Xavier Jacob

Acoustic nonlinearity parameter measurements in solids using the collinear mixing of elastic waves

An alternative method for measuring the nonlinearity parameter β of longitudinal acoustic waves propagating in solids is presented. The method is based on the detection of the phase modulation resulting from the parametric interaction between a high frequency acoustic wave and a lower frequency acoustic pulse. Results are reported for various materials: fused quartz, duraluminum, titanium, and polystyrene.

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.

Nonlinear shear wave interaction in soft solids

This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.

Experimental study of the acoustic radiation strain in solids

Measurements of the static displacement induced by the radiation stress associated with a longitudinal acoustic wave propagating in a solid are presented. Acoustic tone bursts were launched into fused silica and duraluminum samples. The static displacement was measured at the sample free surface with an optical interferometer. The role of the nonlinearity parameter and the variations of the dc pulse amplitude with the acoustic energy confirm results obtained by other authors. However, our conclusions on the dc pulse shape, on the influence of the tone burst duration, and of the propagation distance on the dc pulse amplitude are different.

Plane wave echo particle image velocimetry

The present work deals with the application of Topological Imaging to Ultrasonic Echo-Particle Image Velocimetry (Echo-PIV). Echo-PIV is a recent alternative to optical PIV for measuring the instantaneous velocity field of a fluid flow previously seeded with small particles. It consists in imaging the flow with an ultrasonic array at a high frame rate. Topological imaging is a method that benefits from the refocusing properties of the time-reversal principle in a systematic way, so that a single plane wave illumination of the medium leads to a fine resolution. Multiple insonifications are then possible at very high speed allowing not only static images of the medium but successive images of a moving medium. Experimental results are presented for a fluid seeded with stone powder. Two cases are studied: a vortex flow and the propagation of water surface waves.

Optical measurement of transient ultrasonic shock waves

In order to measure acoustic shock waves generating pressures of some tens of MPa in water, an ideal sensor has to be calibrated, wideband and sufficiently robust to support acoustic cavitation. We measure high intensity ultrasonic displacements and shock waves in water, using the phase modulation of an optical beam reflected by a thin immersed membrane materializing moving particles. With either an analog or a digital demodulation process, a 1-/spl mu/m ultrasonic transient displacement (corresponding to a 22-MPa acoustic pressure in water) has been measured with a standard heterodyne interferometer. Results are in good agreement with those given by a hydrophone designed to measure high pressure waves. This sensitive optical method provides absolute measurements with a 50- /spl mu/m lateral resolution, in a large bandwidth (from 20 kHz to 50 MHz). If the low cost membrane used in the experimental set-up is damaged by the acoustic cavitation, it can be easily replaced. We compare three phase detection techniques that require no calibration. The maximum measurable displacement is limited by the frequency bandwidth of the instrument. Since the photodetector cuts frequencies higher than 120 MHz, the interferometer is able to measure a 22-MPa peak acoustic pressure in water. This performance can be improved by increasing the frequency shift of the probe beam, to obtain a wider bandwidth. For measuring acoustic pressures up to 45 MPa, we have built an interferometer operating at a 140-MHz carrier frequency.

Three-dimensional and real-time two-dimensional topological imaging using parallel computing

We present the Fast Topological IMaging that has shown promising results to quickly process a picture by sending an ultrasonic plane wave within an unknown medium. This imaging algorithm is close to adjoint-based inversion methods but relies on a fast calculation of the direct and adjoint fields formulated in the frequency domain. The radiation pattern of a transducer array is computed once and for all, and then the direct and adjoint fields are obtained as a simple multiplication with the emitted or received signals, in Fourier domain. The resulting image represents the variations of acoustic impedance, and therefore highlights interfaces or flaws. Real-time imaging and high definition visualization both imply an expensive computation cost, that led us to implement this method on GPU (Graphics Processing Unit). Thanks to a massively parallel architecture, GPUs have become for ten years a new way to implement high performance algorithms. We used interoperability between OpenGL and CUDA to enable a real-ti...

Optical measurement of acoustic radiation strains in solids

Measurements of the static displacement, induced by the radiation stress associated with a longitudinal acoustic wave propagating in a solid are presented. High frequency acoustic tone bursts were launched into samples of fused silica and duralumin. The static displacement was measured, at the sample free surface, with a heterodyne optical interferometer. Concerning the role of the nonlinearity parameter and the variations of the amplitude of the DC pulse with the acoustic energy density, these experiments confirm previous results obtained by other authors with a capacitive detector. However, our conclusions on the shape of the DC pulse, on the influence of the tone burst duration and of the distance of propagation on the amplitude of the DC pulse are different.

Acoustic propagation in a fractal network of scatterers

Fractal networks, built on Cantor set, Fibonacci series or Sierpinsky sets are characteristics of a structural organization between periodic and random. On the other hand, they have been proved to be a good descriptor of irregular systems as the well known description of Brittany coasts. Such systems can be seen as irregular boundaries, as in the case of irregular coasts, while the wave equations are still usable inside theses boundaries. Along the boundaries, wave localization is possible. Another case is that where boundaries are regular while the organization of the material where waves are propagating carries the fractality. Wave propagation on such systems can be considered through the aspect of multiple scattering, and on 1D systems as well on 2D systems built on Cantor or sierpinski set, it is possible to show the existence of localized modes. On the contrary to the previous case, localization arises not along the boundaries but inside the propagating medium. Less common organization of scatterers,...

Imaging of a fractal pattern with time and frequency domain topological derivative

While fractal boundaries and their ability to describe irregularity have been intensively studied, only a few studies are available on wave propagation in a medium where a fractal or quasi fractal pattern is embedded. Acoustical propagation in 1D or 2D domains can be modeled using Time Domain Finite Differences or in Frequency domain with Finite element methods. The fractal object is then considered as a subwavelength set of scatterers, and the problem becomes a multiple scattering one leading to acoustic localization. So, as some important part of the energy remains trapped inside the fractal pattern, imaging such a medium becomes difficult and imaging such complex media with classical tools as B-scan or comparable methods is not sufficient. The resolution of the inverse problem of wave propagation can then be achieved with the help of the more efficient imaging methods related with Time Reversal. Using the concept of topological derivative as defined in Time Domain Topological Energy and Fast Topologica...