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Abstract
The ability to quantify and predict the energy absorption/transmission characteristics of multi-layered porous medium is imperative if one is involved in the automotive, launch vehicle, commercial aircraft, architectural acoustics, petroleum exploration, or even in modeling human tissue. A case in point, the first four aforementioned fields rely on effective Noise and Vibration (NV) development for their commercial success. NV development requires the setting of NV targets at different system levels. The targets are then translated to Transmission Loss (TL), Insertion Loss (IL), and absorption (Alpha) performance for the multi-layered porous materials being utilized. Thus, it behooves to have a thorough understanding of the physics behind the energy dissipating mechanism of the material that entails the effects of the fluid meandering through the pores of the material and its interaction with the structural skeleton. In this section of the project the focus is on the thermal interchange that occurs within the porous medium. Via the acoustic modeling at the micro/macro level it is shown how this thermal exchange affects the acoustic compressibility within the porous material. In order to obtain a comprehensive approach the ensuing acoustic modeling includes the effects due to relaxation process, thus bulk viscosity and instantaneous entropy functions (effects due to vibration of diatomic molecules of air) are incorporated into the equation. The instantaneous entropy functions are explained by means of the Boltzmann’s distribution, partition function, and quantum states. The concept of thermal length and its connection to thermal permeability is clarified. Lastly, the results for TL calculations employing the aforementioned thermal exchange into the Transfer Matrix Method with finite size correction, (FTMM), pertaining to a simple multi-layered material is compared with experimentally obtained data.
Highlights
Teagle et al [1] derived a coupled set of fluid/structure equations for a porous medium applying asymptotic and homogenization techniques
The ability to quantify and predict the energy absorption/transmission characteristics of multi-layered porous medium is imperative if one is involved in the automotive, launch vehicle, commercial aircraft, architectural acoustics, petroleum exploration, or even in modeling human tissue
The targets are translated to Transmission Loss (TL), Insertion Loss (IL), and absorption (Alpha) performance for the multi-layered porous materials being utilized
Summary
Teagle et al [1] derived a coupled set of fluid/structure equations for a porous medium applying asymptotic and homogenization techniques. Via this modeling it is established in [1] that there are mainly 3 modes of energy transformation: 1) The first mode is through the connection between the micro and macro structural framework of the porous skeleton, 2) the second is via the viscous boundary layer, and 3) the third interaction is through thermal (entropy) boundary layer. There is a boundary layer where the flow experiences changes in entropy, a loss/gain of energy due to thermal exchange will occur This thermal exchange changes the acoustic bulk modulus at certain frequencies and in turn changing the speed of sound. The bulk of this work is to derive a frequency dependent general expression for
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