Granular State Effects on Wave Propagation
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Granular State Effects on Wave Propagation Stephen R. Hostler and Christopher E. Brennen Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, U.S.A. ABSTRACT Sound and pressure wave propagation in a granular material is of interest not only for its intrinsic and practical value, but also because it provides a non-intrusive means of probing the state of a granular material. By examining wave speeds and attenuation, insight can be gained into the nature of the contacts between the particles. In the present paper, wave speeds and attenuation rates are first examined for a static granular bed for a variety of system parameters including particle size, composition and the overburden of the material above the measuring transducers. Agitation of the bed is then introduced by shaking the material vertically. This causes the bed to transition from a static granular state to a vibrofluidized state. The dilation of the bed allows for relative particle motion and this has a significant effect on the measured wave speeds and attenuation. Further, the fluid-like characteristics of the agitated bed distort the forcechain framework through which the waves are thought to travel. The consequences of bed consolidation, a natural result of shaking, are also examined. INTRODUCTION The characteristics of wave propagation in a granular material are of interest not only on a fundamental level, but also because they provide a means of probing otherwise unobservable quantities. Fundamentally, the wave speed can be related to the stiffness and density of a material. Early work established the critical dependence of the interaction at particle contacts on wave propagation in a granular material [1,2]. These works viewed the granular assembly as a continuum and formulated bulk properties based on contact properties such as the pressure and coordination number [3]. The continuum approach is appropriate when the characteristic wavelength of the sound is larger than the grain size, but as the wavelength approaches and becomes smaller than the granularity of the system, a different formulation is required [4]. In this limit, more recent work has looked at the details of the microstructure to examine the paths of wave propagation. In this view, waves travel through relatively few stressed particles chains that connect the source to the detector. It has been found that even minute displacements of particles can lead to breaking and reconnection of these chains, thus affecting the path through which waves travel [5]. Time fluctuations in the detected signal have been attributed to this rearrangement of the microstructure even by agents as weak as the wave itself [6,7]. The majority of work done on wave propagation in agitated granular material beds has been done in fluidized beds. In a summary of such experiments, the wave speed was found to decrease abruptly and then gradually increase with increasing agitation (excess fluidization velocity) and attenuation was found to primarily decrease. By
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