Poroelastic Hollow Cylinder Research Articles

Study of Magnetic Field Influence on Vibrations of Poroelastic Hollow Cylinder

Study of Magnetic Field Influence on Vibrations of Poroelastic Hollow Cylinder

On torsional vibrations of axial-symmetric infinite hollow poroelastic cylinders

On torsional vibrations of axial-symmetric infinite hollow poroelastic cylinders

Wave propagation in layered poroelastic cylinder in contact with fluid

The present paper investigates the propagation of time harmonic waves in a two layered hollow poroelastic cylinder in contact with inviscid fluids. The hollow poroelastic two layered cylinder is assumed to be infinite in axial direction. The outer and inner surfaces of the two layered cylinder are in contact with fluids and at the interface stresses and displacements are continuous. The frequency equation for wave propagation for a pervious is obtained. Non-dimensional phase velocity is computed as a function of wave number and presented graphically for two types of two layered cylinder for arbitrary parameters of the fluid in contact. Numerical results show that, in general, phase velocity is more in absence of outer fluid compared to the case of absence of inner fluid. Several other particular cases are discussed.

Analysis of radial vibrations in thick walled hollow poroelastic cylinder in the framework of Biot’s extension theory

Purpose In this paper, wave propagation in a poroelastic thick-walled hollow cylinder is investigated in the framework of Biot’s extension theory. Biot’s theory of poroelasticity is valid for isotropic porous solids saturated with non-viscous fluid. The bulk and shear viscosities are not considered in the classical Biot’s theory. Biot’s extension theory takes all these into an account. Biot’s extension theory is applied here to investigate the radial vibrations in thick-walled hollow poroelastic cylinder. The paper aims to discuss these issues. Design/methodology/approach By considering the stress-free boundaries, the frequency equation is obtained in the presence of dissipation. Limiting case when the ratio between thickness and inner radius is very small is investigated numerically. In the limiting case, the asymptotic expansions of Bessel functions are employed so that frequency equation is separated into two parts which gives attenuation coefficient and phase velocity. If the shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory. Findings For the numerical purpose, the solids Berea sandstone and bone are used. The results are presented graphically. Originality/value Radial vibrations of thick-walled hollow poroelastic cylinder are investigated in the framework of Biot’s extension theory. Due to the mathematical complexity, limiting case is considered. The complex valued frequency equation is discussed numerically which gives the attenuation coefficient and phase velocity. If shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory. The comparison has been made between the current results and that of classical results.

Radial vibrations of an infinitely long poroelastic composite hollow circular cylinder

The problem of radial vibrations of an infinitely long poroelastic composite hollow circular cylinder is solved by employing Biot’s theory of wave propagation in poroelastic media. A poroelastic composite hollow cylinder consists of two concentric poroelastic cylindrical layers both of which are made of different poroelastic materials with each poroelastic material as homogeneous and isotropic. The boundaries of composite hollow poroelastic cylinder are free from stress. The frequency equations of radial vibrations of poroelastic composite hollow cylinder with rigid core, poroelastic composite solid cylinder, poroelastic composite solid cylinder with rigid casing and of rigid core and poroelastic composite bore are derived as particular cases. Non-dimensional frequency is computed as a function of ratio of thickness to inner radius of core. The results are presented graphically for two types of poroelastic composite cylinders and then discussed.Keywords:Radial vibrations, Poroelasticity, Composite cylinder, Frequency, Rigid.

Guided Circumferential Waves in Layered Poroelastic Cylinders

The present paper investigates the propagation of time harmonic circumferential waves in a two-dimensional hollow poroelastic cylinder with an inner shaft (shaft-bearing assembly). The hollow poroelastic cylinder and inner shaft are assumed to be infinite in axial direction. The outer surface of the cylinder is stress free and at the interface, between the inner shaft and the outer cylinder, it is assumed to be free sliding and the interfacial shear stresses are zero, also the normal stress and radial displacements are continuous. The frequency equation of guided circumferential waves for a permeable and an impermeable surface is obtained. When the angular wave number vanish the frequency equation of guided circumferential waves for a permeable and an impermeable surface degenerates and the dilatational and shear waves are uncoupled. Shear waves are independent of the nature of surface. The frequency equation of a permeable and an impermeable surface for bore-piston assembly is obtained as a particular case of the model under consideration when the outer radius of the hollow poroelastic cylinder tends to infinity. Results of previous studies are obtained as a particular case of the present study. Nondimensional frequency as a function of wave number is presented graphically for two types of models and discussed. Numerical results show that, in general, the first modes are linear for permeable and impermeable surfaces and the frequency of a permeable surface is more than that of an impermeable surface.

Analysis of flexural wave propagation in poroelastic composite hollow cylinder

Wave propagation in an infinitely long poroelastic composite hollow cylinder in is examined by employing Biot’s theory of wave propagation in poroelastic media. A poroelastic composite hollow cylinder consists of two concentric poroelastic cylindrical layers both of which are made of different poroelastic materials with each poroelastic material as homogeneous and isotropic. The inner and outer boundaries of composite hollow poroelastic cylinder are free from stress. The frequency equation of flexural vibrations of poroelastic composite hollow cylinder is obtained. In addition some particular cases such as poroelastic composite hollow cylinder with rigid casing, poroelastic composite bore and poroelastic bore are discussed. Non-dimensional phase velocity is computed as a function of non-dimensional wavenumber. The results are presented graphically for two types of poroelastic composite cylinders and then discussed.Keywords: Biot’s theory, poroelastic composite hollow cylinder, wavenumber, rigidity, phase velocity

Study of torsional vibrations in an initially stressed composite poroelastic cylinders

This paper investigates torsional vibrations in an initially stressed composite poroelastic cylinder in the framework of Biot's theory of wave propagation in poroelastic solids. Poroelastic composite cylinder consists of two concentric cylindrical layers made of different poroelastic materials. The governing equations are formulated from the Biot's incremental deformation theory. The non-dimensional frequency is computed as a function of ratio of thickness to wavelength. The limiting cases of a poroelastic solid cylinder and poroelastic hollow cylinder are discussed. The results are presented graphically for two poroelastic composite cylinders and then compared with the published results.

Effect of elastic foundations on vibrations of thick-walled hollow poroelastic cylinders

This paper deals with the effect of elastic foundations on the vibrations of thick- walled hollow poroelastic cylinders. The frequency equations of axially symmetric vibrations and non-axially symmetric vibrations, each for pervious and impervious surface are obtained using the analytical model based on Biot's theory. The plots of frequency versus ratio of thickness to inner radius of composite cylinder for different materials are presented graphically.

Investigation of torsional vibrations in thick walled hollow poroelastic cylinder using Biot’s extension theory

This paper deals with the study of torsional vibrations of thick walled hollow poroelastic cylinder using Biot’s extension theory. Considering the boundaries to be stress free, the frequency equation is obtained in the presence of dissipation which is transcendental and complex valued in nature. In the special case of poroelastic thin shell, frequency equation is separated into two real valued equations giving propagation velocity and attenuation coefficient. From the numerical results in the case of sandy sediment, it is clear that the values of propagation velocity are, in general, less than that of attenuation coefficient.

Phase Velocity and Attenuation of Longitudinal Shear Vibrations of Hollow Poroelastic Cylinders

The present paper is devoted to the study of phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic circular cylinders in the presence of dissipation. The explicit expressions for phase velocity and attenuation of longitudinal shear vibrations are derived. The frequency equation of longitudinal shear vibrations and modes obtained in a previous paper are used to compute the phase velocity and attenuation for different dissipations for thin and thick poroelastic cylindrical shells and poroelastic solid cylinder. The physical parameters of sandstone saturated with kerosene and sandstone saturated with water are used for the purpose of computation. It is found that the phase velocity is linear beyond certain frequency. Phase velocity is smaller for a typical anti-symmetric mode compared to the flexural mode. It is greater for the second mode than that of the first mode. Also the phase velocity is larger for a thin poroelastic cylindrical shell than that of a thick poroelastic cylindrical shell. The same is true for attenuation also. Attenuation is very high for the considered dissipations and it increases with the increase in dissipation.

Torsional Vibrations of Finite Hollow Poroelastic Circular Cylinders

In this paper, the problem of torsional vibrations of a homogeneous, isotropic poroelastic hollow cylinder of finite length is solved. Results of solid cylinder of finite length and classical theory of elasticity are obtained as a particular case. Frequency is calculated numerically for different materials and presented in tables.

Wave propagation in poroelastic hollow cylinder immersed in fluid with seismoelectric effect

Based on Pride theory, we studied the propagation of seismoelectric waves in a fluid-filled poroelastic hollow cylinder. We presented the expressions of seismoelectric waves in the poroelastic hollow cylinder, acoustic and electromagnetic field in inner and outer of the hollow cylinder, and we used the boundary condition to determine acoustic and electromagnetic field. Also this problem is accomplished by using the quasi-static method. The numerical simulation is operated on acoustic field and electromagnetic field in inner fluid of hollow poroelastic cylinder, and the transient waveform is obtained. It shows that there is no difference on the graph between the electric field obtained from Pride equations and that obtained from quasi-static method. The influence of hollow cylinder thickness, molarity and permeability on wave amplitude are discussed. The results show that for the acoustic field the amplitude of longitudinal mode and Stoneley wave will increase with hollow cylinder thickness increasing, and for the converted axial electric field the amplitude of Stoneley wave increases with hollow cylinder thickness increasing, while the amplitude of longitudinal mode will decrease. The amplitude of electric field in inner fluid will decrease with the molarity of fluid increasing. The amplitude of the fluid acoustic and electric field will decrease with the permeability increasing. The influence of impermeable outer surface on the amplitude of longitudinal wave is obviously much larger than that of Stoneley wave in the electric field.

Vibrations in a Fluid-Loaded Poroelastic Hollow Cylinder Surrounded by a Fluid in Plane-Strain Form

Plane-strain vibrations in a fluid-loaded poroelastic hollow cylinder surrounded by a fluid are investigated employing Biot’s theory of wave propagation in poroelastic media. The poroelastic hollow cylinder is homogeneous and isotropic, while the inner and outer fluids are homogeneous, isotropic and inviscid. The frequency equation of the fluid-loaded poroelastic cylinder surrounded by a fluid is obtained along with several particular cases, namely, fluid-loaded poroelastic cylinder, fluid-loaded bore, poroelastic cylinder surrounded by a fluid and poroelastic solid cylinder submerged in a fluid. The frequency equations are obtained for axially symmetric, flexural and anti-symmetric vibrations each for a pervious and an impervious surface. Nondimensional frequency for propagating modes is computed as a function of the ratio of thickness to the inner radius of the core. The results are presented graphically for two types of poroelastic cylinders and then discussed.

RADIAL VIBRATIONS OF THICK-WALLED HOLLOW POROELASTIC CYLINDERS

A study of the radial vibrations of hollow poroelastic cylinders of infinite extent is made following Biot's theory of wave propagation in liquid-filled porous media. The frequency equations of these vibrations for a permeable and an impermeable surface are derived. Two limiting cases of ratio of wall thickness to inner radius of the hollow poroelastic cylinder are considered, namely, when these ratios are very small and very large. The first limiting case corresponds to modes of a thin poroelastic shell and plate, while in the second limiting case, modes of a poroelastic solid cylinder and poroelastic bore in an infinite poroelastic medium are obtained. Plots of nondimensional frequency as a function of ratio of wall thickness to inner radius are presented for a permeable and an impermeable surface and are then discussed. By ignoring the liquid effects, the results of a purely elastic solid are obtained as a special case.

On torsional vibrations of infinite hollow poroelastic cylinders

Employing Biot’s theory of wave propagation in liquid saturated poroelastic media, the propagation of torsional vibrations in an infinite homogeneous, isotropic hollow poroelastic circular cylinder is investigated. Considering the boundaries to be stress free, the frequency equation of torsional vibrations is obtained in presence of dissipation. The frequency equation is discussed for the first two modes in the cases of a poroelastic thin shell, a poroelastic thick shell and a poroelastic solid cylinder. Phase velocity, group velocity and attenuation are determined and computed for the first mode of vibration for two different poroelastic materials as a function of frequency. These values are displayed graphically and then discussed.

Natural frequencies of a poroelastic hollow cylinder

Employing Biot's theory for wave propagation in a porous solid, the frequency equation for radial vibrations of a poroelastic cylinder is obtained. The frequency equation has been derived in the form of a determinant involving Bessel functions. The roots of the frequency equation give the values of the characteristic circular frequency parameters of the first four modes for various geometries. These roots, which correspond to various modes, are numerically calculated and presented graphically. The results indicate that the effects of porosity are very pronounced.

Circumferential Waves of Infinite Hollow Poroelastic Cylinders

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.

Modelling poroelastic hollow cylinder experiments with realistic boundary conditions

AbstractA general poroelastic solution for axisymmetrical plane strain problems with time dependent boundary conditions is developed in Laplace domain. Time‐domain results are obtained using numerical inversion of the Laplace transform. Previously published solutions can be considered as special cases of the proposed solution. In particular, we could reproduce numerical results for solid and hollow poroelastic cylinders with suddenly applied load/pressure (Rice and Cleary, Rev. Geophys. Space Phys. 1976; 14:227; Schmitt, Tait and Spann, Int. J. Rock Mech. Min. Sci. 1993; 30:1057; Cui and Abousleiman, ASCE J. Eng. Mech. 2001; 127:391).The new solution is used to model laboratory tests on thick‐walled hollow cylinders of Berea sandstone subjected to intensive pressure drawdown. In the experiments, pressure at the inner boundary of the hollow cylinder is observed to decline exponentially with a decay constant of 3–5 1/s.It is found that solutions with idealized step‐function type inner boundary conditions overestimate the induced tensile radial stresses considerably. Although basic poroelastic phenomena can be modelled properly at long time following a stepwise change in pressure, realistic time varying boundary conditions predict actual rock behaviour better at early time. Experimentally observed axial stresses can be matched but appear to require different values for α and ν than are measured at long time.The proposed solution can be used to calculate the stress and pore pressure distributions around boreholes under infinite/finite boundary conditions. Prospective applications include investigating the effect of gradually changing pore pressure, modelling open‐hole cavity completions, and describing the phenomenon of wellbore collapse (bridging) during oil or gas blowouts. Copyright © 2004 John Wiley & Sons, Ltd.

Exact analysis of the plane-strain vibrations of thick-walled hollow poroelastic cylinders

The paper deals with the plane-strain vibrations of thick walled hollow, composite poroelastic cylinder. The frequency equations of axially and non-axially symmetric vibrations, each for pervious and impervious surfaces are obtained using the analytical model based on Biot’s theory of wave propagation in fluid-saturated porous media. In case of axially symmetric vibrations, dilatational and shear modes are uncoupled, while in non-axially symmetric vibrations, dilatational and shear modes are coupled. The plot of frequency versus ratio of wall thickness to inner radius of composite cylinder for different materials is presented, and then discussed. For axially symmetric vibrations, two limiting cases of ratio of wall thickness to inner radius of composite cylinder are considered, i.e., when these ratios are very small and very large. The first limiting case corresponds to modes of thin poroelastic shell and plate, while in the second limiting case, modes of poroelastic solid cylinder is obtained. Thus, the problem of axially symmetric vibrations describes a transition from the case of plate, thereby thin shell to analogous pochammer case of poroelastic solid cylinder. The results of purely elastic solid are shown as a special case.