Data processing: structural design – modeling – simulation – and em – Simulating nonelectrical device or system
Reexamination Certificate
1997-05-19
2001-07-03
Teska, Kevin J. (Department: 2763)
Data processing: structural design, modeling, simulation, and em
Simulating nonelectrical device or system
C703S001000, C703S002000
Reexamination Certificate
active
06256600
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to the design of homogeneous porous materials and acoustical systems. More particularly, the present invention pertains to the prediction and optimization of acoustical properties for homogeneous porous materials and multiple component acoustical systems.
BACKGROUND OF THE INVENTION
Different types of materials are used in many applications, such as noise reduction, thermal insulation, filtration, etc. For example, fibrous materials are often used in noise control problems for the purpose of attenuating the propagation of sound waves. Fibrous materials may be made of various types of fibers, including natural fibers, e.g., cotton and mineral wool, and artificial fibers, e.g., glass fibers and polymeric fibers such as polypropylene, polyester and polyethylene fibers. The acoustical properties of many types of materials are based on macroscopic properties of the bulk materials, such as flow resistivity, tortuosity, porosity, bulk density, bulk modulus of elasticity, etc. Such macroscopic properties are, in turn, controlled by manufacturing controllable parameters, such as, the density, orientation, and structure of the material. For example, macroscopic properties for fibrous materials are controlled by the shape, diameter, density, orientation and structure of fibers in the fibrous materials. Such fibrous materials may contain only a single fiber component or a mixture of several fiber components having different physical properties. In addition to the solid phase of the fiber components of the fibrous materials, a fibrous material's volume is saturated by fluid, e.g., air. Thus, fibrous materials are characterized as a type of porous material.
Various acoustical models are available for various materials, including acoustical models for use in the design of porous materials. Existing acoustical models for porous materials can generally be divided into two categories: rigid frame models and elastic frame models. The rigid models can be applied to porous materials having rigid frames, such as porous rock and steel wool. In a rigid porous material, the solid phase of the material does not move with the fluid phase, and only one longitudinal wave can propagate through the fluid phase within the porous materials. Rigid porous materials are typically modeled as an equivalent fluid which has complex bulk density and complex bulk modulus of elasticity. On the other hand, the elastic models can be applied to porous materials whose frame bulk modulus is comparable to that of the fluid within the porous materials, e.g., polyurethane foam, polyimide foam, etc. There are three types of waves that can propagate in an elastic porous material, i.e., two compressional waves and one rotational wave. The motions of the solid phase and the fluid phase of an elastic porous material are coupled through viscosity and inertia, and the solid phase experiences shear stresses induced by incident sound hitting the surface of the material at oblique incidence.
However, such rigid and elastic material models, some of which are described below, do not provide adequate modeling of limp fibrous materials, e.g., limp polymeric fibrous materials such as those comprised of, for example, polypropylene fibers and polyester fibers. The term “limp” as used herein refers to porous materials whose bulk elasticity, in vacuo, of the material is less than that of air.
The acoustical study of porous materials can be found as early as in Lord Rayleigh's study of sound propagation through a hard wall having parallel cylindrical capillary pores as described in Strutt et al.,
Theory of Sound,
Vol. II, Article 351, 2
nd
Edition, Dover Publications, NY (1945). Models based on the assumption that the frame of the porous material does not move with the fluid phase of the porous material are categorized as the rigid frame porous models. Various rigid porous material models have been proposed, including those described in Monna, A. F., “Absorption of Sound by Porous Wall,”
Physica
5, pp. 129-142 (1938); Morse, P. M, and Bolt, R. H., “Sound Waves in Rooms,”
Reviews of Modern Physics
16, pp. 69-150 (1944); and Zwikker, C. and Kosten, C. W.,
Sound Absorbing Materials,
Elsevier, N.Y. (1949). These models assumed, similar to Rayleigh's work, that the sound wave propagation within a rigid porous material can be described by using equations of motion and continuity of the interstitial fluid.
Rigid porous materials have also been modeled as an equivalent fluid having complex density, as described in Crandall, I. B.,
Theory of Vibrating Systems and Sound,
Appendix A, Van Nostrand Company, NY (1927), and having complex propagation constants when viscous and thermal effects were considered. In Delany, M. E. and Bazley, E. N., Acoustical Characteristics of Fibrous Absorbent Materials,”
National Physical Laboratories, Aerodynamics Division Report,
AC 37 (1969) the acoustical properties of rigid fibrous materials were studied differently. As described therein, a semi-empirical model of characteristic impedance and propagation coefficient as a function of frequency divided by flow resistance was established. This model was based on the measured characteristic impedance of fibrous materials having a wide range of flow resistance. In Smith, P. G. and Greenkorn, R. A., “Theory of Acoustical Wave Propagation in Porous Media,”
Journal of the Acoustical Society of America,
Vol. 52, pp. 247-253 (1972), the effects of porosity, permeability (inverse of flow resistivity), shape factor and other macrostructural parameters on acoustical wave propagation in rigid porous media were investigated. Further, some rigid porous material theories applied the concept of complex density while others used flow resistance. A comparison of these two approaches was described in Attenborough, K., “Acoustical Characteristics of Porous Materials,”
Physics Reports,
82(3), pp. 179-227 (1982). In summary, the rigid porous material models only allow one longitudinal wave to propagate through the rigid medium and the rigid frame is not excited by the fluid phase within the porous material. Such rigid porous material models do not adequately predict the acoustical properties of limp porous materials.
As opposed to rigid porous models, elastic models of porous materials have also been described. By considering the vibration of the solid phase of a porous material due to its finite stiffness, Zwikker and Kosten arrived at an elastic model taking into account the coupling effects between the solid and fluid phases as described in Zwikker, C. and Kosten, C. W.,
Sound Absorbing Materials,
Elsevier, N.Y. (1949). This work was extended by Kosten and Janssen, as described in Kosten, C. W. and Janssen, J. H., “Acoustical Properties of Flexible Porous Materials,”
Acoustica
7, pp. 372-378 (1957), which adapted the expression of complex density given by Crandall (1927) and complex density of air within pores given by Zwikker and Kosten (1949). A model that corrected the error of fluid compression effects in the work of Zwikker and Kosten (1949) and considered the oscillation of solid phase excited by normally incident sound has also been set forth. In this model, a fourth order wave equation indicated that two longitudinal waves can propagate in elastic porous materials as opposed to the single wave in rigid materials. In Shiau, N. M., “Multi-Dimensional Wave Propagation In Elastic Porous Materials With Applications To sound Absorption, Transmission and Impedance Measurement,” Ph.D. Thesis, School of Mechanical Engineering, Purdue University (1991), Bolton, J. S., Shiau, N. M., and Kang, Y. J., “Sound Transmission Through Multi-Panel Structures Lined With Elastic Porous Materials,”
Journal of Sound and Vibration
191, pp. 317-347 (1996), and Allard, J. F.,
Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials,
Elsevier Science Publishers Ltd., NY (1993) Biot's theory as described in Biot, M. A., “General Solutions of the Equations of Elasticity and Consolidation for a Porous Ma
Alexander Jonathan H.
Bolton John Stuart
Katragadda Srinivas
Lai Heng-Yi
3M Innovative Properties Company
Broda Samuel
Rogers James A.
Teska Kevin J.
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