A Cell Model for the Acoustical Properties of Packings of Spheres
A new relationship between the complex density and the complex compressibility of media containing high volume fractions of spherical particles has been derived using cell models and a coupled phase approach. The combination of this relationship with an analytical expression for complex density gives a model which predicts bulk acoustic characteristics of granular materials using only three parameters: porosity, mean particle radius and an adjustable cell radius. Use of the cell radius corresponding to that of the sphere circumscribing a unit cell of a cubic lattice arrangement is proposed. By this means, the complete cell model requires only porosity and mean particle radius. Alternatively, the new similarity relationship has been combined with a semi-empirical model for the frequency dependence of dynamic density and its extension to the frequency dependence of dynamic compressibility for granular materials. The resulting model requires the knowledge of porosity, tortuosity, dc permeability (flow resistivity), mean particle radius and the cell radius. Predictions of the two models are compared with data for the acoustical properties of stacked spherical particles.
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Document Type: Research Article
Publication date: March 1, 2001
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- Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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