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.

DISPERSION STUDY OF AXIALLY SYMMETRIC WAVES IN CYLINDRICAL BONE FILLED WITH MARROW

2011 ◽  
Vol 04 (01) ◽  
pp. 109-118 ◽  
Author(s):  
P. MALLA REDDY ◽  
B. SANDHYA RANI ◽  
M. TAJUDDIN
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Velocity Versus ◽  
Biot’S Theory ◽  
Axially Symmetric ◽  
Analytical Results ◽  
Versus Ratio ◽  
Frame Work ◽  
Impermeable Boundary ◽  
Existing Data

Bone filled with marrow is modeled as poroelastic bore filled with a fluid in the frame work of Biot's theory in wave propagation phenomena. Axially symmetric unattentuated waves are considered. Frequency equations are derived in the cases of permeable boundary and impermeable boundary, and are found to be dispersive. The existing data of bony materials has been exploited. Phase velocity versus ratio of wavelength to bone diameter curves are plotted. From this model and analytical results, some conclusions are drawn.

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

scholarly journals Effect of Rotation on Wave Propagation in Hollow Poroelastic Circular Cylinder

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
A. M. Abd-Alla ◽  
S. Alqosami
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Phase Velocity ◽  
Frequency Equation ◽  
Wave Number ◽  
Elastic Behavior ◽  
Hollow Circular Cylinder ◽  
Poroelastic Material ◽  
Phase Velocity And Attenuation ◽  
Frequency Phase

The objective of this paper is to study the effect of rotation on the wave propagation in an infinite poroelastic hollow circular cylinder. The frequency equation for poroelastic hollow circular cylinder is obtained when the boundaries are stress free and is examined numerically. The frequency, phase velocity, and attenuation coefficient are calculated for a pervious surface for various values of rotation, wave number, and thickness of the cylinder which are presented for nonaxial symmetric vibrations for a pervious surface. The dispersion curves are plotted for the poroelastic elastic behavior of the poroelastic material. Results are discussed for poroelastic material. The results indicate that the effect of rotation, wave number, and thickness on the wave propagation in the hollow poroelastic circular cylinder is very pronounced.

PROPAGATION OF LOVE WAVE IN FIBER-REINFORCED MEDIUM OVER A NONHOMOGENEOUS HALF-SPACE

2014 ◽  
Vol 06 (05) ◽  
pp. 1450050 ◽  
Author(s):  
SANTIMOY KUNDU ◽  
SHISHIR GUPTA ◽  
SANTANU MANNA ◽  
PRALAY DOLAI
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Dispersion Equation ◽  
Half Space ◽  
Love Wave ◽  
Graphical Representation ◽  
Separation Of Variables ◽  
Classical Equation ◽  
Wave Number ◽  
Fiber Reinforced

The present paper is devoted to study the Love wave propagation in a fiber-reinforced medium laying over a nonhomogeneous half-space. The upper layer is assumed as reinforced medium and we have taken exponential variation in both rigidity and density of lower half-space. As Mathematical tools the techniques of separation of variables and Whittaker function are applied to obtain the dispersion equation of Love wave in the assumed media. The dispersion equation has been investigated for three different cases. In a special case when both the media are homogeneous our computed equation coincides with the classical equation of Love wave. For graphical representation, we used MATLAB software to study the effects of reinforced parameters and inhomogeneity parameters. It has been observed that the phase velocity increases with the decreases of nondimensional wave number. We have also seen that the phase velocity decreases with the increase of reinforced parameters and inhomogeneity parameters. The results may be useful to understand the nature of seismic wave propagation in fiber reinforced medium.

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.

Circumferential Waves of Infinite Hollow Poroelastic Cylinders

2005 ◽  
Vol 73 (4) ◽  
pp. 705-708 ◽  
Author(s):  
M. Tajuddin ◽  
S. Ahmed Shah
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Phase Velocity ◽  
Elastic Solid ◽  
Frequency Equation ◽  
Saturated Porous Media ◽  
Biot’S Theory ◽  
Phase Velocity And Attenuation ◽  
Special Case ◽  
Circumferential Waves

Employing Biot’s theory of wave propagation in liquid saturated porous media, the frequency equation of circumferential waves for a permeable and an impermeable surface of an infinite hollow poroelastic cylinder is derived in the presence of dissipation and then discussed. Phase velocity and attenuation are determined for different dissipations and then discussed. By ignoring liquid effects, the results of purely elastic solid are obtained as a special case.

The effect of boundaries on wave propagation in a liquid-filled porous solid: II. Love waves in a porous layer

1961 ◽  
Vol 51 (1) ◽  
pp. 51-59
Author(s):  
H. Deresiewicz
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Viscous Liquid ◽  
Porous Layer ◽  
Unit Volume ◽  
Transcendental Equation ◽  
Love Waves ◽  
Wave Number ◽  
Velocity Of Propagation ◽  
Approximate Scheme

Abstract The transcendental equation is derived relating frequency and phase velocity of propagation of Love waves in a porous layer containing a viscous liquid. This equation, being complex, can be satisfied only if the wave number of the motion is complex, indicating that the disturbance is dissipative. The general expression being intractable analytically, an approximate scheme is employed to determine the phase velocity and measure of dissipation valid for porous materials in which the mass (per unit volume of aggregate) of the interstitial liquid is smaller than that of the solid.

Wave propagation in fluid-conveying viscoelastic carbon nanotubes under longitudinal magnetic field with thermal and surface effect via nonlocal strain gradient theory

2017 ◽  
Vol 31 (08) ◽  
pp. 1750069 ◽  
Author(s):  
Yaxin Zhen ◽  
Lin Zhou
Keyword(s):  
Magnetic Field ◽  
Carbon Nanotubes ◽  
Wave Propagation ◽  
Phase Velocity ◽  
Longitudinal Magnetic Field ◽  
Surface Effect ◽  
Strain Gradient Theory ◽  
Wave Number ◽  
Gradient Theory ◽  
Nonlocal Strain Gradient

Based on nonlocal strain gradient theory, wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes (SWCNTs) is studied in this paper. With consideration of thermal effect and surface effect, wave equation is derived for fluid-conveying viscoelastic SWCNTs under longitudinal magnetic field utilizing Euler–Bernoulli beam theory. The closed-form expressions are derived for the frequency and phase velocity of the wave motion. The influences of fluid flow velocity, structural damping coefficient, temperature change, magnetic flux and surface effect are discussed in detail. SWCNTs’ viscoelasticity reduces the wave frequency of the system and the influence gets remarkable with the increase of wave number. The fluid in SWCNTs decreases the frequency of wave propagation to a certain extent. The frequency (phase velocity) gets larger due to the existence of surface effect, especially when the diameters of SWCNTs and the wave number decrease. The wave frequency increases with the increase of the longitudinal magnetic field, while decreases with the increase of the temperature change. The results may be helpful for better understanding the potential applications of SWCNTs in nanotechnology.

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.

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