Mathematical Modeling of Porous Medium for Sound Absorption Simulations: Application of Multi-Scales and Homogenization
Journal of Applied Mathematics and Physics
The modeling of porous medium has many applications whose techniques can be used in the fields of automotive, aerospace, oil exploration, and biomedical. This work concentrates on the Noise and Vibration (NV) development of automotive interiors but the ideas can be translated to the aforementioned areas. The NV development requires the setting of NV targets at different levels. These targets are then translated to TL (Transmission Loss), IL (Insertion Loss), and Alpha (absorption) performance.
... herefore, the ability to manage an efficient product development cycle, that entails analyzing vibro-acoustic environments, hinges on the premise that accurate TL, IL, or Alpha values pertaining to the different multi-layered porous materials can be calculated. Thus, there is a need to have a thorough understanding of the physics behind the energy dissipating mechanism that includes the effects of the fluid meandering through the pores of the material. The goal of this series is to model the acoustic and dynamic coupling via multi-scale and homogenizations techniques, thus subsequently understand where to incorporate the concepts of dynamic tortuosity, viscous and thermal permeability, as well as viscous and thermal lengths. This study will allow the ability to get a better understanding of the underlying processes and also provides tools to create practical concepts for determining the coefficients of the macroscopic equations. This will assist in attaining novel ideas for NV absorption and insulation. This body of work takes advantage of tensor notation and tensor calculus. This notational generalization makes it easy to describe the physics regardless of the A. Teagle-Hernandez et al.