This book highlights the mathematical and physical properties of acoustical sources with singularities located in the complex plane and presents the application of such special elements to solve acoustical radiation and scattering problems.
Sources whose origin lies in the complex plane are also solutions of the wave equation but possess different radiating properties as their counterparts with real positions. Such mathematical constructions are known in the fields of optics and electrodynamics, but they are not common in acoustical research. The objective of the book is to introduce this concept to acousticians and motivate them to engage themselves in further research and application of complex sources. Such sources are particularly useful to formulate Green’s functions and related equivalent source and boundary element methods in half-spaces.
Chapter 1 - Introduction.
Chapter 2 - Complex monopoles and the
Helmholtz equation in Cartesian coordinates.
Chapter 3 - Complex monopoles
in oblate spheroidal coordinates.
Chapter 4 - The driving source of the
complex monopole.
Chapter 5 - Application of complex sources for
constructing the Greens function above an impedance plane.
Chapter 6 - New
and old formulas from the Helmholtz equation with half-space driving
sources.
Chapter 7 - Branch cuts of the square root with complex argument.-
Chapter 8 - Realization of complex sources.
Chapter 9 - Simulation of
vibrating and scattering objects with ESM / CEM.
Chapter 10 - Green's
function above homogeneous ground.
Chapter 11 - Boundary element techniques
for sound propagation above impedance planes.
Chapter 12 - Final remarks and
outlook.
Prof. Dr.-Ing. M. Ochmann: After university education in Technical Environmental Engineering (Dipl.-Ing.) and Mathematics (Diploma), he received a doctor degree (1985) and habilitation in Technical Acoustics (1990) at the Technical University of Berlin at the Institute of Technical Acoustics. He was directing the researcher group Computational Acoustics at Beuth University and several corresponding acoustical research projects until his retirement at October 2020. His research activities cover sound radiation from vibrating surfaces, fluidstructure interaction, acoustical scattering, numerical acoustics, boundary element methods, and duct acoustics.
Dr.-Ing. Rafael Piscoya studied Physics at the Catholic University in Peru. In 1994, he obtained his Magister degree with the work Acoustic design of rooms using ray tracing. From 1999 to 2003, he did his Ph.D. studies at the Technical University in Berlin which he concluded with the thesis Influencing the radiation pattern of horns through collocation of impedances on their sidewalls. Since 2003, he has been working in different research projects collecting knowledge and experience in the solution of numerous acoustic problems using numerical methods.
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