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.
Valenza
John
J
Schlumberger-Doll Research, One Hampshire Street, Cambridge, Massachusetts 02139, USA.
Hsu
Chaur-Jian
CJ
Ingale
Rohit
R
Gland
Nicolas
N
Makse
Hernán A
HA
Johnson
David Linton
DL
D000162:Acoustics; D003102:Colloids / Q000737:chemistry*; D003198:Computer Simulation; D004735:Energy Transfer; D008956:Models, Chemical; D014732:Vibration
D003102:Colloids