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Analytical modelling of the acoustic behaviour of multi-neck Helmholtz resonators using the parallel transfer matrix method.

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Title: Analytical modelling of the acoustic behaviour of multi-neck Helmholtz resonators using the parallel transfer matrix method.
Authors: Heck, Philipp M.1 (AUTHOR) philipp.heck@tu-braunschweig.de, Papadakis, Nikolaos M.2 (AUTHOR) nikpapadakis@tuc.gr, Stavroulakis, Georgios E.2 (AUTHOR) gestavroulakis@tuc.gr, Langer, Sabine C.1 (AUTHOR) s.langer@tu-braunschweig.de
Source: Acta Mechanica. May2026, Vol. 237 Issue 5, p1991-2006. 16p.
Subjects: Helmholtz resonators, Transfer matrix, Finite element method, Acoustics, Mathematical analysis, Acoustic impedance, Acoustical materials
Abstract: Since multi-neck Helmholtz resonators (HRs) have attracted considerable research interest in recent years in the context of leakage, and both extended tunability and broader frequency response can be achieved through the targeted use of such resonators, the development of a precise analytical model for predicting the acoustic behaviour of individual multi-neck HRs or those embedded in complex systems is of central importance. In this study, an analytical model based on the parallel transfer matrix method (PTMM) is developed to predict the acoustic behaviour of multi-neck HRs under plane-wave excitation. The analytical PTMM approach is validated by means of impedance tube measurements according to ISO 10534-2 on seven carefully selected symmetrical and asymmetrical specimens and by numerical comparisons of the acoustic parameters predicted by the PTMM approach with the results of the finite element method (FEM) and the predictions of two established analytical models. The results show that the PTMM approach can predict the acoustic behaviour of both symmetrical and asymmetrical samples with high accuracy and has clear advantages in terms of accuracy over one of the established models, the transfer impedance-based model. A comparison with the analytical approach of the model for micro-perforated plates adapted in this article shows that the proposed PTMM approach delivers identical results, but in certain cases is superior in terms of the accuracy of the acoustic prediction. To summarise, the analytical PTMM approach proposed in this study shows superior performance in predicting relevant acoustic parameters compared to the established analytical models as well as FEM and offers significant potential for further applications and extensions in a wider range of contexts and variants. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:Since multi-neck Helmholtz resonators (HRs) have attracted considerable research interest in recent years in the context of leakage, and both extended tunability and broader frequency response can be achieved through the targeted use of such resonators, the development of a precise analytical model for predicting the acoustic behaviour of individual multi-neck HRs or those embedded in complex systems is of central importance. In this study, an analytical model based on the parallel transfer matrix method (PTMM) is developed to predict the acoustic behaviour of multi-neck HRs under plane-wave excitation. The analytical PTMM approach is validated by means of impedance tube measurements according to ISO 10534-2 on seven carefully selected symmetrical and asymmetrical specimens and by numerical comparisons of the acoustic parameters predicted by the PTMM approach with the results of the finite element method (FEM) and the predictions of two established analytical models. The results show that the PTMM approach can predict the acoustic behaviour of both symmetrical and asymmetrical samples with high accuracy and has clear advantages in terms of accuracy over one of the established models, the transfer impedance-based model. A comparison with the analytical approach of the model for micro-perforated plates adapted in this article shows that the proposed PTMM approach delivers identical results, but in certain cases is superior in terms of the accuracy of the acoustic prediction. To summarise, the analytical PTMM approach proposed in this study shows superior performance in predicting relevant acoustic parameters compared to the established analytical models as well as FEM and offers significant potential for further applications and extensions in a wider range of contexts and variants. [ABSTRACT FROM AUTHOR]
ISSN:00015970
DOI:10.1007/s00707-025-04595-0