Computation of acoustic properties and design guidelines of periodic Biot-modeled foams

This paper aims at consolidating research dealing with vibroacoustics of periodic media. The main goal of this work is to develop and to validate tools for the design of global vibroacoustic treatments based on periodic patterns, allowing passive control of acoustic paths in layered concepts. To this aim, some enhancements are introduced to the state of the art on the study and the design of Biot-modeled foams, in order to obtain desired acoustics performances through embedded periodic inclusions. At first, the properties of the studied acoustic package, constituted by a poro-elastic 3D unit cell, is introduced. Successively, through the use of the acoustic-structure coupling that comes from the implementation of Biot model, a non-rigid inclusion test campaign is carried out by considering some solid (but still non-perfectly-rigid) inclusions in a 3D-modeled unit cell; in particular, six setups are discussed herein. Then, some design guidelines are provided in order to predict at which frequency the first performance peak appears, together with its amplitude, as functions of unit cell dimensions, airflow resistivity, tortuosity, viscous and thermal characteristic lengths, frame density, Young modulus and loss factor; conversely, it is shown also the link between the unit cell dimensions and the first performance peak amplitude as functions of the design frequency.