الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 199 |  |  |
| | | from | 199 | | |
Abstract
The aim of thesis is to study both the direct and inverse wave scattering problems in dierent elastic media. For a given outer periodic mechanical load, the direct problem is to determine the displacement waveeld from a known object, which could be an obstacle or a defect in the medium. The inverse is to identify the shape and location of such objects by measuring the scattered surfaceeld over a certainnite boundary of the surface. The direct and inverse scattering problems have wide applications in engineering and geophysical exploration, devices, radar, sensors, sonar, medical imaging, and non-destructive testing. The thesis studies the interaction of electromagnetic
elds and mechanical loads with elastic media or piezoelectric materials having defects or voids. To investigate and analyze the behav- ior and pattern of the scattered waves by objects immersed in such media. Besides studying the problems of reconstructing or detecting defects or cracks inside the medium if the latter is sub- jected to a harmonic load or electric voltage. In the context of the theory of electromagnetic waves and linear elasticity, a math- ematical model based on Maxwell’s equations with the governing equations of deformation is formulated. The solution technique depends on reducing the boundary value problem describing the model into an integral equation of Fred- holm type or a coupled system of boundary integral equations over the defect’s contour that plays a leading role in present- ing the pattern of the outgoing scattered wave from the layer. Green’s function gives the fundamental solutions or basis func- tions of the mathematical model. These functions derived ac- cording to the basic equations of the model with homogeneous boundary conditions. These functions depend on the mathemat- ical structure and conditions. The boundary element method is i one of the most e
cient numerical methods of solving these in- tegral equations which reduces integral equations to an algebraic equations system relative to the unknowns of the displacement wave
eld over each node of the defect’s contour. On the other hand, there are two main types of numerical methods for solving the inverse problem: the direct imaging method and the iterative method. In the iterative, the boundary of the target is identied by minimizing the residual of the scatteredeld. These numer- ical algorithms are developed by reducing the inverse problem into an unconstrained optimization problem. The Quasi-Newton method, the genetic algorithm, and the least square are well- known solving techniques. These methods depend on the model of the direct scattering problem for solving the inverse problem. Because the techniques take advantage of all the information from the direct problem, to develop quite good reconstructions. Chapter one focuses on the fundamental aspects of the topic, the most previous works related to the subject of this thesis, with the mathematical background equations and conditions, concepts, and related theorems. Chapter two is devoted to studying a direct and inverse scat- tering problem for a magnetoelastic layer having a defect, in the frame of the electromagnetic theory. In terms of the displacement
eld over the defect’s contour, a coupled system of boundary in- tegral equations is formulated, for magnetically permeable and impermeable defects. To identify the position and size of the de- fect, an e
cient numerical algorithm is developed by using the quasi-Newton iterative method. In order to check the in uence of the magnetic
eld upon the scattering waves from the layer, a series of numerical examples is presented with di
erent noise levels. The results showed that the magnetic
eld has a sensitive ii e
ect on the identi
cation process when the external magnetic
eld increases, especially for the materials having a high mag- netic permeability factor r. Also, a special inverse problem for predicting the externally applied magnetic
eld, upon a copper layer having a defect with various sizes, has been performed. Chapter three is concerned with studying the e
ect of the mechanical load and electric voltage on the scattering waves of a buried object in a piezoelectric layer, added to that, the study examines the detection of the buried object through its scat- tering surface waves. The procedure of the study includes two cases which include two steps each. During step one of case one, the researchers applied a periodic mechanical load upon a layer containing an elliptic void, where the size and location are pre- determined. A system of coupled boundary integral equations utilizing the generalized Green’s identity and the reciprocal work theorem is formulated. The boundary element method supported by Green’s Functions was employed to solve the formulated integral equa- tions. Hence, the deformation and electric potential over the object’s contour are identi
ed. Step two examined optimization problem to identify the object’s parameters, i.e., its size and lo- cation, by minimizing a structure of discrepancy functional. The quasi-Newton iterative method BFGS and the genetic algorithm (GA) are used for solving the inverse problem. Case two of the study examined the e
ect of electric voltage on the scattering waves of a buried object in the piezoelectric layer. The procedures of case one are administered to case two to com- pare the accuracy of detection results in both cases of the study. A series of practical examples are presented with random noisy data to compare the e
ect of such loads on the process of de- tection. The results indicate that using the mechanical load in iii detecting buried object is clearly accurate compared to voltage load detection. Chapter four investigates the e
ect of a mechanical load on the pattern of the scattered waves by a defect on the interface of two di
erent piezoelectric layers, where the size and location of the object are predetermined. The results of this step is re- duced to two coupled systems of boundary integral equations over the upper arc and lower of the object’s contour. The respective Green’s functions of each piezoelectric layer are constructed. By using the BEM, the integral equations system are reduced to an algebraic system of the unknown deformation
eld on each arc of the defect’s contour. The scattered
eld is computed by solving the algebraic system numerically. A series of practical examples to analyze the pattern of such waves from the elliptical shapes are presented. Chapter
ve is devoted for the general conclusions and the future work.