Inverse acoustical characterization of open cell porous media using impedance tube measurements
Keywords:Acoustic impedance, Algorithms, Mathematical models, Optimization, Porosity, Porous materials, Viscous flow, Champoux-Allard model, Inverse characterization methods, Particular absorbing materials, Thermal characteristics
AbstractUnlike porous models developed for particular absorbing materials and frequency ranges, the Johnson-Champoux-Allard model is a generalized model for sound propagation in porous materials over a wide range of frequencies. This model is nowadays used widely across the acoustic research community and by industrial sector. However to use this model, the knowledge, particularly, of the intrinsic material properties defining the model is necessary. Using the proposed porous model and with the knowledge of the intrinsic properties, the calculation of the desired acoustical indicators as well as the design and optimization of several acoustic treatments for noise reduction can be done efficiently and rapidly. The model of Johnson-Champoux-Allard is based on five intrinsic properties of the porous medium: the flow resistivity, the porosity, the tortuosity, the viscous characteristic length, and the thermal characteristic length. While the open porosity and airflow resistivity can be directly measured without great difficulties, the direct measurements of the three remaining properties are usually complex, less robust, or destructive. To circumvent the problem, an inverse characterization method based on impedance tube measurements is proposed. It is shown that this inverse acoustical characterization can yield reliable evaluations of the tortuosity, and the viscous and thermal characteristic lengths. The inversion algorithm contains an optimization process and hence it is verified that the identified optimal three parameter, even though derived from a mathematical optimum for a given experimental configuration (sample's thickness, measured frequency range), are the intrinsic properties of the characterized porous material.
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