Definition of analytical models of non-acoustical parameters for randomly-assembled symmetric and asymmetric radii distribution in parallel fiber structures

Abstract

Fibrous materials for acoustical applications have been extensively studied over the past years. A considerable number of experimental tests have been carried out as a function of fiber geometrical characteristics (for example, overall density, fiber diameter and density, open porosity, etc.) in order to determine analytical formulations for the prediction of physical parameters, primarily the airflow resistivity. Due to the increase of computational capabilities micro-to-macro structure approach is the subject of current research in order to determine transport and acoustic properties starting from certain arrangements of fiber in space. Almost all research assumes fiber having the same radius with regular or random position within a representative volume of material. To this end, the aim of the present paper is to provide a revision of existing analytical formulations of non-acoustical parameters for two-dimensional structures having random positioning in space and symmetric and asymmetric distribution of radii. Proposed formulations will be compared with existing models and finite element simulations.