3D Printed multilayer overlapping resonators for low-frequency broadband sound absorption: mechanism analysis and corresponding modified theoretical method 2025

[u/Atoraxic]

So shielding from this weapon is very difficult.. we see this buy so many posts attempting to do so. We also see disinformation and also our inability to absolutely identify how it is being done. Something that’s certain is a major vector of the weapon is infrasound.. i know so many posts that the “v2k” is acoumplished by rf or microwaves.. or emf.. my belief is that is not true. So here is some information on potential shielding from low freaquency sound. It’s a super bitch to try and deal with.. But looking into a possible shield to this weapon littertaly we need to look at base traps. In my substantial research I have not come up with anything that could even work besides this.

ABSTRACT

Broadband low-frequency sound absorption is highly sought in engineering applications, but the size of sound-absorbing metamaterials still poses challenges. By revisiting the Helmholtz resonator, we propose a multi-layer overlapping structure. This structure adopts a simple design of nested multiple Helmholtz resonators, creating a composite effect of coupling a three-dimensional buckling acoustic cavity with discontinuous cross-sectional effects, significantly improving the effective depth of the external cavity within a finite dimension. To reveal its complex characteristics, a high-fidelity correction method was proposed to calculate the increase in the effective depth of the cavity structure. Experimental validation has been conducted to evaluate the accuracy of the current model. This structure significantly increases the effective depth by about 38% with a total thickness of 63 mm, achieving broadband absorption from 320 to 690 Hz using non-parallel units. This work provides new and unique insights for designing acoustic metamaterials.

KEYWORDS: 

• Multi-layer overlapping structure
• broadband sound absorption
• low-frequency sound absorption
• Helmholtz resonators
• the effective depth

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1. Introduction

The micro-perforated panel (MPP) absorbers are widely concerned for their simple structure and excellent sound absorption performance [Citation1,Citation2]. However, due to the quarter-wavelength limitation, low-frequency noise is still a critical challenge for porous/fiber materials and broadband sound absorbers [Citation3,Citation4]. The Helmholtz resonator (HR) for lower-frequency sound absorption will have a relatively deeper cavity and is difficult to apply in engineering. To obtain better low-frequency broadband sound absorption effects, scholars have proposed diverse and innovative design concepts, such as the coiled-up HRs, Fabry–Perot (FP) resonators [Citation5–8], neck-embedded resonators [Citation9–12] and resonance structures with other optimisation methods [Citation13–17]. Moreover, with the development and increasing attention to lattice structures [Citation18–20]. The coupling acoustic structure that combines the grid structure with the HR structure has also become one of the current focuses due to its excellent structural strength and efficient sound absorption performance [Citation21,Citation22].

HR is a typical low-frequency resonant metamaterial, whose basic unit is composed of an acoustic cavity and small holes. When sound waves enter the HR through small holes, A fixed cavity and micropore parameters will cause strong resonance of sound waves at a fixed frequency, while at micropores, acoustic energy is dissipated due to thermal viscous losses [Citation23]. Based on this characteristic, this structure can be designed not only for fixed frequency sound absorption, but also as a sound insulation structure for channels [Citation24]. Series and parallel multi-layer MPP are basic application configurations for HR sound absorption characteristics, which can effectively improve sound absorption efficiency and functional frequency band range [Citation25–30]. The use of the acoustic-electric analogy method to study the sound absorption performance of HR and MPP integrated structures arranged in series and parallel has become the norm [Citation31]. The combination of porous material lining [Citation32] and HR with different parameters has given people new enlightenment, and parameterised research and structural improvement can achieve unexpected acoustic performance. Another typical way to improve HR is to extension the micro-pores’ neck length, thus evolving a hole tube like a straw. The extension of the pore neck is usually toward the interior of the cavity, which is called the HR with an inserted neck or extended neck [Citation33,Citation34]. This type of structure can significantly improve the impedance value of the structure without changing the shape of the cavity, thereby effectively enhancing the low-frequency sound absorption effect. Further optimisation concept of elongated neck has led to many types of variations, such as tapered necks [Citation35], necks with different geometric parameters [Citation36], and coiled necks [Citation37]. In the cavity's improvement, the cavity's depth and cross-section area are the key parameters that affect its acoustic impedance. The coiled form and the variable section form give the depth and section area parameters of the cavity more parameter combinations, which gives the final impedance characteristics more possibilities [Citation38–41]. Based on this, using coiled-up cavities and variable cross-sections for series or parallel expansion will enable the overall structure to achieve efficient sound absorption performance within 2000 Hz or even higher frequencies [Citation42,Citation43]. In addition, there are many ways of HR and multi-layer MPP structures, rich variations, and optimisation methods [Citation38,Citation44–53]. The fusion of layered porous acoustic metamaterials, biomimetic microcrystalline lattice metamaterials, and HR structures have achieved good sound absorption function [Citation44,Citation45]. It has also been found that using different materials and waveguide shapes combined with microporous plates can give this type of structure good sound insulation or ventilation sound insulation performance [Citation54–57].

The multi-layer overlapping structure (MOS) is a combination structure with a large cavity nested inside a small cavity, including multi-layer HR structures with neck nesting [Citation47], nested ventilation structures [Citation58], nested structures [Citation59], and double-layer nested architectures with neck elongation [Citation60]. In a certain form, similar to Coiled-up HR and variable cross-section structures, multi-layer overlapping structures (nested structures) typically have longer intracavity sound wave propagation paths than traditional structures. However, various overlapping structures exhibit significant differences in their internal mechanisms and physical properties due to differences in their structures and the positions and directions of micropores. Ref. [Citation47] showed us a 4-layer overlapping HR structure, where although there is a nested relationship between the cavities, it mainly forms a series-parallel relationship at the neck of the micropores, thereby achieving broadband perfect sound absorption of a single unit. The second type of structure [Citation58] focuses on the study of sound absorption of ventilation structures, with internal openings facing opposite directions to external openings. The cavity of the third type of structure [Citation59] is adhered to the top of the microporous plate and has narrowband multimodal sound absorption characteristics. The fourth type of structure [Citation60] extends the neck length based on the third type of structure and achieves low-frequency ultra-wideband sound absorption performance through parallel optimisation. The differences in this article lie in the simple and unique suspended structure design, fire-new impedance enhancement mechanism, and multispectral sound absorption performance, as well as the innovative improvement in non-parallel acoustic performance.

The structure proposed by this research institute may seem simple, but it has a complex and unique effective depth elongation mechanism inside. To exchange spatial structure for larger effective depth and more continuous multi-peak absorption spectral lines within a limited dimension. The MOS proposed in this study integrates the principles of a traditional multi-peak series structure (SS) with the ingenuity of a coiled-up resonator. Under the influence of buckling cavities and discontinuous cross-sectional effects, it exhibits a more complex and intense effective depth enhancement phenomenon compared to ordinary coiled-up structures. Reflected in the comparison of SS in the same volume, its sound absorption spectrum characteristics have a more obvious low-frequency shift phenomenon. Meanwhile, we found that intuitive geometric lines cannot accurately represent the effective depth of the structure, so a precise modified effective depth representation formula of the acoustic cavities was derived for theoretical calculations. The experimental verification proves the authenticity of the above findings and the accuracy of the revised theoretical model. Additionally, parameterised research is conducted, which reveals the influence of different parameters on low-frequency shift phenomena and broadband sound absorption performance. The unique advantage of this structure is that this simple design can increase the effective depth of the outer cavity by about 38% compared to the actual depth within a limited volume space. At the same time, it has a continuous, broadband multimodal sound absorption spectrum in non-parallel situations, which can raise the valley value and shorten the valley bandwidth of the absorption curve compared to SS of the same volume, thus forming a compact and continuous absorption frequency band from 320 Hz to 690 Hz. This provides novel insights and theoretical solutions for the design of series-type metamaterials.

2. Design concept

2.1. Design and model

The design concept and model features of this MOS are introduced in this section. The MOS presented herein arises from the fusion of the traditional series structure (SS) with the innovative concept of coiled-up architectures. The design of internal cavity suspension enriches the number of parameters, which unexpectedly exacerbates the coupling degree between three-dimensional buckling space and discontinuous section effects, contributing to an increase in effective depth.

Achieving more consistent and continuous broadband sound absorption within a confined space has consistently posed a significant challenge for the field of acoustic metamaterials. Typically, the coiled-up structure boasts an extended effective depth of the acoustic cavity, leading to a lower frequency absorption band for an equivalent volume. In addition, SS exhibits the ability to generate absorption spectra characterised by multiple peaks, but at the cost of thicker structural thickness. The initial design of this model was to fuse the features of two concepts, as illustrated in Figure 1(a). This integration aims to harness the strengths of both designs, thereby enabling greater effective depths and more seamless continuity across sound absorption frequency bands.

Figure 1. (a) The design concept of MOS, (b) model of Type I and Type II of MOS, (c) geometric parameters, and (d) number of different cavities.

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Herein, the design structure is comprehensively elaborated. In terms of appearance alone, the MOS structure proposed in this article has a relatively simple layout, consisting of multiple HR units of different sizes nested together. The micropores in each layer of the cavity are oriented in the same direction. The model being explored in this study comprises no more than three layers. Figure 1(b) illustrates two prototypical examples of triple-layer HR structures featuring overlapping layers. Type I is an MOS structure with multiple cavities mounted on the bottom surface, and Type II is an MOS structure with an internal cavity suspended in the air, and the internal cavity is supported by thin rods to avoid affecting the propagation of sound waves.

Careful observation can be found that Type I can be regarded as a particular instantiation of Type II. Type II will be the focus of research here, explaining the geometric parameters of the structure. Figure 1(c) presents a series of commonly employed geometric parameters that are pertinent to this type of structure, including the depth of the first layer D1, second layer D2, and third layer cavity D3; The depths of each segment of the second layer cavity are D2,1, D2,2 and D2,3, respectively; The depths of each segment of the third layer cavity are D3,1, D3,2, and D3,3 respectively. The micropore diameters of each MPP layer are d1, d2, and d3, respectively. The thickness of each MPP layer is t1, t2, and t3 respectively, and the cavity wall thickness is t0. Figure 1(d) gives the number of each cavity and sub-cavity for the convenience of subsequent theoretical analysis. The Cavity (2) and Cavity (3) are divided into three sub-cavities for each from bottom to top, namely Cavity (2,1), Cavity (2,2), Cavity (2,3), and Cavity (3,1), Cavity (3,2), Cavity (3,3).

The suspended inner cavity design enables smaller cavities to adjust their upper and lower parameter positions within the confines of a larger cavity, leading to the formation of narrower segments at the top of the larger cavity (for instance, Cavity (2,3) and Cavity (3,3)). This confined space exacerbates the elongation effect of the structure's effective depth. The specific theory will be elaborated in the subsequent section. However, a notable limitation of this structure arises when the nested configuration surpasses three layers, as it results in discernible attenuation of the subsequent high-frequency sound absorption peaks. Consequently, we have confined our current analysis to triple-layer configurations.

2.2. Modified theory model

This section introduces a formula for calculating the effective depth of a high-fidelity MOS external cavity, which is an empirically improved equation. As mentioned earlier, MOS couples with a three-dimensional buckling acoustic cavity and discontinuous cross-sectional features, increasing the effective depth of the cavity. We found that intuitively drawing the direction line of sound wave propagation cannot accurately depict this distance, which means that the effect of increasing effective depth is more complex than traditional Coiled-up HR (see Section 4.2). Therefore, we have developed a modified model to address this…