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 / Martin Ochmann, Rafael Piscoya
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 planes -- Chapter 12 -- Final remarks and outlook
Summary
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
