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Compact acoustic metasurfaces via impedance optimization in time-domain framework for reducing tonal noise from rotating point forces
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DOI：10.1016/j.advengsoft.2026.104191.png)
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Abstract
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This study presents a computational design framework based on time-domain optimization with frequencydependent impedance boundary conditions for a compact acoustic metasurface to reduce low-frequency tonal noise from rotating point forces in a short duct, capturing essential acoustic features of unsteady loading noise generated by rotating blades. Unlike previous frequency-domain approaches, the proposed time-domain framework directly resolves unsteady acoustic pressure fields in the time-domain, thereby accounting for the temporal, spatial, and spectral radiation characteristics induced by unsteady loading. Based on the time-domain analysis, complex-valued surface impedances along the duct wall are manipulated to effectively mitigate temporal pressure fluctuations and consequently minimize radiated acoustic energy at the blade passing frequency and its harmonics. A theoretical model for the effective impedance of coupled sub-wavelength Helmholtz resonators is employed to determine the metasurface geometry that matches the optimized impedances, establishing a direct theoretical link between the time-domain optimization and the metasurface design. Numerical results demonstrate that the designed metasurface effectively reduces tonal noise in the near field, and that the reduction performance is maintained even in the far field. The proposed design method, originally formulated for a single target frequency, is systematically extended to simultaneously address multiple harmonics. This extension yields reductions of 54.3% and 90% in acoustic energy at the two most dominant peak frequencies of 300 Hz and 450 Hz, using a metasurface with a thickness of lambda/28 at 300 Hz. These results suggest that the proposed time-domain optimization framework provides a systematic approach to design compact metasurfaces for multi-frequency tonal noise.
Keywords:
Time-domain optimization framework
Complex-valued acoustic impedance
Acoustic metasurface
Rotating point force
Low-frequency tonal noise
Noise reduction
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