scholarly journals Simulation of elastic wave diffraction by a sphere in semibounded region

2020 ◽  
pp. 22-27
Author(s):  
A.N. Khimich ◽  
◽  
I.T. Selezov ◽  
V.A. Sydoruk ◽  
◽  
...  
Keyword(s):  
Scattered Wave ◽  
Approximate Solutions ◽  
Wave Number ◽  
Plane Boundary ◽  
Rigid Sphere ◽  
Rigid Boundary ◽  
Reflected Waves ◽  
Rayleigh Approximation ◽  
Tangential Stresses ◽  
Definition Of

The problem of scattering of plane elastic waves by a rigid sphere located near a plane rigid boundary is considered, which leads to the generation of multiply re-reflected dilatation and shear waves. The formulation of the problem is given when slippage conditions are specified on a flat boundary (equality of tangential stresses to zero). The problem is reduced to the definition of scalar functions. General solutions are written down, and approximate solutions are constructed for the field in the far zone characterized by the fact that the distance from the plane boundary to the obstacle is much greater than the radius of the sphere. In addition, the Rayleigh approximation is used, when the wave number is much lesser than the radius of the sphere. The method of images is used to construct multiply reflected waves. Approximate formulas are given for the field in the far zone and in the case of the long-wave Rayleigh approximation. The calculations of scattered wave fields, presented in the form of scattering diagrams, are carried out, from which a strongly oscillating wave field can be seen.

scholarly journals Scattering of an elastic wave by a rigid sphere in a semi-bounded domain

2019 ◽  
pp. 81-91
Author(s):  
Ihor Selezov
Keyword(s):  
Elastic Waves ◽  
Shear Waves ◽  
Scattered Wave ◽  
Rigid Sphere ◽  
Image Method ◽  
Rigid Boundary ◽  
Reflected Waves ◽  
Rayleigh Approximation ◽  
Vector Operator ◽  
Definition Of

The problem of scattering of plane elastic waves by a rigid sphere near a rigid boundary is considered. This leads to the appearance of multiply re-reflected dilatation and shear waves, which generate strong oscillations of the wave field. The problem for a vector operator of the shear waves is reduced to the definition of scalar functions as a consequence of symmetry. Approximate formulas for the far field and the long-wave Rayleigh approximation are presented. The construction of multiply re-reflected waves by the image method is presented and analyzed. Calculations of the scattered wave fields are plotted in the form of scattering diagrams.

scholarly journals Construction of a Class of Copula Using the Finite Difference Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Remi Guillaume Bagré ◽  
Frédéric Béré ◽  
Vini Yves Bernadin Loyara
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Scheme ◽  
Approximate Solutions ◽  
Copula Function ◽  
Common Technique ◽  
The Finite Difference Method ◽  
Definition Of ◽  
General Method

The definition of a copula function and the study of its properties are at the same time not obvious tasks, as there is no general method for constructing them. In this paper, we present a method that allows us to obtain a class of copula as a solution to a boundary value problem. For this, we use the finite difference method which is a common technique for finding approximate solutions of partial differential equations which consists in solving a system of relations (numerical scheme) linking the values of the unknown functions at certain points sufficiently close to each other.

Information on elastic parameters obtained from the amplitudes of reflected waves

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1426-1436 ◽  
Author(s):  
Wojciech Dȩbski ◽  
Albert Tarantola
Keyword(s):  
Mass Density ◽  
Seismic Velocities ◽  
Elastic Parameters ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Reflected Waves ◽  
Seismic Amplitude ◽  
Earth Models ◽  
Definition Of ◽  
Proper Analysis

Seismic amplitude variation with offset data contain information on the elastic parameters of geological layers. As the general solution of the inverse problem consists of a probability over the space of all possible earth models, we look at the probabilities obtained using amplitude variation with offset (AVO) data for different choices of elastic parameters. A proper analysis of the information in the data requires a nontrivial definition of the probability defining the state of total ignorance on different elastic parameters (seismic velocities, Lamé’s parameters, etc.). We conclude that mass density, seismic impedance, and Poisson’s ratio constitute the best resolved parameter set when inverting seismic amplitude variation with offset data.

Study on the Flow Characteristics of Synthetic Jets Near a Rigid Plane Boundary

2011 ◽  
Author(s):  
Ryota Tsunoda ◽  
Koichi Nishibe ◽  
Yuki Fujita ◽  
Kotaro Sato ◽  
Kazuhiko Yokota ◽  
...  
Keyword(s):  
Flow Characteristics ◽  
Maximum Velocity ◽  
Stokes Number ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Plane Boundary ◽  
Jet Flows ◽  
Rigid Boundary ◽  
Wire Method ◽  
Rigid Plane

The jet flows have been applied to various fields to control the flow separation. Over the last decade, several studies have investigated synthetic jets. However, there are still many clarifications needed, including details of the structure and Coanda effect of synthetic jets. The present study clarifies some fundamental flow characteristics of free synthetic jets and synthetic jets near a rigid boundary by conducting an experiment and numerical simulations. As the main results, it is found that the velocity distribution of free synthetic jets depends on K = Re/S2 (the ratio of the Reynolds number to the square of the Stokes number) and can be identified by the maximum velocity at the centerline and the jet half-width. Flow visualization is carried out applying the smoke wire method. In addition, it is confirmed that the flow characteristics of the synthetic jet near a rigid boundary and re-attachment length of the synthetic jet are determined not only by H1/b0 (normalized step heights) but also K.

Stress-Intensification Near a Semi-Infinite Rigid-Smooth Strip Due to Diffraction of Elastic Waves

1967 ◽  
Vol 34 (1) ◽  
pp. 119-126 ◽  
Author(s):  
S. A. Thau ◽  
Yih-Hsing Pao
Keyword(s):  
Radial Distance ◽  
Scattered Wave ◽  
Wave Number ◽  
Parabolic Cylinder ◽  
Principal Stresses ◽  
Plane Barrier ◽  
Diffraction Of Elastic Waves ◽  
Parabolic Cylinder Functions ◽  
P And Sv Waves ◽  
Rigid Smooth

Scattering of plane harmonic compressional and shear waves (P and SV-waves) by a semi-infinite rigid-smooth strip or ribbon which is a plane barrier with its top and bottom surfaces being confined normally, but free in lateral directions, is treated. Under the condition that displacements must be regular, exact solutions for the combined incident and scattered-wave fields are obtained in terms of Weber’s parabolic cylinder functions. Principal stresses are calculated on both sides of the strip and the stresses are shown to be singular of the order (kr)−1/2, where k is the incident wave number and r the radial distance from the tip.

scholarly journals IMPROVING THE DESIGNING METHOD OF THERMAL NETWORKS: SERIAL CONNECTION OF STREAMS

2021 ◽  
Vol 4 (2) ◽  
pp. 146-154
Author(s):  
Georgy V. Derevyanko ◽  
Vladimir I. Mescheryakov
Keyword(s):  
Heat Exchange ◽  
Heat Exchangers ◽  
Moving Objects ◽  
Mutual Influence ◽  
Flow Distribution ◽  
Approximate Solutions ◽  
Design Parameters ◽  
Existence Of A Solution ◽  
Serial Connection ◽  
Definition Of

The paper presents an approach to the design of technical systems, the elements of which are interconnected and carry out an internal exchange of energy. The above analysis showed that for heat-exchange equipment when combining devices into systems, only iterative methods are currently used, a representative of which is Pinch analysis. A limitation of the iterative approach is the impossibility of obtaining an exact solution to such problems, which can only be achieved by analytical methods, which also make it possible to reveal some effects in systems that are practically unavailable for numerical solution. This indicates the absence of a rigorous proof of the existence of a solution and a problem in the construction of approximate solutions, due to the need to involve complementary hypotheses. The topological representation of the system modules allows us to consider the architecture as a network, which contributes to the analysis of the connections between the constituent elements and the identification of their mutual influence. Highlighted the typical connections of network elements such as serial, parallel, contour, which allows to unify the principles of building connections in the system. As an optimality criterion, the NTU parameter was chosen, which includes the heat exchange surface and is usually used when searching for a solution for heat exchangers of moving objects. An analytical solution to the problem of flow distribution and energy exchange efficiency in a system of two series-connected heat exchangers is obtained. His analysis showed that the formulation of the design problem based on the definition of matrix elements in relation to determinants allows not only to meet the requirements for the system, but also to determine the design parameters of its elements that satisfy their extreme characteristics

The effect of boundaries on wave propagation in a liquid-filled porous solid: III. Reflection of plane waves at a free plane boundary (general case)

1962 ◽  
Vol 52 (3) ◽  
pp. 595-625 ◽  
Author(s):  
H. Deresiewicz ◽  
J. T. Rice
Keyword(s):  
Electromagnetic Waves ◽  
Plane Waves ◽  
Body Waves ◽  
Porous Solid ◽  
Plane Boundary ◽  
Field Equations ◽  
Attenuation Coefficients ◽  
Reflected Waves ◽  
Three Body ◽  
Analytical Expressions

abstract A general solution is derived of Biot's field equations governing small motions of a porous solid saturated with a viscous liquid. The solution is then employed to study some of the phenomena attendant upon the reflection from a plane, traction-free boundary of each of the three body waves predicted by the equations. The problem, though more complex, bears some similarity to that of electromagnetic waves in a conducting medium, in that some of the reflected waves are inhomogeneous, planes of constant amplitude not coinciding with planes of constant phase. Analytical expressions are displayed for the phase velocities, attenuation coefficients, angles of reflection and the amplitude ratios, and explicit formulas are given for the limiting cases of low and high frequencies, representing first-order corrections for porosity of the solid and viscosity of the liquid, respectively. The paper concludes with a presentation of results of numerical calculations pertinent to a kerosene-saturated sandstone.

On the operational solutions of fuzzy fractional differential equations

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Djurdjica Takači ◽  
Arpad Takači ◽  
Aleksandar Takači
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Software Package ◽  
Approximate Solutions ◽  
Algebraic Equations ◽  
Fractional Differential ◽  
Definition Of ◽  
The Given ◽  
Fuzzy Fractional Differential Equations

AbstractFuzzy fractional differential equations with fuzzy coefficients are analyzed in the frame of Mikusiński operators. Systems of fuzzy operational algebraic equations are obtained, in view of the definition of fuzzy derivatives. Their exact and approximate solutions are constructed and their characters are analyzed, considering them as the corresponding solutions of the given problem. The described procedure of the construction of solutions is illustrated on an example and the obtained approximate solutions of the considered problems are visualized by using the GeoGebra software package.

scholarly journals The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Roman Janjgava
Keyword(s):  
Approximate Solution ◽  
Stress Concentration ◽  
General Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Theory Of Elasticity ◽  
Plane Boundary ◽  
Moment Theory ◽  
The Moment

We consider a two-dimensional system of differential equations of the moment theory of elasticity. The general solution of this system is represented by two arbitrary harmonic functions and solution of the Helmholtz equation. Based on the general solution, an algorithm of constructing approximate solutions of boundary value problems is developed. Using the proposed method, the approximate solutions of some problems on stress concentration on the contours of holes are constructed. The values of stress concentration coefficients obtained in the case of moment elasticity and for the classical elastic medium are compared. In the final part of the paper, we construct the approximate solution of a nonlocal problem whose exact solution is already known and compare our approximate solution with the exact one. Supposedly, the proposed method makes it possible to construct approximate solutions of quite a wide class of boundary value problems.

scholarly journals Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Panayiotis Vafeas
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Analytical Form ◽  
Wave Number ◽  
Closed Form Solutions ◽  
Rayleigh Approximation ◽  
Time Harmonic ◽  
Ellipsoidal Harmonic ◽  
Type Boundary ◽  
Complex Valued

This contribution deals with the scattering by a metallic ellipsoidal target, embedded in a homogeneous conductive medium, which is stimulated when a 3D time-harmonic magnetic dipole is operating at the low-frequency realm. The incident, the scattered, and the total three-dimensional electromagnetic fields, which satisfy Maxwell’s equations, yield low-frequency expansions in terms of positive integral powers of the complex-valued wave number of the exterior medium. We preserve the static Rayleigh approximation and the first three dynamic terms, while the additional terms of minor contribution are neglected. The Maxwell-type problem is transformed into intertwined potential-type boundary value problems with impenetrable boundary conditions, whereas the environment of a genuine ellipsoidal coordinate system provides the necessary setting for tackling such problems in anisotropic space. The fields are represented via nonaxisymmetric infinite series expansions in terms of harmonic eigenfunctions, affiliated with the ellipsoidal system, obtaining analytical closed-form solutions in a compact fashion. Until nowadays, such problems were attacked by using the very few ellipsoidal harmonics exhibiting an analytical form. In the present article, we address this issue by incorporating the full series expansion of the potentials and utilizing the entire subspace of ellipsoidal harmonic eigenfunctions.

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