Experiments on stress dependent borehole acoustic waves.

In the laboratory setup, a borehole traverses a dry sandstone formation, which is subjected to a controlled uniaxial stress in the direction perpendicular to the borehole axis. Measurements are made in a single loading-unloading stress cycle from zero to 10 MPa and then back down to zero stress. The applied stress and the presence of the borehole induce anisotropy in the bulk of the material and stress concentration around the borehole, both azimuthally and radially. Acoustic waves are generated and detected in the water-filled borehole, including compressional and shear headwaves, as well as modes of monopole, dipole, quadrupole, and higher order azimuthal symmetries. The linear and non-linear elastic parameters of the formation material are independently quantified, and utilized in conjunction with elastic theories to predict the characteristics of various borehole waves at zero and finite stress conditions. For example, an analytic theory is developed which is successfully used to estimate the changes of monopole tube mode at low frequency resulted from uniaxial stress, utilizing the measured material third order elasticity parameters. Comparisons between various measurements as well as that between experiments and theories are also presented.

Effect of granular media on the vibrational response of a resonant structure: theory and experiment.

The acoustic response of a structure that contains a cavity filled with a loose granular material is analyzed. The inputs to the theory are the effective masses of each subsystem: that of the empty-cavity resonating structure and that of the granular medium within the cavity. This theory accurately predicts the frequencies, widths, and relative amplitudes of the various flexural mode resonances observed with rectangular bars, each having a cavity filled with loose tungsten granules. Inasmuch as the dominant mechanism for damping is due to adsorbed water at the grain-grain contacts, the significant effects of humidity on both the effective mass of the granular medium as well as on the response of the grain-loaded bars are monitored. Here, depending upon the humidity and the preparation protocol, it is possible to observe one, two, or three distinct resonances in a wide frequency range (1-5 kHz) over which the empty bar has but one resonance. These effects are understood in terms of the theoretical framework, which may simplify in terms of perturbation theories.

Dynamic effective mass of granular media.

We develop the concept of frequency dependent effective mass, M[over ](omega), of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of M[over ](omega) provide signatures of the dissipation of acoustic modes, elasticity, and aging effects in the granular medium. We perform humidity controlled experiments and interpret the data in terms of a continuum model and a "trap" model of thermally activated capillary bridges at the contact points. The results suggest that attenuation of acoustic waves in granular materials can be influenced significantly by the kinetics of capillary condensation between the asperities at the contacts.

Dynamic effective mass of granular media and the attenuation of structure-borne sound.

We report a theoretical and experimental investigation into the fundamental physics of why loose granular media are effective deadeners of structure-borne sound. Here, we demonstrate that a measurement of the effective mass, M(omega), of the granular medium is a sensitive and direct way to answer the question: what is the specific mechanism whereby acoustic energy is transformed into heat? Specifically, we apply this understanding to the case of the flexural resonances of a rectangular bar with a grain-filled cavity within it. The pore space in the granular medium is air of varying humidity. The dominant features of M(omega) are a sharp resonance and a broad background, which we analyze within the context of simple models. We find that: (a) on a fundamental level, dampening of acoustic modes is dominated by adsorbed films of water at grain-grain contacts, not by global viscous dampening or by attenuation within the grains. (b) These systems may be understood, qualitatively, in terms of a height-dependent and diameter-dependent effective sound speed [approximately 100-300 (m.s-1)] and an effective viscosity [approximately 5x10(4) Poise]. (c) There is an acoustic Janssen effect in the sense that, at any frequency, and depending on the method of sample preparation, approximately one-half of the effective mass is borne by the side walls of the cavity and one-half by the bottom. (d) There is a monotonically increasing effect of humidity on the dampening of the fundamental resonance within the granular medium which translates to a nonmonotonic, but predictable, variation in dampening within the grain-loaded bar.