A self-consistent approach for the acoustical modeling of vegetal wools

Abstract

Vegetal wools have the capacity to store atmospheric carbon dioxyde, one of the main gases responsible for climate change. So, these insulating materials are used as key elements for green buildings. Moreover, vegetal wools present high sound absorption level performances contributing to the acoustic comfort of indoor living spaces. These properties are directly related to the morphology and the size of their vegetal fibres. Thus, to take their microstructural specificities into account for the modeling of their sound absorption properties, a micro-macro homogenization approach based on a cylindrical geometry is developed. This modeling method, based on a mix between Homogenization of Periodic Media (HPM) and Self-Consistent Method (SCM), is called SCMcyl. The macroscopic behaviour laws of materials are rigorously obtained by using HPM. Then, the SCM leads to the establishment of two possible analytical solutions (a velocity approach v and a pressure approach p) under the fundamental assumption of the energy equivalence between a generic cylindrical inclusion, representative of the vegetal wools physical and geometrical properties at microscopic scale, and the homogeneous equivalent medium at the macroscopic scale. The two modeling approaches developed in this paper, SCMcyl−v and SCMcyl−p, can be used to determine the sound absorption of fibrous materials using only two parameters, an equivalent fibre radius value and the material porosity. Finally, these solutions are validated for the vegetal wools case by comparison with experimental measurements.