.

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

The passage of an electric current through a chain of metallic beads causes a contact temperature rise and a permanent change of the contact area between beads, which in turn modify the electrical resistance of the chain. These effects are analyzed by measuring the voltage–current characteristics of a chain. These characteristics exhibit nonlinear and hysteretic behaviors. In this article, we particularly focus on the electrical behavior under cycles of increasing and decreasing current. Experimental results compare well with those of a model derived on the assumption of equilibrium between Joule heating in the contact between beads and thermal dissipation by conduction within the material. It is shown however that models based on the Wiedemann – Franz ’s law fail to describe the electro-thermo-mechanical behaviors of chains of beads carrying currents and submitted to a small static compression force. We finally analyze the strong modifications of the electrical behavior of a chain of beads subjected to electromagnetic perturbations produced by a spark.

Rectification (demodulation) of high-frequency shear acoustic bursts is applied to probe the distribution of contact forces in 3D granular media. Symmetry principles allow for rectification of the shear waves only with their conversion into longitudinal mode. The rectification is due to nonlinear dynamic dilatancy, which is found to follow a quadratic or Hertzian power law in the shear wave amplitude. Evidence is given that a significant portion of weak contact forces is localized below 10(-2) of the mean force-a range previously inaccessible by experiment. Strong anisotropy of nonlinearity for shear waves with different polarization is observed.

Received 27 February 2004DOI:https://doi.org/10.1103/PhysRevLett.92.099903©2004 American Physical Society

Granular materials are widely used in different branches of industry from the building construction to pharmaceutics and production of the nanostructured materials. Classical acoustical methods for their diagnostics are well known to be very useful. In the present communication we would like to attract the attention to the possible applications of the emerging nonlinear acoustical methods for the non-destructive evaluation of granular materials. Three potential applications are discussed. Firstly, due to high nonlinearity of the granular materials the parametric emitting antenna can operate with sufficient efficiency in these materials. Thus, similarly to the advantages achieved in underwater applications of the parametric sonar, compact sources of highly directive low-frequency sound waves can be created for the acoustic spectroscopy, tomography and depth-profiling of the granular piles and columns. Secondly, the (low frequency) acoustic signal, emitted by the parametric antenna, carries information on the processes of the absorption and scattering of high frequency waves, and also on their dispersion related to the discrete nature of the granular assemblages. It contains information on the transition in the high-frequency wave transport from ballistic to diffusive regime, and from propagative to evanescent. Thirdly, due to high sensitivity of the nonlinear phenomena to the state of the inter-grain contacts, the processes involving polarized (shear) waves are sensitive to the anisotropy in the force chains network induced by uniaxial static loading.

In point-to-plane corona discharges in air, the collisions of charged particles with neutral particles induce a gas movement between the point to the plane called electric wind. A one-dimensional model of the neutral particle velocity along the discharge axis and between the electrodes is first developed. Laser Doppler Anemometry is used to measure the axial velocity pro. le of the gas between the electrodes. Discrepancies between experimental results and predictions of the on-axis velocity are discussed. Finally, the measured velocity profile compares quite well with a cos(5) theta distribution. Significant differences between measured and cos(5) theta profiles are observed near the discharge axis which could be attributed to the presence of seeding particles.

The present Note describes some experimental work related to the nonlinear propagation of acoustic waves in granular media such as unconsolidated glass beads. The studied nonlinear effect is a self-demodulation process performed with the operation of the. so-called parametric transmitting antenna. The pump (or carrier) wave is generated by a high power ultrasonic broad-band transducer (100 kHz central frequency) which is LF (low frequency, i.e., a few kHz) amplitude modulated. As the attenuation of acoustic waves increases with frequency, only the LF demodulated wave can be transmitted. A parametric study is performed where the HF central frequency is monitored between 60 and 300 kHz. The LF demodulation profile versus the HF frequency is modified, its shape being temporally derived almost twice. A numerical analysis of the order of temporal derivation is done in the Fourier domain, its value varying from 1.25 to 2.7. Qualitative agreement with current theoretical models is described, and an advanced theoretical analysis by the same authors [Phys. Rev. E66 (2002) 041303], taking into account absorption, nonlinearity, dispersion and scattering, is briefly discussed. (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.

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.

In this paper, electrical and acoustical characteristics of negative point-to-plane corona discharge loudspeakers are investigated. In the rst part, the electrical behaviour of point-to-plane corona discharges is modelled by a three-parameters (r(i), r(u), C(u)) equivalent circuit. An experimental set-up for estimating these electrical parameters has been developed and improved. Based on the experimental results, evolution of the parameters with discharge conditions has been traced. In the second part, the electrode gap in negative point-to-plane corona discharges is divided into an ionisation region near the point, and a drift region. In each region, interactions between charged and neutral particles in the ionised gas lead to a perturbation of surrounding air, and so generate an acoustic field. For each region, seen as a separate acoustic source, an acoustical model is developed. An experimental set-up for measuring acoustic pressure has been developed, and allows us to confirm expectations based on directivity pattern, monopolar and dipolar directivities being associated to the ionisation and drift region respectively.

The acoustic sources from negative point to plane discharges in an ionized gas are studied both theoretically and experimentally. Inside the gap, the two main mechanisms responsible for the transfers between ionized and neutral particles (heat and momentum transfer) are determined to be at the origin of the acoustic generation. The effects associated to these two mechanisms are shown to have the same order of magnitude, the heat transfer giving rise to a monopole radiation at lower frequencies, and the momentum transfer being more or less dipolar and predominant in the higher frequency range. In order to validate the theoretical models proposed, two transducers and an experimental set-up were developed. The experimental results seem to validate these basic results, although the calculus for the pressure field still needs some improvements.

This study deals with the acoustic behaviour of a source using a weakly ionized gas issued from all electric discharge of the corona type in the ambiant air. The two main mechanisms responsible for the transfers between ionized and neutral particles (heat and momentum transfers) are modelized in the ease of a point-to-plane geometry. Expressions are proposed for the pressure variations associated to each of them; they are compared to measurements of a prototype.

Many studies have dealt with the realisation of ionic transducers, the most famous remaining the ionophone. These transducers combine two effects, one related to a heat source, and the other corresponding to a force distributed in the volume of the ionized area. This paper gives some basic equations describing the acoustic field generated by these two effects in the case of a Corona discharge; these show that each source predominates in a separate frequency range. These analytical results are compared with experiments, and show a good agreement.