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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]
Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 193713627
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  Data: Analytical modelling of the acoustic behaviour of multi-neck Helmholtz resonators using the parallel transfer matrix method.
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  Data: <searchLink fieldCode="AR" term="%22Heck%2C+Philipp+M%2E%22">Heck, Philipp M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> philipp.heck@tu-braunschweig.de</i><br /><searchLink fieldCode="AR" term="%22Papadakis%2C+Nikolaos+M%2E%22">Papadakis, Nikolaos M.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> nikpapadakis@tuc.gr</i><br /><searchLink fieldCode="AR" term="%22Stavroulakis%2C+Georgios+E%2E%22">Stavroulakis, Georgios E.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> gestavroulakis@tuc.gr</i><br /><searchLink fieldCode="AR" term="%22Langer%2C+Sabine+C%2E%22">Langer, Sabine C.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> s.langer@tu-braunschweig.de</i>
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  Data: <searchLink fieldCode="JN" term="%22Acta+Mechanica%22">Acta Mechanica</searchLink>. May2026, Vol. 237 Issue 5, p1991-2006. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Helmholtz+resonators%22">Helmholtz resonators</searchLink><br /><searchLink fieldCode="DE" term="%22Transfer+matrix%22">Transfer matrix</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Acoustics%22">Acoustics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Acoustic+impedance%22">Acoustic impedance</searchLink><br /><searchLink fieldCode="DE" term="%22Acoustical+materials%22">Acoustical materials</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00707-025-04595-0
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 1991
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        Type: general
      – SubjectFull: Transfer matrix
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      – SubjectFull: Finite element method
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      – SubjectFull: Acoustics
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      – SubjectFull: Mathematical analysis
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      – SubjectFull: Acoustic impedance
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      – SubjectFull: Acoustical materials
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      – TitleFull: Analytical modelling of the acoustic behaviour of multi-neck Helmholtz resonators using the parallel transfer matrix method.
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            NameFull: Heck, Philipp M.
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              M: 05
              Text: May2026
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              Y: 2026
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