Influence of ballistics to diffusion transition in primary wave propagation on parametric antenna operation in granular media

Asymmetric Acoustic Propagation of Wave Packets Via the Self-Demodulation Effect

This Letter presents the experimental characterization of nonreciprocal elastic wave transmission in a single-mode elastic waveguide. This asymmetric system is obtained by coupling a selection layer with a conversion layer: the selection component is provided by a phononic crystal, while the conversion is achieved by a nonlinear self-demodulation effect in a 3D unconsolidated granular medium. A quantitative experimental study of this acoustic rectifier indicates a high rectifying ratio, up to 10^{6}, with wide band (10 kHz) and an audible effect. Moreover, this system allows for wave-packet rectification and extends the future applications of asymmetric systems.

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

We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.

Propagation of acoustic waves in a one-dimensional array of noncohesive cylinders

By means of a photoelastic method, we access the visualization of acoustic waves propagating in a one-dimensional array of noncohesive cylinders. As pointed by Nesterenko in the case of spherical grains [V. F. Nesterenko, J. Appl. Mech. Tech. Phys. 24, p. 567 (1983)], the nonlinearity of the contact law between the grains induces a dependence of the wave velocity both on its amplitude and on the confinement force. Our experimental method allows one to access the evolution in time of the internal state of stress of individual grains with excellent accuracy. We show that the velocity of the sound presents two regimes as a function of the confining force. For low forces, the dependence is strongly nonlinear, while it weakens for higher forces. By means of the direct visualization of the contact zone, we show that both micro- and macroscale imperfections of the surface of contact explain the low forces behavior. We test the consistency of our experimental findings results with both the theoretical expectations and with the experimental determination of the force-displacement dependence. We show, moreover, that the main damping process originates in solid friction.

Shock wave propagation in vibrofluidized granular materials

Shock wave formation and propagation in vertically vibrated quasi-two-dimensional granular materials are studied by digital high speed photography. Steep density and temperature wave fronts form at the bottom of the granular layer when the layer collides with vibrating plate. Then the fronts propagate upwards through the layer. The temperature front is always in the transition region between the upward and downward granular flows. The effects of driving parameters and particle number on the shock are also explored.

Self-demodulation of elastic waves in a one-dimensional granular chain

The self-demodulation process in a nonlinear granular chain of identical beads is studied analytically and numerically. In such a medium, in accordance with the dispersion relation, longitudinal waves that have a frequency higher than the so-called cutoff frequency of the chain are evanescent. Here, we study the influence on the self-demodulation process of the transition from the propagative to the evanescent regime in pump wave propagation that takes place when the pump frequency increases. An analytical solution in discrete coordinates is derived for the case of two primary frequencies mixing into a single difference frequency. This solution is then numerically integrated in order to analyze the demodulation of the acoustic wave packet (i.e., of the harmonic acoustic wave modulated in a pulse mode). Temporal demodulated profiles can be strongly sensitive to the regime (propagative or evanescent) of primary wave transport. This model allows us to detect the cutoff frequency of longitudinal elastic waves in the chain, without receiving the primary waves, but receiving the low frequency nonlinearly radiated signal. The roles of frequency dependent attenuation, velocity dispersion, and observation distance are analyzed.