Adjustable sound absorbing metastructures for low-frequency variable discrete sources

<sec>Low-frequency noise has always been a thorny problem in the field of noise control. In recent years, the development of sound-absorbing metastructures has provided new ideas for controlling low-frequency noise. In this work, we propose a low-frequency sound-absorbing metastructure constructed by Helmholtz resonators with embedded slit. Analytical and numerical models are established to analyze the sound absorption performance and mechanism of the proposed sound-absorbing metastructure, and optimization design is conducted to achieve low-frequency wideband absorption performance. The analytical modeling method and the performance of the proposed sound-absorbing metastructure are also experimentally verified. The main conclusions are summarized as follows.</sec><sec>1) By using transfer matrix method and finite element method, analytical and numerical models for calculating sound absorption coefficient are established. It is shown that analytical predictions are in good agreement with numerical calculations. It is demonstrated that a typical design of a 30-mm-thick single-cell metastructure can achieve a sound absorption coefficient of 0.88 at 404 Hz. Typical designs of two-cell parallel structure and the four-cell parallel structure (both with a thickness of 50 mm) can achieve two and four nearly perfect low-frequency sound absorption peaks in a frequency band of 200–400 Hz, respectively.</sec><sec>2) The low-frequency sound absorption mechanisms of the proposed metastructures are explained from four aspects: simplified equivalent model parameters, normalized acoustic impedance, complex-plane zero/pole distribution, and sound pressure cloud image and particle velocity field distribution. It is demonstrated that the main sound absorption mechanism is related to the thermal viscous loss of sound waves, caused by the inner wall of embedded slit.</sec><sec>3) The design for broadband low-frequency absorption performance is optimized by using differential evolution optimization algorithm. An optimized parallel-multi-cell coupled metastructure with multiple perfect sound absorption peaks below 500 Hz is realized. For a thickness of 90 mm, the sound absorption coefficient curve of an optimized metastructure exhibits 8 almost perfect sound absorption peaks and an average sound absorption coefficient of 0.86 in a frequency range of 170－380 Hz.</sec><sec>4) Experimental samples are fabricated to test sound absorption. Experimental results are basically consistent with the analytical predictions. The results from analytical model, numerical calculations and experimental measurements are mutually verified.</sec><sec>In summary, the sound-absorbing metastructures with a thickness of sub-wavelength, proposed in this work, exhibit outstanding sound absorption performance at low frequencies. We demonstrate that they are suitable for low frequency broadband sound absorption below 500 Hz. Owing to their thin thickness and relatively simple construction, they have broad application prospects in practical noise control engineering.</sec>

A double cavity resonant device embedded with porous material and microperforated panel

The noise attenuation ability of a single material or structure, especially for low-frequency noise, is limited by its thickness. Aiming to achieve high-efficiency noise attenuation at low frequencies, this paper proposes the methods of porous material filling and micro-perforated plate (MPP) embedding to design a perfect sound absorber at different frequencies using the under-loss Helmholtz resonator (HR). Based on the transfer matrix method, the theoretical calculation models of the sound absorption coefficients of the HR, Helmholtz resonator with porous material (HRP), and Helmholtz resonator with micro-perforated plates (HRM) are constructed. Based on the theoretical models, the under-loss absorber HR1 with the peak absorption at 243 Hz, and the HRP and HRM with perfect absorption at 212 Hz and 157 Hz are designed, respectively. The impedance analysis and complex frequency plane method are used to analyze the sound absorption mechanisms of the HR1, HRP, and HRM. The accuracy of the theoretical model is verified by the finite element method. Finally, the three acoustic absorbers are manufactured using 3D printing technology, and the absorption coefficients are evaluated experimentally. The experimental results show that the HR1 has a high working frequency at 245 Hz and a narrow bandwidth of high-efficiency sound absorption ([Formula: see text]), which is only 12 Hz. The working frequency of the HRP is 214 Hz, and its high-efficiency sound absorption bandwidth is 54 Hz. The HRP has the lowest working frequency at 157 Hz and the widest high-efficiency sound absorption bandwidth of 58 Hz among the three absorbers. The research results presented in this paper provide a reference for the realization of low-frequency broadband noise attenuation designs and have certain application potential in noise control.

Most of the sound absorption methods in noise control used fibrous materials, which are prone to generate dust particles and other problems. Micro-perforated sound absorption structure can have good sound absorption performance without filling any sound absorption materials. It can effectively solve the problem of dust particles caused by fibrous soundabsorbing materials. Based on the micro-perforation theory, the sound absorption structure of double-layer composite metal plate is studied according to the acoustic and electrical analogy method, and the sound absorption performance of different size structures is calculated and simulated in MATLAB. The two structures with ideal simulation results are processed for sample preparation, and the performance test verification is completed in the reverberation room.

The experiences of stress are common to all living things. Noise is one of the most widespread sources of environmental stress. Noise is a pervasive aspect of many modern community and work environments. So, it is important to consider noise when we design human-oriented products. This study investigates the responses of electrocardiogram (ECG) and eye tracker data in order to evaluate the direct effects of low, middle, and high frequency noise on the two main physiological stress axes: the autonomic nervous system, and cognitive responses for a human-oriented product design. A subject was exposed to low (100 Hz), middle (1000 Hz), and high frequency (100000 Hz) noise while awake. ECG and eye tracker data were collected during noise exposure. Sympathetic nervous system (SNS) activity was less in the low and high frequency noise ranges compared to the no sound. On the other hand, parasympathetic nervous system (PNS) activity was greater in the low and high frequency noise ranges than the SNS activity in the no sound. The cognitive responses or latency saccadic eye movement (LSEM), in low or high frequency noise was greater than that in the no sound. And results of EEG and eye movement were statistically significant in low and high frequency noise (r > 0.93, p < 0.05). The findings of this study indicate that the stress induced by low frequency noise is as stressful as the stress induced by high frequency noise. Additionally, utilizing eye tracker data and acquiring the LSEM is useful in the analysis of human stress responses during various stressful situations in addition to the analysis of human stress responses during noise exposure.

Although crucial transport equipment in coal mining enterprises, tubular belt conveyors cause serious noise pollution. In this paper, the sound absorption and isolation performance of three kinds of highly efficient sound-absorbing and -insulating materials were studied by finite element multiphysics field software COMSOL and acoustic tests, and the structure of highly efficient sound-absorbing and -insulating materials was optimized and designed. The results show that the acoustic superstructure plate has an excellent sound insulation effect of 36 dB, and achieves an excellent sound absorption coefficient of 0.95 at 210 Hz on the acoustic simulation test. The simulated weighted sound insulation of acoustic metamaterial plate is 37 dB, and the simulated weighted sound insulation of acoustic metamaterial plate filled with particle material is 42 dB, which improves the sound insulation effect by 4~7 dB after filling with particle material, and the comprehensive absorption coefficient of the high-frequency noise of more than 800 Hz reaches 0.94, and it can effectively absorb and block the low-frequency noise as well; rock wool acoustic panels in the 500 Hz to achieve a better acoustic capacity, the absorption coefficient of 0.8 or more, but the low-frequency noise acoustic capacity is still lacking, and can not be a good solution to the full-frequency band of the acoustic problem. It can be seen that the acoustic metamaterial plate has the best sound absorption and insulation effect. At the same time, the acoustic metamaterials based on the honeycomb structure are optimized, and the sound absorption and insulation structure with the angle of 60° of the inclined plate and the length of 693 mm of the inclined plate is the optimal structure. It provides a solution to the noise pollution caused by tubular belt conveyors.

The sound absorption effect of a Helmholtz resonator was induced by creating an aperture in a nonwoven fabric sheet with a back air space, thus obtaining a sufficient sound absorption effect in a broad frequency range. In this study, transfer matrices were used to obtain the sound absorption coefficient. Transfer matrices were used to represent the following mathematically: a nonwoven fabric model based on the simplified limp-frame model, an acoustic element that considers the vibration of the nonwoven fabric sheet, the air space behind the nonwoven fabric sheet, and the aperture of the nonwoven fabric sheet. Equivalent circuits combining these transfer matrices were used to obtain sound absorption coefficient. The Helmholtz resonator sound absorption effect was more pronounced for the nonwoven fabric sheets with greater ventilation resistance. The results showed consistency between the experimental and theoretical trends. As for the sound absorption coefficient derived using the theoretical models for nonwoven fabric sheets, the results of the simplified limp-frame model were the closest to the experimental values. As the length of the back air space increased, the peak sound absorption value shifted toward low frequencies due to the sound absorption principles of both the nonwoven fabric sheet with a back air space and the Helmholtz resonator.

Brick/block absorbing walls with openings backed with porous materials are often used for sound absorptive treatments in buildings. This type of brick/block walls have a frequencyselective sound absorption at low frequencies, which is usually explained as the Helmholtz resonance. In addition, they often have peaks of sound absorption at frequencies much different from the Helmholtz resonance frequency. In this paper, the sound absorption mechanism of this type of walls was investigated by experiments. As a result, it has been confirmed that the sound absorption is caused by the effect of open-pipe resonance which happens in the openings. In the case of brick/block sound absorptive constructions made of materials with a thickness of about 10 cm, sound absorption caused by the open-pipe resonance is considerably significant at high frequencies. Therefore, when this type of sound absorption construction is used for room acoustic treatment, sound absorption at high frequencies must be carefully considered in acoustical design.

Re-entrant auxetic designs, known for their superior mechanical properties, are increasingly explored in various industrial applications. This study aims to enhance the multifunctionality of such designs by preserving their mechanical characteristics while improving their acoustic performance. A multi-layer hybrid structure integrating microperforated panels with auxetic geometry was proposed. This design enabled each auxetic cavity to function as a Helmholtz resonator. Sample fabrication was performed with fused deposition modeling (FDM), an Additive Manufacturing technique, using PLA as build material. The perforations and minimum structural features were designed to maintain structural integrity and mechanical properties while facilitating ease of manufacturing. A computational modeling approach was verified and validated using numerical and experimental results from the literature. Impedance tube testing techniques were employed to validate the numerical model for sound transmission loss (STL) and sound absorption coefficient (SAC), ensuring precise measurement of acoustic properties and confirming the accuracy of the simulations. A total of 18 variants of proposed design were numerically examined in the low to mid-frequency range (50–1800 Hz). The effects of various geometric and material parameters on acoustic performance were recorded. Results indicate substantial enhancement in SAC as well as STL from baseline design of the same dimensions. SAC above 0.5 was achieved for a broad frequency range of 1180 Hz with an average STL of 55 dB. This research advances the development of multifunctional subwavelength metamaterials by presenting a structure that exhibits exceptional STL and SAC—a combination not previously documented in recent literature.

An acoustic metasurface gives a broadband sound absorption by a planar periodic array combining small resonant modules tuned at different frequencies. The resonant module is often applied by a Helmholtz resonator, a membrane backed by an airtight cavity and a quarter wavelength closed tube, which have equivalent small area to a fraction of the wavelength. The author has studied the sound absorption of resonators by applying a multiple folded long neck and an airtight cavity for a thin sound-absorbing structure with high sound absorption at low frequencies below 100 Hz. In this paper, the author prototypes an acoustic metasurface by planar periodic array of Helmholtz resonators at various resonant frequency tuned by this neck and cavity of the resonator as a unit cell, and discusses the sound absorption characteristics. The prototyped acoustic metasurface gives a 40 % - 70 % sound absorption from 125 Hz to 250 Hz when it is combined with a 6.4 mm thickness of top plate including a 24 mm - 96 mm length of the multiple folded long neck and a 43.2 mm depth of the airtight cavity. And, more broadband sound absorption will be discussed by a theoretical analysis.

Metamaterials show perfect physics characteristics for controlling elastic wave propagation. Their potential offers a lot of useful applications in low-frequency sound absorption and vibration reduction systems. However, traditional materials have inherent deficiencies in terms of functionality. There are a few designs in both acoustic and solid-mechanics domains that simultaneously exhibit sound attenuation bands and vibration bandgaps. The question poses new challenges for metamaterial development. To address this, we propose a gradient-symmetric multilayered metamaterial. The structure is capable of concurrent sound and vibration absorption. First, we established an acoustic model based on Helmholtz resonators and a vibration model by spring-mass systems. This model can predict the sound attenuation frequencies and natural frequency positions accurately. Second, through a combined simulation and experimental approach, we investigated how variations in the number of structural layers affect sound attenuation bandwidth. In addition, we analyzed the mechanisms of sound pressure distribution inside and outside the bandgaps. Finally, we elucidated the influence of lattice constants on vibration bandgap positions, demonstrating possibilities for passive control of metamaterials. This research provides robust support for the dynamic design of acoustic and mechanical metamaterials, structural modeling methodologies, bandwidth regulation strategies, and the development of sound-absorbing and vibration-damping devices.

The application of solutions based on conventional porous materials for low-frequency sound absorption is often limited to the available space for their installation, as these require a significant thickness to be efficient. A system combining of a microperforated panel with an array of Helmholtz resonators, properly designed, can provide effective noise absorption at low- and mid-frequencies with a limited thickness. In this work, the sound absorption coefficient of several systems of this type was assessed by analytical calculations, numerical simulations and experiments carried out in an impedance tube according to the standard ISO 10534-1:1996. The prototypes were 3-D printed using recycled materials. The absorption coefficient, analytically obtained, was significantly higher than that measured. However, the results from numerical simulations are in good agreement with measurements, showing that the numerical model carried out can be used for further studies to optimize the system design. An example is given by increasing of the number of Helmholtz resonators in the array, that yields an increase in the sound absorption. Results show the potential of this type of solutions to be used for low-frequency noise absorption in applications where the available space is limited.

With the development of the industry and the society, noise pollution becomes increasingly severe, especially in large cities. Generally, there are three major noise sources, namely industrial noise, traffic noise and community noise. In response, several measurements have been developed to achieve effective noise control. Examples of noise control methods are reduction of noise at source and abatement of noise during the transmission. Since noise sources are more difficult to control, and sometimes already fixed, noise control during sound transmission is more broadly applied. Traditional passive noise control techniques include Helmholtz resonators and noise absorption materials like felt, glass mineral. The sound absorption materials (SAM) are found to be efficient in attenuating noise in high frequency domain, but their performance at low frequencies is quite poor. On the other hand, the Helmholtz resonator works perfect at any target frequency but suffers from its narrow absorption bandwidth, so that it’s only effective within a limited frequency band.&#13;\n&#13;\nAs an innovative solution to passive noise control problem, micro-perforated panel absorber (MPPA) has attracted great interest in recent years. It turns out to be a competitive alternative to sound absorption materials and Helmholtz resonator. The parallel and series arrangement of MPPAs backed with cavities of different depths allows them to obtain decent noise absorption performance over a relatively broad frequency range. However, the performance of MPPA is restricted by its volume, as large volume is demanded for decent low-frequency absorption, which is also the case for noise absorption materials.&#13;\n&#13;\nIn this thesis, a potential way to improve the low-frequency performance of the MPPA without occupying extra volume is proposed and implemented to tests. The focus is the adjustment of speed of sound and it is beneficial in different applications such as the following. In low frequency noise control, the size of the absorber in at least one dimension is often related to the wavelength and it is often too long. With a reduced speed of sound one can reduce this size while keeping the overall volume constant. Along this line of thinking, the effect of cavity configuration on its acoustic properties is investigated by two steps. Firstly, the property of a waveguide consisting of several identical elements is studied. The number of element is chosen to magnify the effect of the configuration. It turns out the irregularity of the duct shape can slow down the speed of sound of the plane wave by increasing the acoustic mass. Secondly, the absorption performance of an MPPA backed with an irregular cavity is evaluated. The shape of the cavity is the same as the element in the first step. In advance, the parallel arrangement of two MPPAs backed with irregular cavities is investigated, in order to look into the effect of cavity shape on inter-resonator interaction. The final results indicate that cavity design is an effective method to enhance the noise absorption performance of the MPPA arrays in the low-frequency domain.

Aiming at the unsatisfactory low-frequency sound absorption effect of Helmholtz resonator, a novel broadband low-frequency ventilation absorber with rough neck is proposed. The roughness is introduced into the neck of Helmholtz resonator to change the shape of the neck and achieve the structure of rough neck Helmholtz resonator. The proposed absorber can effectively provide the acoustic impedance required for low-frequency sound absorption without changing the overall size, thereby reducing the resonant frequency. The finite element method is used to simulate the structure, and the impedance tube sound absorption test is carried out to verify it. The experimental and simulation results show high consistency with each other. The results also indicate that the rough neck Helmholtz resonator absorber with roughness introduced in the neck achieves an absorption peak at 58 Hz, with an absorption coefficient of about 0.63. Comparing with the absorber without roughness introduced, the resonant peak frequency becomes low, from 70 Hz to 58 Hz, reducing 17.1%. Therefore, adjusting the neck roughness can serve as a method of tuning the acoustic performance, and the absorption peak frequency can be adjusted by appropriately increasing the neck roughness so as to move it in the low frequency direction. Based on the verification that the roughness of the neck can effectively reduce the absorption peak frequency of Helmholtz resonator, a broadband low-frequency ventilation absorber with a rough neck, which is composed of eight absorption units, is designed. Through simulation calculation and experimental exploration, the absorption coefficient can achieve more than 0.8 in a target working frequency band of 500－1100 Hz. On this basis, the acoustic impedance of the structure can be adjusted by introducing roughness into the neck of Helmholtz resonator, so as to obtain the optimized broadband low-frequency ventilation absorber with a rough neck, which achieves a broadband sound absorption coefficient higher than 0.8 in a frequency range of 400–1200 Hz. The optimized structure also has 8 consecutive absorption peaks with amplitudes above 0.95. The proposed low-frequency broadband ventilation absorber provides a reference for designing and optimizing efficient low-frequency subwavelength acoustic absorbers. It has a wide range of applications in pipeline noise control.

Acoustic properties of honeycomb like sandwich acoustic metamaterials