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.
Autorentext
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.Inhalt
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 Green's 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 planesChapter 12 - Final remarks and outlook.