Elastodynamics of a Two-Dimensional Square Lattice With Entrained Fluid—Part I: Comparison With Biot's Theory

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Alessandro Spadoni
Keyword(s):  
Wave Propagation ◽  
Shear Waves ◽  
Wave Spectrum ◽  
Fluid Pressure ◽  
Element Model ◽  
Square Lattice ◽  
Porous Solids ◽  
Cellular Solids ◽  
Biot’S Theory ◽  
Biot's Theory

In the present paper, the performance of Biot's theory is investigated for wave propagation in cellular and porous solids with entrained fluid for configurations with well-known drained (no fluid) mechanical properties. Cellular solids differ from porous solids based on their relative density ρ*<0.3. The distinction is phenomenological and is based on the applicability of beam (or plate) theories to describe microstructural deformations. The wave propagation in a periodic square lattice is analyzed with a finite-element model, which explicitly considers fluid-structure interactions, structural deformations, and fluid-pressure variations. Bloch theorem is employed to enforce symmetry conditions of a representative volume element and obtain a relation between frequency and wavevector. It is found that the entrained fluid does not affect shear waves, beyond added-mass effects, so long as the wave spectrum is below the pores' natural frequency. One finds strong dispersion in cellular solids as a result of resonant scattering, in contrast to Bragg scattering dominant in porous media. Configurations with 0.0001≤ρ*≤1 are investigated. One finds that Biot's theory, derived from averaged microstructural quantities, well estimates the phase velocity of pressure and shear waves for cellular porous solids, except for the limit ρ*→1. For frequencies below the first resonance of the lattice walls, only the fast-pressure mode of the two modes predicted by Biot's theory is found. It is also shown that homogenized models for shear waves based on microstructural deformations for drained conditions agree with Biot's theory.

scholarly journals Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Rajitha Gurijala ◽  
Malla Reddy Perati
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Spherical Shell ◽  
Wave Number ◽  
Biot’S Theory ◽  
Impervious Surfaces ◽  
Axially Symmetric ◽  
Spherical Shells ◽  
Biot's Theory

This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease.

Wave propagation in cancellous bone in terms of Biot's theory

2008 ◽  
Vol 123 (5) ◽  
pp. 3513-3513
Author(s):  
Michal Pakula ◽  
Frederic Padilla ◽  
Mariusz Kaczmarek ◽  
Pascal Laugier
Keyword(s):  
Wave Propagation ◽  
Cancellous Bone ◽  
Biot’S Theory ◽  
Biot's Theory

Elasto-Dynamic Behavior of a Two-Dimensional Square Lattice With Entrained Fluid II: Microstructural and Homogenized Models

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Alessandro Spadoni
Keyword(s):  
Relative Density ◽  
Coupled System ◽  
Element Model ◽  
Square Lattice ◽  
Porous Solids ◽  
Cellular Solid ◽  
Resonance Frequencies ◽  
Shear Modes ◽  
Structural Deformations ◽  
Analysis Of Dispersion

This paper presents a detailed study of the pressure waves and effective mechanical properties of a closed-cell cellular solid with entrained fluid. Plane-harmonic-waves are analyzed in a periodic square with a finite-element model of a representative-volume element, which explicitly considers fluid-structure interactions, structural deformations, and the fluid dynamics of entrained fluid. The wall, cavity, and coupled-system resonance frequencies are identified as key parameters that describe the propagation characteristics. A tube-piston model based on computed microstructural deformations allows us to determine the effective stiffness tensor of an equivalent continuum at the macroscale. The analysis of dispersion surfaces indicates a single isotropic pressure mode for frequencies below resonance of the lattice walls, unlike Biot's theory which predicts two pressure modes. Shear modes are instead strongly anisotropic for all values of relative density ρ* describing both cellular ρ*<0.3 and porous solids ρ*≥0.3. The dependence of the pressure wave phase velocity on the relative density is analyzed for varying properties of the entrained fluid. Depending on the relative density and mass coupling of the solid and fluid phases, the microstructural deformations can be of three types: bending, through-the-thickness, and the combination of the two. For heavy and stiff entrained fluid, the bending regime is confined to extremely small values of relative density, whereas for light fluid such as a gas, deformations are of the bending-type for ρ*<0.1. Through-the-thickness deformations appear only for the heavy entrained fluid for large values of ρ*.

IN VITROACOUSTIC WAVE PROPAGATION IN HUMAN AND BOVINE CANCELLOUS BONE AS PREDICTED BY BIOT'S THEORY

2008 ◽  
Vol 08 (02) ◽  
pp. 183-201 ◽  
Author(s):  
LUIS CARDOSO ◽  
ALAIN MEUNIER ◽  
CHRISTIAN ODDOU
Keyword(s):  
Wave Propagation ◽  
Wave Velocity ◽  
Cancellous Bone ◽  
Slow Wave ◽  
Mass Density ◽  
Bone Mass Density ◽  
Biot’S Theory ◽  
Structural Index ◽  
Biot's Theory ◽  
Wave Velocities

Recent in vitro studies have provided evidence of the propagation of two different longitudinal wave modes at ultrasonic frequencies in cancellous bone. The genesis of these two plane waves in fluid-saturated porous media is predicted by the poroelastic approach to wave propagation originally developed by Biot. However, wave velocity is usually analyzed as a function of bone mass density only; therefore, the influence of the cancellous bone microstructure over the wave velocity is not taken into account. In the present study, a descriptor of the microstructure is considered in Biot's theory. This model is used to evaluate the large experimental variability of both fast and slow wave velocities measured on randomly oriented human and bovine cancellous bone samples. The role of the anisotropic solid structure and fluid in the behavior of fast and slow wave velocities is examined. Experimental and theoretically predicted velocities are found in close agreement when analyzed as a function of both porosity and structural index. This model has the potential to be used to determine an acoustically derived structural index in cancellous bone.

scholarly journals Extension of Biot’s theory of wave propagation to frozen porous media

1994 ◽  
Vol 96 (6) ◽  
pp. 3753-3768 ◽  
Author(s):  
Ph. Leclaire ◽  
F. Cohen‐Ténoudji ◽  
J. Aguirre‐Puente
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Biot’S Theory ◽  
Biot's Theory
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