Energy flow analysis of equivalent fluid models for porous media

Based on a heat conduction analogy that enables the energy flow analysis (EFA) to describe the smoothed energy variations, the EFA has been applied to a variety of structures to predict vibrational responses at high-frequency regions. In this paper, energy equations in the form of heat conduction laws are derived to represent dilatational waves in rigid- and limp-frame porous media using equivalent fluid models. Homogeneous and inhomogeneous waves are considered. Within the EFA framework, the group velocity and loss factor included in the energy models for structures are replaced with the energy velocity and effective loss factor, respectively. The capabilities of the energy models are illustrated using configurations in which the porous layer backed by a rigid wall is in a normal and oblique incident sound field. The results of the numerical simulations confirm the feasibility of the energy model. From an energy perspective, the adequacy of using rigid- and limp-frame equivalent fluid models is also discussed. It is shown that the use of a rigid-frame equivalent model for predicting the energy distribution is more restrictive than predicting acoustic performance such as sound absorption.

A transverse isotropic equivalent fluid model combining both limp and rigid frame behaviors for fibrous materials

Due to the manufacturing process, some fibrous materials like glasswool may be transversely isotropic (TI): fibers are mostly parallel to a plane of isotropy within which material properties are identical in all directions whereas properties are different along the transverse direction. The behavior of TI fibrous material is well described by the TI Biot's model, but it requires one to measure several mechanical parameters and to solve the TI Biot's equations. This paper presents an equivalent fluid model that can be suitable for TI materials under certain assumptions. It takes the form of a classical wave equation for the pressure involving an effective density tensor combining both limp and rigid frame behaviors of the material. This scalar wave equation is easily amenable to analytical and numerical treatments with a finite element method. Numerical results, based on the proposed model, are compared with experimental results obtained for two configurations with a fibrous material. The first concerns the absorption of an incident plane wave impinging on a fibrous slab and the second corresponds to the transmission loss of a splitter-type silencer in a duct. Both configurations highlight the effect of the sample orientation and give an illustration of the unusual TI behavior for fluids.

Ironless transducer for measuring the mechanical properties of porous materials

This paper presents a measurement setup for determining the mechanical properties of porous materials at low and medium frequencies by extending toward higher frequencies the quasistatic method based on a compression test. Indeed, classical quasistatic methods generally neglect the inertia effect of the porous sample and the coupling between the surrounding fluid and the frame; they are restricted to low frequency range (<100 Hz) or specific sample shape. In the present method, the porous sample is placed in a cavity to avoid a lateral airflow. Then a specific electrodynamic ironless transducer is used to compress the sample. This highly linear transducer is used as actuator and sensor; the mechanical impedance of the porous sample is deduced from the measurement of the electrical impedance of the transducer. The loss factor and the Young's modulus of the porous material are estimated by inverse method based on the Biot's model. Experimental results obtained with a polymer foam show the validity of the method in comparison with quasistatic method. The frequency limit has been extended from 100 Hz to 500 Hz. The sensitivity of each input parameter is estimated in order to point out the limitations of the method.