Sohbi Sahraoui

Convergence of poroelastic finite elements based on Biot displacement formulation

The convergence of linear poroelastic elements based on Biot displacement formulation is investigated. The aim is to determine a mesh criterion that provides reliable results under a given frequency limit. The first part deals with 1D applications for which resonance frequencies can be related to Biot wavelengths. Their relative contributions to the motion are given in order to determine if the mesh criteria for monophasic media are suitable for poroelastic media. The imposition of six linear elements per wavelength is found for each Biot wave as a primary condition for convergence. For 3D applications, convergence rules are derived from a generic configuration, i.e., a clamped porous layer. Because of the complex deformation, the previous criterion is shown to be insufficient. Influence of the coupling between the two phases is demonstrated.

Frequency dependence of elastic properties of acoustic foams

Polyurethane (PU) and other plastic foams are widely used as passive acoustic absorbers. For optimal design, it is often necessary to know the viscoelastic properties of these materials in the frequency range relevant to their application. A nonresonance technique (dynamic stiffness) based on a forced vibrations procedure is used to investigate the frequency dependent complex shear modulus of a PU foam. This modulus is first measured, in a quasistatic configuration, in the frequency range (0.016–16 Hz) at different temperatures between 0 and 20 °C. It is afterwards predicted over a wide frequency range (0.01–3000 Hz) using the frequency-temperature superposition principle. The validation of this principle is discussed through quasistatic experiments. Under the assumption that Poisson’s ratio of polymeric foams is real and frequency independent on the frequency range used, the frequency dependence of the complex shear modulus obtained is used to predict the complex stiffness of the acoustic foam on a wide ...

Investigation and modelling of damping in a plate with a bonded porous layer

Behavior of a poro-elastic material bonded onto a vibrating plate is investigated in the low-frequency range. From the analysis of dissipation mechanisms, a model accounting for damping added by the porous layer on the plate is derived. This analysis is based on a 3-D finite element formulation including poro-elastic elements based on Biot displacement theory. First, dissipated powers related to thermal, viscous and viscoelastic dissipation are explicited. Then a generic configuration (simply-supported aluminium plate with a bonded porous layer and mechanical excitation) is studied. Thermal dissipation is found negligible. Viscous dissipation can be optimized as a function of airflow resistivity. It can be the major phenomenon within soft materials, but for most foams viscoelastic dissipation is dominant. Consequently an equivalent plate model is proposed. It includes shear in the porous layer and only viscoelasticity of the skeleton. Excellent agreement is found with the full numerical model.

Influence of static compression on mechanical parameters of acoustic foams

The modification of elastic properties of compressed acoustic foams is investigated. The porous sample is first submitted to a static compression and then to a dynamic excitation of smaller amplitude, corresponding to acoustical applications. The static compression induces the modification of the dynamic elastic parameters of the material. This work focuses on Youngs modulus. The variation is measured with two different experimental methods: The classical rigidimeter and an absorption measurement. The effective Youngs modulus is directly measured with the first method and is indirectly determined through the quarter-wave length resonance of the frame with the second one. The results of the two measurements are compared and give similar tendencies. The variation of the dynamic Youngs modulus as a function of the degree of compression of the sample is shown to be separated in several zones. In the zones associated with weak compression (those usually zones encountered in practice), the variation of the effective Youngs modulus can be approximated by a simple affine function. The results are compared for different foams. A simple model of the dependency of the Youngs modulus with respect to the static degree of compression is finally proposed for weak compressions.

Vibrations of Poroelastic Plates: Mixed Displacement-Pressure Modelisation and Experiments

This paper presents the equations of motion of air saturated rectangular poroelastic plates. The model is based on a mixed displacement-pressure formulation of Biots theory. Two equations of motion are obtained and solved with the Galerkin method for any boundary conditions. These equations take into account the solid-fluid coupling effects. Simulations of the bending vibrations of a rectangular water saturated sandstone and air saturated acoustic foam are performed for studying the influence of the viscous damping through the permeability. Experiments on clamped plates made of low density acoustic materials (fibrous and polyurethane foam) are used to check the limits of this model. On these materials the structural damping is predominant compared to viscous damping.

Normalized stiffness ratios for mechanical characterization of isotropic acoustic foams

This paper presents a method for the mechanical characterization of isotropic foams at low frequency. The objective of this study is to determine the Youngs modulus, the Poissons ratio, and the loss factor of commercially available foam plates. The method is applied on porous samples having square and circular sections. The main idea of this work is to perform quasi-static compression tests of a single foam sample followed by two juxtaposed samples having the same dimensions. The load and displacement measurements lead to a direct extraction of the elastic constants by means of normalized stiffness and normalized stiffness ratio which depend on Poissons ratio and shape factor. The normalized stiffness is calculated by the finite element method for different Poisson ratios. The no-slip boundary conditions imposed by the loading rigid plates create interfaces with a complex strain distribution. Beforehand, compression tests were performed by means of a standard tensile machine in order to determine the appropriate pre-compression rate for quasi-static tests.

VIBROACOUSTIC BEHAVIOR OF A POROUS LAYER BONDED ONTO A PLATE

Damping added by a poroelastic material on a vibrating plate is investigated. The goal is to understand dissipation mechanisms within the porous layer in order to optimize damping. This analysis is based on a 3-D finite element formulation including poroelastic elements. First, dissipated powers related to thermal, viscous and viscoelastic dissipation are explicited. Then a generic configuration (simply supported aluminium plate with a bonded porous layer and mechanical excitation) is studied. Thermal dissipation is found negligible. Viscous dissipation can be optimized as a function of air flow resistivity. It is the major phenomenon within glasswool materials, whereas viscoelastic dissipation is dominant for polymeric foams. Finaly, a model of equivalent plate is proposed. It includes shear in the porous layer and only viscoelasticity of the squeleton. Good results are found for foam materials.

Modeling of porous material added damping on a vibrating plate

Porous materials like plastic foam are well known for their ability to absorb sound. When bonded onto a vibrating structure they may add damping. Their damping performance is investigated here. The generic configuration is a free aluminum plate (28 cm×22 cm×1 mm) mechanically excited (20–500 Hz), damped by a 1‐ to 5‐cm‐thick foam layer. The analysis of porous material behavior, based on Biot–Allard theory [J.‐F. Allard (Chapman and Hall, 1993)] shows that damping is mainly related to the frame viscoelasticity. A formulation of an equivalent plate, substituting the porous layer by a monophasic viscoelastic material, is presented. This formulation gives behavior indicators, like amount of added stiffness and damping. It also accelerates the computation of the structure vibration, compared with a 3‐D finite element code, including poroviscoelastic elements [R. Panneton and N. Atalla, J. Acoust. Soc. Am. 100, 346–354 (1996)]. Good agreement is found with both the complete discretized formulation and experimen...