Multiple scattering of an ultrasonic shock wave in bubbly media.

This experimental study deals with the propagation of an ultrasonic shock wave in a random heterogeneous medium, constituted of identical 75µm radius bubbles, trapped in a yield-stress fluid. The fundamental frequency of the incident wave (in the MHz range) was much larger than the resonance frequency of bubbles (38kHz). A well-expanded coda, resulting from the multiple scattering of the incident shock wave through the heterogeneous medium, was experimentally measured in transmission. Despite the significant amplitude of the shock wave (90kPa), no sign of nonlinear response of the bubbles was detected. Both the coherent and incoherent fields were successfully described by linear theories. Using a shock wave presents the advantage of characterizing the medium over a large frequency range (1.5-15MHz).

Coherent transmission of an ultrasonic shock wave through a multiple scattering medium.

We report measurements of the transmitted coherent (ensemble-averaged) wave resulting from the interaction of an ultrasonic shock wave with a two-dimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (2-15 MHz) in only one experiment. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled.

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.

Optical measurements of the self-demodulated displacement and its interpretation in terms of radiation pressure.

Using a sensitive optical interferometer, the low frequency displacement nonlinearly generated by an ultrasonic tone burst propagating in a liquid is studied. Close to the source, the low frequency displacement contains a quasi-static component, which is affected by diffraction effects farther from the transducer. The experimental setup provides quantitative results, which allow the determination of the nonlinearity parameter of the liquid with a good accuracy. Such measurements are carried out in water and ethanol. Finally, the pressure associated with the low frequency displacement is discussed. Introducing the temporal mean value of the displacement, as already done in lossless solids, the noncumulative part of this second order pressure is associated with the static part of the low frequency displacement. This interpretation leads to extend the definition of the Rayleigh radiation pressure usually introduced for a continuous plane wave radiated in a confined fluid.