scholarly journals ON ONE PROBLEM FOR A STATIONARY SYSTEM IN A TWO-LIQUID MEDIUM IN A HALF-SPACE

2019 ◽  
Vol 4 (1) ◽  
pp. 156-162
Author(s):  
Kholmatzhon Imomnazarov ◽  
Mikhail Urev ◽  
Ilham Iskandarov
Keyword(s):  
Fourier Transform ◽  
Boundary Value Problem ◽  
Half Space ◽  
Boundary Value ◽  
Stationary System ◽  
Fluid Medium ◽  
Thermodynamic And Kinetic Parameters ◽  
The Fourier Transform ◽  
Two Fluid ◽  
Second Order Equations

This paper considers a classical solution in the half-space of the second boundary value problem for an overdetermined stationary system of second order equations arising in a two-fluid medium with a single pressure. The solution of the considered boundary value problem using the Fourier transform apparatus has been obtained. The effect of thermodynamic and kinetic parameters of the medium is shown on the solution to the system in question.

scholarly journals On a boundary value problem for a mixed equation with three planes of type change in an infinite prismatic domain

2021 ◽  
pp. 19-28
Author(s):  
Б.И. Исломов ◽  
Г.Б. Умарова
Keyword(s):  
Fourier Transform ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
Type Change ◽  
Mixed Equation ◽  
Uniqueness And Existence ◽  
The Fourier Transform

В данной работе в бесконечной призматической области формулируется и изучается одна задача для параболо-гиперболического уравнения c тремя плоскостями изменения типа. Основным методам исследования поставленной задачи является преобразование Фурье. Доказана единственность и существование решения поставленной задачи In this paper, in an infinite prismatic domain, one problem is formulated and studied for a parabolic-hyperbolic equation with three planes of type change. The main methods for studying the problem posed is the Fourier transform. The uniqueness and existence of a solution to the problem is proved.

scholarly journals The Effect of Defects in Piezoelectric Composite Half-Planes with Surface Electrodes

2020 ◽  
Vol 4 (2) ◽  
pp. 43
Author(s):  
Jacob Aboudi
Keyword(s):  
Fourier Transform ◽  
Boundary Value Problem ◽  
Half Plane ◽  
Iterative Procedure ◽  
Boundary Value ◽  
Piezoelectric Composite ◽  
Rectangular Region ◽  
Surface Electrodes ◽  
The Fourier Transform ◽  
Electromechanical Field

An analysis for the prediction of the electromechanical field in composite piezoelectric half-planes with attached surface electrode is presented. The composite half-planes are composed of distinct constituents and may include internal defects in various locations. The solution is carried out in a sufficiently large rectangular region, the boundary conditions of which are obtained from the corresponding solution of a homogeneous piezoelectric half-plane. This is followed by the application of the discrete Fourier transform at the domain of which a boundary-value problem is formulated. The solution of this boundary-value problem, followed by the inversion of the Fourier transform, provides, in conjunction with an iterative procedure, the electromechanical field at any point of the rectangular region. Applications are given for a piezoelectric half-plane with defects in the form of a cavity and of short and semi-infinite cracks as well as of a periodically bilayered composite with a crack in one of its layers.

scholarly journals The Induced Stress Field in Cracked Composites by Heat Flow

2017 ◽  
Author(s):  
Jacob Aboudi
Keyword(s):  
Fourier Transform ◽  
Heat Flow ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Porous Ceramic ◽  
Polymeric Composite ◽  
Stress Fields ◽  
Finite Domain ◽  
Induced Stress ◽  
The Fourier Transform

A multiscale (micro-macro) approach is proposed for the establishment of the full thermal and induced stress fields in cracked composites that are subjected to heat flow. Both the temperature and stresses distributions are determined by the solution of a boundary value problem with one-way coupling. In the micro level and for combined thermomechanical loading, a micromechanical analysis is employed to determine the effective moduli, coefficients of thermal expansion and thermal conductivities of the undamaged composite. In the macro level, the representative cell method is employed according to which the periodic damaged composite region is reduced, in conjunction with the discrete Fourier transform, to a finite domain problem. As a result, a boundary value problem is obtained in the Fourier transform domain which is appropriately discretized and solved. The inverse transform and an iterative procedure provide the full thermal and stress fields. The proposed method is verified by comparisons with exact solutions. Applications are given for the determination of the thermal and stress fields in cracked fiber-reinforced polymeric composite, cracked porous ceramic material and cracked periodically layered ceramic composite caused by the application of heat flow. The presented formulation admits however the application of a combined mechanical and heat flux on cracked composites.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

Bleustein-Gulyaev Waves in an Inhomogeneous Layered Piezoelectric Half-Space

2006 ◽  
Vol 306-308 ◽  
pp. 1223-1228
Author(s):  
Fei Peng ◽  
Hua Rui Liu
Keyword(s):  
Fourier Transform ◽  
Phase Velocity ◽  
Half Space ◽  
Electric Potential ◽  
Piezoelectric Layer ◽  
Field Equations ◽  
Transform Method ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
The Fourier Transform

The propagation of Bleustein-Gulyaev (BG) waves in an inhomogeneous layered piezoelectric half-space is investigated in this paper. Application of the Fourier transform method and by solving the electromechanically coupled field equations, solutions to the mechanical displacement and electric potential are obtained for the piezoelectric layer and substrate, respectively. The phase velocity equations for BG waves are obtained for the surface electrically shorted case. When the layer and the substrate are homogenous, the dispersion equations are in agreement with the corresponding results. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO3 except that they are polarized in opposite directions. Effects of the inhomogeneities induced by either the layer or substrate are discussed in detail.

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