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Meng Y, Romero-García V, Gabard G, Groby JP, Bricault C, Goudé S, Sheng P. Fundamental constraints on broadband passive acoustic treatments in unidimensional scattering problems. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0287] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In a passive lossy acoustical system, sum rules derived from passivity explicitly relate the broadband response to the spatial dimension of the system, which provide important design criteria as well. In this work, the theory of Herglotz function is applied systematically to derive sum rules for unidimensional scattering problems relying on passive acoustic treatments which are generally made of rigid, motionless and subwavelength structures saturated by air. The rigid-boundary reflection, soft-boundary reflection and transmission problems are analysed. The derived sum rules are applied for guiding the designs of passive absorbers and mufflers: the required minimum space is directly predicted from the target (i.e. the desired absorption or transmission-loss spectra) without any specific design. Besides, it is possible to break this type of sum rules and fundamental constraints in particular cases. This property, if well used, could result in ultra-compact absorbers working at long wavelength up to infinity.
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Affiliation(s)
- Yang Meng
- Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique—Graduate School, CNRS, Le Mans Université, Le Mans, France
| | - Vicente Romero-García
- Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique—Graduate School, CNRS, Le Mans Université, Le Mans, France
- Departamento de Matemática Aplicada, Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera, s/n, València 46022, Spain
| | - Gwénaël Gabard
- Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique—Graduate School, CNRS, Le Mans Université, Le Mans, France
| | - Jean-Philippe Groby
- Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique—Graduate School, CNRS, Le Mans Université, Le Mans, France
| | - Charlie Bricault
- Vibrations and Acoustics Laboratory, Valeo Thermal Systems, Paris, France
| | - Sébastien Goudé
- Vibrations and Acoustics Laboratory, Valeo Thermal Systems, Paris, France
| | - Ping Sheng
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China
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