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TU Berlin

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Dr.-Ing. Jens Prager

Former Academic Staff

On the acoustics of small partially open enclosures densely packed with active and passive installations

In the study presented different aspects are investigated of air borne sound propagation inside a partially open enclosure densely packed with active and passive installations. Primarily the work is aimed at predicting the sound field at the interfaces of the enclosure to the adjacent fluid space. The prediction procedure is subdivided into the description of the sound sources inside the enclosure and the prediction of the transfer impedance linking the sound sources to the sound field at the interface to the adjacent fluid. Depending on the relation between wavelength and the geometrical dimension of the system the sound field structure inside the enclosure is found to vary markedly with frequency. Common analysis tools are adapted for their applicability in the given context.

The Statistical Energy Analysis (SEA), which is assumed to be applicable in the high frequency region, is supplemented by an approach including the influence of source and receiver positions close to boundaries or field discontinuities. Therefore a correction is integrated into the SEA considering the first order reflections by including the corresponding image sources.

From testing the applicability of common analysis tools it is shown a lack of appropriate analysis tools for the intermediate frequency range, which also provide information about the reliability of the analysis results. Two novel approaches are presented to predict the sound field in a frequency region of low modal density. The approaches are based on probabilistic descriptions of the system geometry, which appear promising with regard to the engineering practice. It is shown that the acoustical behaviour can be extracted by either modelling the remaining free fluid space or the installations inside the enclosure. Although the validity limitations of the approaches presented are different, both approaches produce similar results in the considered frequency region. The validity and applicability of the probabilistic approaches is demonstrated by comparing the results with those from a numerical calculation.

Strategies are presented for integrating the sound sources into the modelling. For the coupling between source characterisation and sound propagation it is suggested to use a decomposition of complex shaped sound sources into multipoles of different order. The decomposition in terms of spherical Nearfield Holography (NAH), however, is found to be limited to simple source geometries. For complex shaped sound sources, not fulfilling the validity conditions of the Rayleigh hypothesis a method using a truncated series of Gegenbauer polynomials is proposed to overcome the problems arising from singularities in the sound field.

The validity of the proposed approaches, methods and simplifications is verified by comparing the results with those of dedicated experiments.

Dissertation : http://opus.kobv.de/tuberlin/volltexte/2008/1770/
Supervisor : Prof. Dr.-Ing. B.A.T. Petersson


B.A.T. Petersson and J. Prager (2006). Influence of the first order reflection on statistical energy analysis.. Proceedings of the IX International Conference on Recent Advances in Structural Dynamics. Southampton, UK (CD).

J. Prager and B.A.T. Petersson (2003). Schallabstrahlung von teilweise geöffneten Strukturen. DAGA 2003

J. Prager and B.A.T. Petersson (2007). Modelling of sound in small fitted enclosures using probabilistic approaches.. Acta Acustica, 93, 750-759


Dr.-Ing. Jens Prager
Bundesanstalt für Materialforschung und -prüfung (BAM)
Fachgruppe VIII.4 (Akustische und Elektrische Verfahren)
Federal Institute of Materials Research and Testing
Division VIII.4 (Acoustic and Electrical Methods)
Tel.: +49 30 8104-3873
Fax: +49 30 8104-1845

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