Theory and application of acoustical multipoles with complex singularities

• Applicant: Professor Dr.-Ing. Martin Ochmann
• Subject Area: Acoustics
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 257103641

Sources with complex source positions are mathematical structures that have been used to describe propagation of waves in fields like optics and electrodynamics but are not well known in acoustics. The objective of this project is to understand the mathematical and physical properties of these elements, referred as “complex multipoles” and apply them to describe wave phenomena in acoustics.In the first period of the project, the analysis of the complex multipoles has been performed. Complex monopoles were incorporated into the equivalent source method and proved to be advantageous in combination with real monopoles to simulate the sound radiation from baffled drivers at high frequencies with a low number of sources. The focused radiation of the complex monopoles turns out to be key in the reconstruction of the driver’s directivity. Complex monopoles, dipoles and quadrupoles have been used to describe the 3D half-space Green’s function and its derivatives over a locally reacting ground. This representation has shown a better convergence ratio and applicability than other existing forms. Focused radiation was used to generate scattering from special acoustic elements and diffraction.Based on the results obtained in the first project phase, the theoretical and numerical investigations of those sources will be continued and completed in the second project period. A 3D half-space Green’s function over a non-locally reacting ground based on complex multipoles is planned to derive. An extension of the applicability of the complex multipoles to 2D problems is intended. In particular, a representation of the 2D half-space Green’s function with complex line sources can be obtained probably by using the same approach as in three dimensions and should exhibit the same favourable analytical properties. Finally, the emphasis will be shifted from the frequency domain to the time domain. Sources with a complex time coordinate in addition to the complex spatial coordinate generate pulsed beams. Solutions of particularly selected problems should be efficiently represented by an expansion in beam functions.

• DFG Programme: Research Grants