Resonant peak tuning of a nonlinear multi-mode perforated panel absorber by pre-setting its deflection profile

Kongzheng Liang; Di Zeng; Yiuyin Lee; Zongxian Wang; Kongzheng Liang; Di Zeng; Yiuyin Lee; Zongxian Wang

doi:10.3934/math.2026051

AIMS Mathematics

2026, Volume 11, Issue 1: 1202-1218. doi: 10.3934/math.2026051

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Resonant peak tuning of a nonlinear multi-mode perforated panel absorber by pre-setting its deflection profile

1.
Institute of Systems Science, Beijing Wuzi University, Beijing 101149, China
2.
Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China
3.
Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong

Received: 29 September 2025 Revised: 27 December 2025 Accepted: 06 January 2026 Published: 16 January 2026
MSC : 37M05, 65M99, 65P99

In this paper, we addressed the absorption of sound by a nonlinear multi-mode panel absorber. Nonlinear structural vibration has been greatly investigated in recent decades, but very few researchers have considered structural nonlinearities in structural–acoustic models. Importantly, the first structural resonant frequency of a perforated panel absorber with typical dimensions is much lower than the absorption peak frequency. The results of this study indicated that such resonant vibration cannot enhance the absorption performance. Thus, a novel approach was proposed, namely to increase the first nonlinear panel resonant frequency by pre-setting the initial deflection profile, enabling the resonant vibration effect to be used for widening the absorption bandwidth. A new solution method, termed the phase angle elimination method, was developed for cases of damped nonlinear vibration. The principle of the method was to transform the nonlinear governing equation of a perforated panel into a set of multi-mode formulations. A numerical case study was conducted to examine the effects of various parameters on the absorption performance.
- panel absorber,
- noise and vibration,
- sound absorption,
- acoustics
Citation: Kongzheng Liang, Di Zeng, Yiuyin Lee, Zongxian Wang. Resonant peak tuning of a nonlinear multi-mode perforated panel absorber by pre-setting its deflection profile[J]. AIMS Mathematics, 2026, 11(1): 1202-1218. doi: 10.3934/math.2026051

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Abstract

In this paper, we addressed the absorption of sound by a nonlinear multi-mode panel absorber. Nonlinear structural vibration has been greatly investigated in recent decades, but very few researchers have considered structural nonlinearities in structural–acoustic models. Importantly, the first structural resonant frequency of a perforated panel absorber with typical dimensions is much lower than the absorption peak frequency. The results of this study indicated that such resonant vibration cannot enhance the absorption performance. Thus, a novel approach was proposed, namely to increase the first nonlinear panel resonant frequency by pre-setting the initial deflection profile, enabling the resonant vibration effect to be used for widening the absorption bandwidth. A new solution method, termed the phase angle elimination method, was developed for cases of damped nonlinear vibration. The principle of the method was to transform the nonlinear governing equation of a perforated panel into a set of multi-mode formulations. A numerical case study was conducted to examine the effects of various parameters on the absorption performance.

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