Theory and Application of Acoustic Sources Using Complex Analysis
Complex Acoustic Sources, Green’s Functions and Half-Space Problems, Acoustic Radiation and Scattering Using Equivalent Source and Boundary Element Methods
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Beschreibung
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.
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.
Highlights the mathematical and physical properties of acoustical sources with singularities located in the complex plane Provides explicit formulas for Green’s functions in half-spaces above impedance and homogeneous ground Presents the application of complex acoustical sources to solve acoustical radiation and scattering problems in free space and half-spaces by using the equivalent source method and the boundary element method
Autor*in
Martin Ochmann
Themen in »Theory and Application of Acoustic Sources Using Complex Analysis«
Acoustical radiation Scattering problems Complex multipoles Complex monopoles Gaussian beam modes Sound focussing Complex sources Equivalent Source Method (ESM) Scattering of sound beams Half-space problem Special Green’s function Cauchy Principal Value (CPV) Complex source pulsed beams (CSPB)