Acoustic calculations utilizing the Transfer Matrix Method (TMM) occasionally underestimate the sound absorption performance of multi-layered porous material when compared to experimentally obtained data. This is particularly true when experimental data pertains to reverberant (Diffuse-Sabine) absorption. When there is a large impedance mismatch between the reverberant wall and the porous specimen, experimental data indicates Absorption Coefficients greater than 1, which defies the law of conservation of energy. It is hypothesized that the extra absorption is due to the diffraction of waves occurring at the edge of the tested materials, thus increasing the area where energy is absorbed. This contradiction of the law of energy is often referred to as the “edge effect”. This study aims in creating a tool to predict and further understand the edge effect phenomena within reverberation and anechoic rooms and to determine the true absorption performance of the multi-layered porous material by using the TMM, Green’s function, and the variational technique. A plate-foam system is used as a test bed; computation results are compared to experimental absorption data. The outcome of the research will support automobile, aerospace, and architectural companies in reaching sound and vibration targets required for new vehicle/building models.
The application of porous medium has a myriad of applications in different industries: automotive, aerospace, civil (commercial, residential), environmental noise control, and biomedical. In the past, design questions involving porous material were addressed with seat-of-the-pants decisions that led to multiple/iterative prototypes and experiments that were costly and time consuming. The objective, in this series of publications pertaining to porous medium, is to establish tools that will lead to effective and accurate simulations involving porous medium. In this third installment of this series the focus is on establishing the constitutive equations using tensors and then applying Transfer Matrix Method (TMM) to calculate diffuse field Transmission Loss (TL) across structures that comprises of layers of different porous medium. The constitutive equations are obtained by relating information regarding the micro-structure make-up to macro level properties. In order to apply the TMM, the equations for wave propagation across different mediums need to be developed and in turn represent these propagation properties in a matrix format. Additionally, the boundary condition between each layer type is defined in order to ensure numerical stability. The author's current research effort is running simulations for the automotive industry to predict NVH environments. Therefore, TL calculations pertaining to the materials that are utilized in the interior of automobiles are used, in this paper, as a test bed for the developed analytical tools. Case in point, the TL for a multi-layered material consisting of one panel and two different layers of foam is calculated and compared to experimental data. Future publication goals will be to apply these tools in the biomedical field; an
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