Optimization of uncertain acoustic metamaterial with Helmholtz resonators based on interval model

Xia, Baizhan; Qin, Yuan; Chen, Ning; Yu, Dejie; Jiang, Chao

doi:10.1007/s11431-016-0562-1

Cited by 23 publications

(7 citation statements)

References 51 publications

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“…The resonant similarity condition is expressed aswhere ω a is the resonant angular speed and f 0 is the resonant frequency of HR. In terms of an acoustic system with the designed parameters satisfying equation (8), the working state of HR can be presented as a parallel resonance (Monteiro et al, 2018; Xia et al, 2017; Yuan et al, 2018). For a general angular speed ω = 2π f , the equivalent acoustic impedance Z a of HR can be expressed as…”

Section: Acoustic Theoretical Model Establishmentmentioning

confidence: 99%

Theoretical model and dynamic wave-amplification effect of the high intensity Helmholtz sound source

Qiao

Cheng

Jin

2021

Journal of Vibration and Control

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Helmholtz sound source consists of Helmholtz resonator and speaker and belongs to a new type of high-intensity sound source. It has potential industrial advantage in the aerodynamic acoustic application for the large amplitude wave. Based on the lumped parameter principle of acoustic impedance, an acoustic theoretical model is suggested. The model reveals the amplification regulation of the sound source on the acoustic wave. Through the acoustic theoretical computation, a dynamic amplification and an amplification limitation are analyzed. The wave-amplification effect attributes to the parameter regulation of the macro, micro, and dynamic-varied sizes of the sound source. The repetitive motion of the vibrating membrane of speaker causes three working states of balance, squeeze, and stretch. The three states act as specific boundary conditions and demonstrate as three different theoretical curves. The theoretical boundary curves codetermine an experimental curve, which essentially limits the practical amplification effect. Nevertheless, the amplification gain of sound pressure amplitude reaches up to 1.8 times, and the potential maximum amplitude reaches up to 3600 Pa (164 dB). The two quantitative characteristics indicate the maximum capability of the sound source on wave-amplification effect. The control sensitivity of the complicated impedance parameters on wave amplification is 0.26 Pa/Hz. The acoustic theoretical model is valuable in the series aspects of the industrial design, manufacture, and application of the sound source. Especially, the theoretical innovation lays the foundation of solid to these aspects.

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Section: Acoustic Theoretical Model Establishmentmentioning

confidence: 99%

Theoretical model and dynamic wave-amplification effect of the high intensity Helmholtz sound source

Qiao

Cheng

Jin

2021

Journal of Vibration and Control

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“…1. For the HR with a rigid wall, the acoustic impedance can be expressed as [2,9,21] Z H = i ωM ha − 1…”

Section: Model and Governing Equations 21 Acoustic Impedance And Reso...mentioning

confidence: 99%

“…By introducing repeated shunted rigid HRs, the propagation of acoustic waves in a pipe is analyzed. [2,[20][21][22] To the best of our knowledge, in the available literature, the propagation of acoustic waves in a fluid-filled pipe system with periodic HRs was studied but the elastic pipe walls have not been taken into consideration.…”

Section: Introductionmentioning

confidence: 99%

Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators

Shen

Liu

et al. 2018

Chinese Phys. B

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Helmholtz resonators are widely used to reduce noise in a fluid-filled pipe system. It is a challenge to obtain lowfrequency and broadband attenuation with a small sized cavity. In this paper, the propagation of acoustic waves in a fluid-filled pipe system with periodic elastic Helmholtz resonators is studied theoretically. The resonance frequency and sound transmission loss of one unit are analyzed to validate the correctness of simplified acoustic impedance. The band structure of infinite periodic cells and sound transmission loss of finite periodic cells are calculated by the transfer matrix method and finite element software. The effects of several parameters on band gap and sound transmission loss are probed. Further, the negative bulk modulus of periodic cells with elastic Helmholtz resonators is analyzed. Numerical results show that the acoustic propagation properties in the periodic pipe, such as low frequency, broadband sound transmission, can be improved.

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“…The design of PnCs without considering the effects of uncertainties may be incorrect. () Thus, how to accurately describe and efficiently handle uncertainties presented in PnCs is one of the main works in this paper.…”

Section: Introductionmentioning

confidence: 99%

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

Xie

Liu

Huang

et al. 2018

Numerical Meth Engineering

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Summary The design and analysis of phononic crystals (PnCs) are generally based on the deterministic models without considering the effects of uncertainties. However, uncertainties that existed in PnCs may have a nontrivial impact on their band structure characteristics. In this paper, a sparse point sampling–based Chebyshev polynomial expansion (SPSCPE) method is proposed to estimate the extreme bounds of the band structures of PnCs. In the SPSCPE, the interval model is introduced to handle the unknown‐but‐bounded parameters. Then, the sparse point sampling scheme and the finite element method are used to calculate the coefficients of the Chebyshev polynomial expansion. After that, the SPSCPE method is applied for the band structure analysis of PnCs. Meanwhile, the checkerboard and hinge phenomena are eliminated by the hybrid discretization model. In the end, the genetic algorithm is introduced for the topology optimization of PnCs with unknown‐but‐bounded parameters. The specific frequency constraint is considered. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

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Optimization of uncertain acoustic metamaterial with Helmholtz resonators based on interval model

Cited by 23 publications

References 51 publications

Theoretical model and dynamic wave-amplification effect of the high intensity Helmholtz sound source

Theoretical model and dynamic wave-amplification effect of the high intensity Helmholtz sound source

Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators

A polynomial‐based method for topology optimization of phononic crystals with unknown‐but‐bounded parameters

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