DPSM for modeling engineering problems

This book is the first book on this technique; it describes the theory of DPSM in detail and covers its applications in ultrasonic, magnetic, electrostatic and electromagnetic problems in engineering. For the convenience of the users, the detailed theory of DPSM and its applications in different engineering fields are published here in one book making it easy to acquire a unified knowledge on DPSM.

Author Notes

Dominique Placko , PhD, is a Professor in the Department of Electrical Engineering at the Ecole Normale Supérieure de Cachan in France. He is the author/coauthor of over 100 scientific papers, editor/coeditor of eight books, and holder of fifteen patents. He started a new Interdisciplinary Conference on Instrumentation in 1998 and the scientific French journal Instrumentation, Mesure, Métrologie in 2001. He received the Blondel Award in 1998.

Tribikram Kundu , PhD, is a Professor at the University of Arizona and winner of the Humboldt Research Prize from Germany. He has been an invited professor in France, Sweden, Denmark, Russia, and Switzerland. He is the editor of twelve books and three research monographs and author/coauthor of two textbooks and over 200 scientific papers, three of which received Best Paper awards.

Chapter 1 Basic Theory of Distributed Point Source Method (DPSM) and its Application to Some Simple ProblemsD. Placko and T. Kundu

1.1 Introduction and Historical Development of DPSM

1.2 Basic Principles of DPSM Modeling

1.2.1 The fundamental idea

1.2.1.1 Basic equations

1.2.1.2 Boundary conditions

1.2.2 Example in the case of a magnetic open core sensor

1.2.2.1 Governing equations and solution

1.2.2.2 Solution of coupling equations

1.2.2.3 Results and discussion

1.3 Examples from Ultrasonic Transducer Modeling

1.3.1 Justification of modeling a finite plane source by a distribution of point sources

1.3.2 Planar piston transducer in a fluid

1.3.2.1 Conventional surface integral technique

1.3.2.2 Alternative distributed point source method (DPSM) for computing the ultrasonic field

1.3.2.2.1 Matrix formulation

1.3.2.3 Restrictions on rS for point source distribution

1.3.3 Focused transducer in a homogeneous fluid

1.3.4 Ultrasonic field in a non-homogeneous fluid in presence of an interface

1.3.4.1 Pressure field computation in fluid 1 at point P

1.3.4.2 Pressure field computation in fluid 2 at point Q

1.3.5 DPSM technique for ultrasonic field modeling in non-homogeneous fluid

1.3.5.1 Field computation in fluid

1.3.5.1.1 Approximations in computing the field

1.3.5.2 Field in fluid

1.3.6 Ultrasonic field in presence of a scatterer

1.3.7 Numerical results

1.3.7.1 Ultrasonic field in a homogeneous fluid

1.3.7.2 Ultrasonic field in a non-homogeneous fluid - DPSM technique

1.3.7.3 Ultrasonic field in a non-homogeneous fluid - surface integral method

1.3.7.4 Ultrasonic field in presence of a finite size scatterer

References

Chapter 2 Advanced Theory of DPSM - Modeling Multi-Layered Medium and Inclusions of Arbitrary ShapeT. Kundu and D. Placko

2.1 Introduction

2.2 Theory of Multi-Layered Medium Modeling

2.2.1 Transducer faces not coinciding with any interface

2.2.1.1 Source strength determination from boundary and interface conditions

2.2.2 Transducer faces coinciding with the interface

Case 1 Transducer faces modeled separately

2.2.2.1 Source strength determination from interface and boundary conditions

2.2.2.2 Counting number of equations and number of unknowns

2.2.3 Transducer faces coinciding with the interface

Case 2 Transducer faces are part of the interface

2.2.3.1 Source strength determination from interface and boundary conditions

2.2.4 Special case involving one interface and one transducer only

2.3 Theory for Multi-layered Medium Considering the Interaction Effect on the Transducer Surface

2.3.1 Source strength determination from interface conditions

2.3.2 Counting number of equations and number of unknowns

2.4 Interference between two Transducers: Step-by-Step Analysis of Multiple Reflection

2.5 Scattering by an Inclusion of Arbitrary Shape

2.6 Scattering by an Inclusion of Arbitrary Shape - An Alternative Approach

2.7 Electric Field in a Multi-Layered Medium

2.8 Ultrasonic Field in a Multi-Layered Fluid Medium

2.8.1 Ultrasonic field developed in a three-layered medium

2.8.2 Ultrasonic field developed in a four-layered fluid medium

References

Chapter 3 Ultrasonic Modeling in Fluid MediaT. Kundu and R. Ahmad and N. Alnuaimi and D. Placko

3.1 Introduction

3.2 Primary and Secondary Sources

3.3 Modeling Ultrasonic Transducers of Finite Dimension Immersed in a Homogeneous Fluid

3.3.1 Numerical results - ultrasonic transducers of finite dimens

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Summary

Summary

Author Notes

Table of Contents