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 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.

Field distributions in piezoelectric composites with semi-infinite cracks

2016 ◽  
Vol 28 (4) ◽  
pp. 547-562 ◽  
Author(s):  
Jacob Aboudi
Keyword(s):  
Fourier Transform ◽  
Single Cell ◽  
Order Theory ◽  
Piezoelectric Composite ◽  
Piezoelectric Composites ◽  
Cell Method ◽  
Representative Cell ◽  
The Fourier Transform ◽  
Higher Order Theory ◽  
Electromechanical Field

A method is offered for the prediction of the electromechanical field in periodic piezoelectric composites with embedded semi-infinite cracks. It is based on the knowledge of the K-field in piezoelectric materials in which the material constants are replaced by the effective moduli of the piezoelectric composite. In addition to the existing semi-infinite crack, the proposed method can analyze localized inhomogeneities near the crack tip. The established effective K-field is applied at the boundaries of a rectangular domain that should be sufficiently far away from the crack tip and the other inhomogeneities. The proposed approach is based on the combined utilization of a micromechanical analysis, the representative cell method and the higher-order theory. The micromechanical analysis establishes the effective electromechanical constants of the piezoelectric composite, and the representative cell method reduces the periodic composite that is discretized into numerous identical cells to a single cell problem in the Fourier transform domain. The governing equations and constitutive relations that are formulated in this single cell are solved by employing the higher-order theory where discretization into subcells is employed. The inverse of the Fourier transform provides the electromechanical field at any point in the composite. The proposed approach is verified for crack fronts that are parallel and perpendicular to the poling direction (axis of symmetry). Applications are given for a cracked porous piezoelectric material, cracks that have been arrested by cavities and for a periodically bilayered composite with a semi-infinite crack.

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 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.

Magnetic Fields Generated by a Mechanical Singularity in a Magnetized Elastic Half Plane

1989 ◽  
Vol 56 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Chau-Shioung Yeh
Keyword(s):  
Fourier Transform ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Plane ◽  
Elastic Solids ◽  
Soft Ferromagnetic ◽  
Single Force ◽  
The Fourier Transform

The induced magnetic fields generated by a line mechanical singularity in a magnetized elastic half plane are investigated in this paper. One version of linear theory for soft ferromagnetic elastic solids which has been developed by Pao and Yeh (1973) is adopted to analyze the plane strain problem undertaken. By applying the Fourier transform technique, the exact solutions for the generated magnetic inductions due to various mechanical singularities such as a single force, a dipole, and single couple are obtained in a closed form. The distributions of the generated inductions on the surface are shown with figures.

scholarly journals On a semi-nonlocal boundary value problem for the three-dimensional Tricomi equation of an unbounded prismatic domain

2021 ◽  
pp. 8-16
Author(s):  
С.З. Джамалов ◽  
Р.Р. Ашуров ◽  
Х.Ш. Туракулов
Keyword(s):  
Boundary Value Problem ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Three Dimensional ◽  
Generalized Solution ◽  
Nonlocal Boundary Value Problem ◽  
Tricomi Equation ◽  
The Fourier Transform

В данной статье изучаются методами «ε-регуляризации» и априорных оценок с применением преобразования Фурье однозначная разрешимость и гладкость обобщенного решения одной полунелокальной краевой задачи для трехмерного уравнения Трикоми в неограниченной призматической области. In this article, the methods of «ε-regularization» and a priori estimates using the Fourier transform are studied the unique solvability and smoothness of the generalized solution of one semi-nonlocal boundary value problem for the three-dimensional Tricomi equation in an unbounded prismatic domain.

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