Work

Use of complex frequency plane for perfect absorption with a Helmholtz resonator: From lossless linear to viscothermal nonlinear cases

Year: 2026

Type: article

Abstract: We investigate the acoustic absorbing properties of a Helmholtz resonator attached to the end of a semi-infinite waveguide across the linear and nonlinear regimes. The reflection coefficient can be characterized by a complex pair of pole and zero at low frequencies. Using them in the complex frequency plane, we demonstrate how perfect absorption can be achieved by fine-tuning either the resonator geometry or the excitation amplitude. We extract this pair, with and without viscothermal losses, directly by solving eigenvalue problems in the linear regime using perfectly matched layers for the pole and the conjugate perfectly matched layers for the zero. Then, with the inherent loss in air, tuning the geometry allows us to achieve perfect absorption by steering the zero onto the real axis. We finally extend the use of the complex frequency plane for higher amplitude excitation, where nonlinearity effects are non negligible. By tracking the pole and zero, we determine how to achieve perfect absorption for the reflection component of the fundamental frequency by increasing the excitation amplitude.

Source: Journal of Sound and Vibration

DOI: 10.1016/j.jsv.2026.120000

Authors: Joar Zhou Hagström, Jean-Philipe Groby, Yves Aurégan, Vincent Pagneux, Vassos Achilleos

Institutions: Centre National de la Recherche Scientifique, Le Mans Université, Laboratoire d'Acoustique de l'Université du Mans

Language: English

Topic: Acoustic Wave Phenomena Research

Subfield: Acoustics and Ultrasonics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,190

Funder: H2020 Excellent Science