Use of complex frequency plane for perfect absorption with a Helmholtz resonator: From lossless linear to viscothermal nonlinear cases
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.
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BibTeX
@article{hagstrom2026complex,
title = {{Use of complex frequency plane for perfect absorption with a Helmholtz resonator: From lossless linear to viscothermal nonlinear cases}},
author = {Joar Zhou Hagström and Jean-Philipe Groby and Yves Aurégan and Vincent Pagneux and Vassos Achilleos},
journal = {Journal of Sound and Vibration},
year = {2026},
month = jul,
doi = {10.1016/j.jsv.2026.120000},
url = {https://hal.science/hal-05759978v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Use of complex frequency plane for perfect absorption with a Helmholtz resonator: From lossless linear to viscothermal nonlinear cases
AU - Joar Zhou Hagström
AU - Jean-Philipe Groby
AU - Yves Aurégan
AU - Vincent Pagneux
AU - Vassos Achilleos
PY - 2026
DA - 2026/07/11
JO - Journal of Sound and Vibration
DO - 10.1016/j.jsv.2026.120000
UR - https://hal.science/hal-05759978v1
AB - 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.
SN - 0022-460X
SN - 1095-8568
ER -