Theorie und Anwendung akustischer Multipolstrahler mit komplexen Singularitäten
Zusammenfassung der Projektergebnisse
The sound radiation of acoustic multipoles with complex source positions was investigated. The introduction of an imaginary part into the real source position makes it possible to change the radiation pattern of the multipole. It is convenient to define the complex position as the sum of the real position plus an imaginary vector (a real vector multiplied by the imaginary number j) because the second real vector defines a plane where the singularity is embedded. Additionally, the complex vector defines the direction where the change in the directivity occurs. The change is basically a focusing of the sound radiation in the direction of the complex vector which depends also on the frequency. For a monopole that radiates uniformly in all directions, it is easy to imagine the result of the focusing. For higher order multipoles, that is more difficult since the original directivity is not uniform. The complex multipoles represent additional acoustic elements that can be used to simulate or reproduce sound fields since they are also solutions of the Helmholtz equation. The especial features that these new elements have, make it possible to apply them in specific situations, being in some cases more suitable than conventional real multipoles. That has been demonstrated for example in the case of the simulation of the sound radiation from an embedded vibrating cone, where the addition of complex sources to the collection of real sources can provide an improvement in the final results. Complex multipoles are mathematical constructions, therefore one cannot find radiators in nature that generate such radiation. But with the use of an array of loudspeakers it is possible to reproduce those radiation patterns. The amplitude and phase of each loudspeaker need to be previously determined, and that is obtained by means of a numerical approach that combines the BEM and the ESM. An excellent application of complex multipoles is the use of these elements to represent the Green’s function of the 3D half-space problem and its derivatives. For impedance grounds, a representation that uses real monopoles proves to be convergent for a ground with mass-like impedance but not for spring-like impedance. On the contrary, a representation including complex monopoles is convergent for all type of impedances. With such Green’s function a more efficient BEM approach for half-space problems is possible since the discretization can be limited to the radiating or scattering objects. For homogeneous grounds, it is found that the reflected wave as well as the transmitted wave can also be represented by equivalent source distributions with complex positions. Also, the Green's function of a moving monopole above an absorbing impedance can be represented by complex monopoles in the Lorentz space. Compared to the stationary case, the motion of the source produces a rotation of the imaginary vector by an angle proportional to the Mach number. But not only complex source positions are useful for constructing 3D half-space Green's functions, integration paths in the complex plane serve to build Green's function for 2D half-space problems, too.
Projektbezogene Publikationen (Auswahl)
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Physical realization of the radiation of complex multipoles, 23rd International Congress on Acoustics, Aachen, Germany, (2019)
Piscoya R. Piscoya, M. Ochmann
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Contributions of Manfred Heckl to the equivalent source method and its extension to sources with complex singularities, Proceedings of the Internoise 2016, Hamburg, Germany, (2016)
M. Ochmann, R. Piscoya
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Acoustical Green’s function and boundary element techniques for 3D half-space problems, Journal of Computational Acoustics, Vol. 25(4), (2017)
R. Piscoya, M. Ochmann
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Vergleich von 3D-Greenschen Funktionen für eine Halbraum-BEM- Implementierung, 43. Deutsche Jahrestagung für Akustik DAGA 2017, Kiel, Germany, (2017)
R. Piscoya, M. Ochmann
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Exact solution for the acoustical impulse response of a line source above an absorbing plane, Journal of the Acoustical Society of America, 144, 1539-1549 (2018)
M. Ochmann
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Schallabstrahlung eines Hochtonlautsprechers in einer Schallwand mittels der komplexen Ersatzstrahlermethode (CESM), 44. Deutsche Jahrestagung für Akustik DAGA 2018, Munich, Germany, (2018)
R. Piscoya, M. Ochmann
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Implementation of different formulas for special Green’s functions in a 3D half-space BEM, Journal of Computational Acoustics, Vol. 27(1), (2019)
R. Piscoya, M. Ochmann
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Realisierung der Richtcharakteristik komplexer Multipole, 45. Deutsche Jahrestagung für Akustik DAGA 2019, Rostock, Germany, (2019)
Piscoya R. Piscoya, M. Ochmann
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Das Schallfeld eines sich bewegenden und ein beliebiges Zeitsignal abstrahlenden Monopols über Impedanzboden, 46. Deutsche Jahrestagung für Akustik DAGA 2020, Hannover, Germany, (2020)
R. Piscoya, M. Ochmann
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Theory and application of acoustic sources using complex analysis, Springer Nature
M. Ochmann, R. Piscoya
