• Coupled systems mechanics
• /
• v.12 no.1
• /
• pp.41-68
• /
• 2023

The present work is concerned with the study of the influence of inhomogeneous initial stresses in a hollow cylinder containing a compressible inviscid fluid on the propagation of axisymmetric longitudinal waves propagating in this cylinder. The study is carried out using the so-called three-dimensional linearized theory of elastic waves in bodies with initial stresses to describe the motion of the cylinder and using the linearized Euler equations to describe the flow of the compressible inviscid fluid. It is assumed that the inhomogeneous initial stresses in the cylinder are caused by the internal pressure of the fluid. To solve the corresponding eigenvalue problem, the discrete-analytic solution method is applied and the corresponding dispersion equation is obtained, which is solved numerically, after which the corresponding dispersion curves are constructed and analyzed. To obtain these dispersion curves, parameters characterizing the magnitude of the internal pressure, the ratio of the sound velocities in the cylinder material and in the fluid, and the ratio of the material densities of the fluid and the cylinder are introduced. Based on these parameters, the influence of the inhomogeneous initial stresses in the cylinder on the dispersion of the above-mentioned waves in the considered hydro-elastic system is investigated. Moreover, based on these results, appropriate conclusions about this influence are drawn. In particular, it is found that the character of the influence depends on the wavelength. Accordingly, the inhomogeneous initial stresses before (after) a certain value of the wavelength lead to a decrease (increase) of the wave propagation velocity in the zeroth and first modes.

• Coupled systems mechanics
• /
• v.13 no.3
• /
• pp.247-275
• /
• 2024

The paper studies the influence of the fluid flow velocity and flow direction in the initial state on the dispersion of the axisymmetric waves propagating in the inhomogeneously pre-stressed hollow cylinder containing this fluid. The corresponding eigenvalue problem is formulated within the scope of the three-dimensional linearized theory of elastic waves in bodies with initial stresses, and with linearized Euler equations for the inviscid compressible fluid. The discrete-analytical solution method is employed, and analytical expressions of the sought values are derived from the solution to the corresponding field equations by employing the discrete-analytical method. The dispersion equation is obtained using these expressions and boundary and related compatibility conditions. Numerical results related to the action of the fluid flow velocity and flow direction on the influence of the inhomogeneous initial stresses on the dispersion curves in the zeroth and first modes are presented and discussed. As a result of the analyses of the numerical results, it is established how the fluid flow velocity and flow direction act on the magnitude of the influence of the initial inhomogeneous stresses on the wave propagation velocity in the cylinder containing the fluid.

• Proceedings of the KSME Conference
• /
• 2002.08a
• /
• pp.803-806
• /
• 2002

The dispersion of Lagrangian fluid particles in a turbulent channel flow is studied by a direct numerical simulation. Four points Hermite interpolation in the homogeneous direction and Chebyshev polynomials in the inhomogeneous direction is adopted by assesing the acceleration of fluid particles. In order to characterize the inhomogeneous Lagrangian statistics, accurate single particle Lagrangian statistics are obtained along the wall normal direction. Integral time scales of Lagrangian velocity can be normalized by Eulerian mean shear stresses.

• Bulletin of the Korean Space Science Society
• /
• 2004.04a
• /
• pp.35-35
• /
• 2004

Inhomogeneity Is important in wave coupling and mode conversion. We numerically examine the conversion of extraordinary(X) waves into upper hybrid(UH) waves in inhomogeneous plasmas by using a three-dimensional multi-fluid numerical model. A one-dimensional Inhomogeneous density profile is assumed in a cold and collisionless plasma. The density gradient is taken to be perpendicular to the magnetic field. An impulsive input is assumed to excite the X waves in the inhomogeneous box model. (omitted)

• Geomechanics and Engineering
• /
• v.15 no.1
• /
• pp.645-657
• /
• 2018

The paper aims to analyze the behaviour of torsional type surface waves propagating through fluid saturated inhomogeneous porous media clamped between two inhomogeneous anisotropic media. We considered three types of inhomogeneities in upper anisotropic layer which varies exponentially, quadratically and hyperbolically with depth. The anisotropic half space inhomogeneity varies linearly with depth and intermediate layer is taken as inhomogeneous fluid saturated porous media with sinusoidal variation. Following Biot, the dispersion equation has been derived in a closed form which contains Whittaker's function and its derivative, for approximate result that have been expanded asymptotically up to second term. Possible particular cases have been established which are in perfect agreement with standard results and observe that when one of the upper layer vanishes and other layer is homogeneous isotropic over a homogeneous half space, the velocity of torsional type surface waves coincides with that of classical Love type wave. Comparative study has been made to identify the effects of various dimensionless parameters viz. inhomogeneity parameters, anisotropy parameters, porosity parameter, and initial stress parameters on the torsional wave propagation by means of graphs using MATLAB. The study has its own relevance in connection with the propagation of seismic waves in the earth where fluid saturated poroelastic layer is present.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.167-178
• /
• 2007

This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.7
• /
• pp.867-876
• /
• 2003

The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Four points Hermite interpolation in the homogeneous direction and Chebyshev polynomials in the inhomogeneous direction is adopted to simulate the fluid particle dispersion. An inhomogeneity of Lagrangian statistics in turbulent boundary layer is investigated by releasing many particles at several different wall-normal locations and tracking those particles. The fluid particle dispersions and Lagrangian structure functions of velocity are scaled by the Kolmogorov similarity. The auto-correlations of velocity and acceleration are shown at the different releasing locations. Effect of initial particle location on the dispersion is analyzed by the probability density function at the several downstreams and time instants.

• Nuclear Engineering and Technology
• /
• v.54 no.9
• /
• pp.3390-3397
• /
• 2022

Among the different techniques available, nuclear methods, including gamma-gamma logging tools, are of special importance. Though the real environment which surrounds the drilled borehole is a complex fractured medium which the fluid can flow through the porosities, simulation studies generally use the traditional model of a homogeneous mixture of formation and the liquid. Considering a previously published study, which shows that modeling of fluid flow in fractured reservoirs and simulating the formation as an inhomogeneous fractured medium leads to different results compared with those of homogeneous mixture, here we study the effect of the presence of drilling fluid (mudcake) on the response of the detectors in both the models. To study this effect, a typical gamma-gamma logging tool was modeled by using the MCNPX Monte Carlo code. The results show that the responses of the detectors in the mixture model in the presence of various thicknesses of mudcake are sensitive to the density of the formation material. However, this effect is not notable in the inhomogeneous fractured medium. These results emphasize the importance of the model employed for simulation of the medium in gamma-gamma well-logging.

• Bulletin of the Korean Space Science Society
• /
• 2003.10a
• /
• pp.82-82
• /
• 2003

It is well known that electromagnetic (EM) waves are mode converted to electrostatic (ES) waves in inhomogeneous plasmas. We examine this issue in a three-dimensional multi-fluid numerical model. First, we derive a set of coupled linear wave equations when a one-dimensional inhomogeneous density profile is assumed in a cold and collisionless plasma. The massive ions are considered as fixed because we are interested in high frequency waves in plasmas. It is shown that the EM mode satisfies the 0th order modified Bessel equation near the resonant region where the frequency matches the local electron plasma frequency. It is expected that the EM waves are coupled and damped to the ES waves owing to the logarithmic singular behavior at such resonances. Second, we numerically test the same case in a 3-D multi-fluid model. An impulsive input is assumed to excite EM waves in the inhomogeneous 3-D box model. The wave spectra of electric and magnetic fields are presented and compared with the analytical results. Our results suggest that the EM energy is irreversibly converted into the ES energy wherever the resonant condition is satisfied. Finally we discuss how the mode conversion appears in both electric and magnetic fields by analyzing time histories of each component. We also compare our results with MHD wave coupling. It is numerically confirmed in this study that the coupling of EM and ES waves is similar to that of compressional and transverse MHD waves.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.10a
• /
• pp.257-266
• /
• 1999

This paper presents a method of seismic analysis for a cylindrical liquid storage structure on/in horizontally layered half.space considering the effects of the interior fluid and exterior soil medium in the frequency domain. To capture the essence of fluid-structure-soil interaction effects effectively, a mixed finite element with two-field (u, p) approximation is employed to model the compressive inviscid fluid, while the structure and soil medium are presented by the 3-D axisymmetric finite elements and dynamic infinite elements. The present FE-based method can be applied to the system with complex geometry of fluid region as well as with inhomogeneous near-field soil medium, since it can directly model both the fluid and the soil. For the purpose of verification, dominant peak frequencies in transfer functions for horizontal motions of cylindrical fluid storage tanks with rigid massless foundation on a homogeneous viscoelastic half.space are compared with those by two different added mass approaches for the fluid motion. The comparison indicates that the Present FE-based methodology gives accurate solution for the fluid-structure-soil interaction problem. Finally, as a demonstration of versatility of the present study, a seismic analysis for a real-scale LNG storage tank embedded in layered half.space is carried out, and its member forces along the height of the structure are compared with those by an added mass approach developed by the present writers.