Double-spiral Helmholtz resonator for low-frequency sound absorption

Abstract

The double-spiral Helmholtz resonator comprises a cavity, an upper cover of the cavity is provided with at least two open holes, each open hole is internally embedded with a spiral pipe, the spiral pipes surround downwards along the interior of the cavity, the openings located above the spiral pipes are connected with a water area, a rubber coating is arranged in the cavity, and the rubber coating is arranged in the cavity. The spiral pipes are hollow spiral pipes which are not overlapped with one another, it is guaranteed that the water cavity and the resonant cavity are connected and communicated, and Helmholtz resonance is triggered through the physical interaction between the rubber coating and the embedded spiral pipes. Helmholtz resonance is triggered through the physical interaction of the rubber coating and the embedded spiral neck, an excellent sound absorption effect is achieved, theoretical prediction is well matched with a finite element simulation result, the sound absorption coefficient of the proposed double-spiral Helmholtz resonator structure cell element at 105Hz reaches 0.91, and the sound absorption coefficient of the double-spiral Helmholtz resonator structure cell element at 105Hz reaches 0.91. The wavelength k of the sound wave is 300 times of the thickness H of the metamaterial, and perfect absorption is achieved on the deep sub-wavelength scale.

Description

Technical Field

[0001] The invention relates to a Helmholtz resonator, in particular to a double-helix Helmholtz resonator used for low-frequency sound absorption. Background Art

[0002] With the continuous acceleration of industrialization, noise can be seen everywhere in life. Low-decibel noise affects people's normal life and even mental health to a certain extent, while high-decibel noise will directly damage buildings, which may shorten the service life of buildings and eventually cause immeasurable safety hazards. In addition, low-frequency noise has the characteristics of large wavelength, strong propagation ability, and not easy to attenuate. Acoustic metamaterials are highly valued by more and more researchers.

[0003] Acoustic metamaterials originate from electromagnetic waves. They are artificially manufactured periodic composite materials or structures that can achieve small size control of large wavelengths. They also have many extraordinary properties that natural materials do not have, such as negative equivalent mass density and negative equivalent bulk modulus. They can be used for negative refraction of sound waves, sound focusing, and sound stealth. Compared with traditional sound-absorbing materials, acoustic metamaterials can achieve the regulation of sound waves by precisely designing their microstructures, especially in terms of sound absorption performance in the low-frequency range, showing great potential.

[0004] The Helmholtz resonance mechanism is one of the core principles of acoustic metamaterials to achieve low-frequency sound absorption. Through the use of cavities or structures with certain geometric shapes in the material, the Helmholtz resonance can produce a strong resonance phenomenon at a specific frequency, thereby significantly enhancing the material's ability to absorb sound energy. Therefore, the development of new underwater acoustic metamaterials to achieve effective control of underwater sound waves has important scientific significance and application value. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to propose a double-helix Helmholtz resonator for low-frequency sound absorption to achieve a lower sound absorption coefficient.

[0006] Technical solution: The present invention includes a cavity, the upper cover of the cavity is provided with at least two openings, each opening is embedded with a spiral tube, the spiral tube surrounds downward along the inside of the cavity, the opening above the spiral tube is connected to the water area, a coating is provided in the cavity, the spiral tubes are hollow spiral tubes that do not overlap each other, and the Helmholtz resonance is triggered by the physical interaction between the coating and the embedded spiral tubes.

[0007] The coating in the cavity is a rubber coating, which ensures additional acoustic resistance and acoustic capacitance and triggers quasi-Helmholtz resonance.

[0008] The rubber coating provides elasticity and damping, ensures additional acoustic resistance and acoustic capacitance and triggers quasi-Helmholtz resonance.

[0009] The hollow spiral tube enables water to flow into or out of the resonator under acoustic excitation, thereby providing acoustic mass and acoustic resistance to the resonator.

[0010] Single Helmholtz resonators are arranged periodically to obtain an underwater acoustic metamaterial that achieves deep wavelength absorption.

[0011] The process for preparing the hydroacoustic metamaterial comprises the following steps:

[0012] a. Design the geometric parameters of the double helix channel;

[0013] b. According to the designed geometric parameters, the double helix channel is manufactured using 3D printing technology or CNC machine tool processing technology;

[0014] c. Assembling the manufactured double helix channel into a Helmholtz resonator unit;

[0015] d. Combine multiple Helmholtz resonator units into a metamaterial and cover it with a metal film.

[0016] The geometric parameters of the double helix channel include the thickness of the helical tube, the diameter of the hole and the pitch of the double helix channel.

[0017] The calculation process of the sound absorption coefficient of the hydroacoustic metamaterial is as follows:

[0018] Assuming that the backing condition of the metamaterial is rigid, the sound absorption coefficient of the double-helix Helmholtz resonator is calculated by

[0019] α=1-|R| 2 =1-|(Z s -1) / (Z s +1)| 2 (1)

[0020] Where R is the reflection coefficient and Zs is the surface acoustic impedance ratio of the metamaterial. To determine Zs, the acoustic impedance of the resonant cavity and the embedded neck needs to be calculated. The total acoustic impedance of the resonant cavity is expressed as

[0021]

[0022] Among them, Zr and Zw are the acoustic impedances of the rubber coating and the water cavity in the resonant cavity, respectively. The acoustic impedance of the rubber coating is

[0023]

[0024] Where j is the imaginary unit, V r =S c HkD w (h-t3) is the volume of the rubber coating, h is the cavity height, are the cross-sectional areas of the resonant cavity and the water cavity, ρ rand c r are the density of rubber and the longitudinal wave velocity, w = 2πf is the angular frequency, f is the frequency, and a is the side length of the hexagon;

[0025] Introducing complex bulk modulus The longitudinal sound wave velocity is expressed as in, η r and v r are the bulk modulus, loss factor, Young's modulus and Poisson's ratio of rubber respectively; the density, loss factor, Young's modulus and Poisson's ratio of rubber are ρ r =1100kg / m 3 , η r =0.3, E r =10MPa, v r =0.49.

[0026] The acoustic impedance of the water cavity is expressed as

[0027]

[0028] Where, ρ0=1000kg / m 3 and c0 = 1500 m / s are the density of water and the speed of sound waves, V w =S w (h-t3)-2S n (l-t1) is the volume of the water cavity at the spiral neck, S n =πd 2 / 4 is the internal cross-sectional area of ​​the helical neck, d is the helical tube diameter, l is the helical tube length, and substituting equations (3) and (4) into (2) yields the total acoustic impedance of the resonator;

[0029] The acoustic impedance of the embedded neck is given by

[0030]

[0031] in, is the perforation ratio of the panel, J n (X) is a first-order Bessel function of order n, is the ratio of the embedded neck radius to the viscous boundary layer thickness, η0 = 1.01 × 10 -5 Pa·s is the dynamic viscosity of water. By adjusting the dimensions of the rubber coating and the embedded neck, the acoustic impedance of the metamaterial is adjusted under a constant external morphology. The surface acoustic impedance ratio of the metamaterial is expressed as

[0032] Z s =δZ =δ(Z n +Z c ) / Z0 (6)

[0033] Where Z = (Z n +Z c ) / Z0 is the surface acoustic impedance ratio of the resonator, is the area correction factor used to describe the effect of honeycomb wall thickness on acoustic impedance. By substituting (5) into (1), the sound absorption coefficient of the metamaterial is obtained.

[0034] The resonant cavity consists of a rubber coating and a water cavity.

[0035] The acoustic impedances of the rubber coating and the water cavity are connected in parallel.

[0036] Beneficial effects: The physical interaction between the rubber coating and the embedded spiral neck triggers the Helmholtz resonance, resulting in excellent sound absorption effect. The theoretical prediction is in good agreement with the finite element simulation results. The proposed double-helix Helmholtz resonator structure cell has a sound absorption coefficient of 0.91 at 105 Hz. At the absorption peak, the wavelength k of the sound wave is 300 times the thickness H of the metamaterial, achieving perfect absorption on a deep subwavelength scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic structural diagram of a double-helix Helmholtz resonator of the present invention;

[0038] Figure 2 It is a sound absorption curve diagram of the double-helix Helmholtz resonator of the present invention. DETAILED DESCRIPTION

[0039] The present invention will be further described below in conjunction with the accompanying drawings.

[0040] like Figure 1 As shown, the double-helix Helmholtz resonator for low-frequency sound absorption of the present invention includes a cavity, the upper cover of the cavity is provided with at least two openings, each opening is embedded with a spiral tube, the spiral tube surrounds downward along the inside of the cavity, the opening above the spiral tube is connected to the water area, and a rubber coating is provided in the cavity. The cavity of this embodiment uses a regular hexagonal prism cavity, the upper cover of the regular hexagonal prism cavity is provided with two circular openings, each opening is embedded with a spiral tube, the two spiral tubes surround downward along the inside of the cavity, the opening above the spiral tube is connected to the water area, and the opening at the other end of the spiral tube is connected to the inside of the cavity; the inner side of the regular hexagonal prism cavity is provided with a rubber coating.

[0041] The spiral tube is a hollow spiral tube that does not overlap each other and is open at both ends, ensuring the connection between the water cavity and the resonance cavity. The geometric parameters of the double helix channel, including the thickness of the spiral tube, the diameter of the hole and the pitch of the double helix channel, can be adjusted according to the frequency of the sound wave to be absorbed.

[0042] The shape of the regular hexagonal prism cavity and the shape of the rubber coating can be adjusted according to the frequency of the sound wave to be absorbed. The double-helix Helmholtz resonator of the present invention has a lightweight acoustic metamaterial structure cell with deep subwavelength thickness and strong load-bearing capacity. The structure of the cell achieves excellent absorption performance of low-frequency sound waves by introducing a rubber coating and an embedded double-helix neck.

[0043] By periodically arranging single Helmholtz resonators, a hydroacoustic metamaterial that achieves deep wavelength absorption can be obtained. Hydroacoustic metamaterials are used in underwater noise control, acoustic stealth or underwater communications.

[0044] The preparation process of underwater acoustic metamaterials includes the following steps:

[0045] a. Design the geometric parameters of the double helix channel;

[0046] b. According to the designed geometric parameters, the double helix channel is manufactured using 3D printing technology or CNC machine tool processing technology;

[0047] c. Assembling the manufactured double helix channel into a Helmholtz resonator unit;

[0048] d. Combine multiple Helmholtz resonator units into a metamaterial and cover it with a metal film.

[0049] The calculation process of the sound absorption coefficient of the underwater acoustic metamaterial is:

[0050] Assuming that the backing condition of the metamaterial is rigid to simplify the analysis, in this case, the sound absorption coefficient of the double helix Helmholtz resonator can be calculated by

[0051] α=1-|R| 2 =1-|(Z s -1) / (Z s +1)| 2 (1)

[0052] Where R is the reflection coefficient and Zs is the surface acoustic impedance ratio of the metamaterial. To determine Zs, the acoustic impedance of the resonant cavity and the embedded neck needs to be calculated. The resonant cavity consists of a rubber coating and a water cavity. According to the electroacoustic analogy, the acoustic impedances of the rubber coating and the water cavity are in parallel. Therefore, the total acoustic impedance of the resonant cavity can be expressed as

[0053]

[0054] Where Zr and Zw are the acoustic impedances of the rubber coating and the water cavity, respectively. The acoustic impedance of the rubber coating is

[0055]

[0056] Where j is the imaginary unit, V r =Sc HkD w (h-t3) is the volume of the rubber coating, h is the cavity height, and are the cross-sectional areas of the resonant cavity and the water cavity, ρ r and c r are the density and longitudinal wave velocity of the rubber respectively, w=2πf is the angular frequency, f is the frequency, and a is the side length of the hexagon.

[0057] The linear viscoelastic constitutive law is usually used to describe the elastic and damping behavior of rubber materials in underwater sound absorbers. Specifically, the complex bulk modulus is introduced The longitudinal sound wave velocity can be expressed as in η r and v r The bulk modulus, loss factor, Young's modulus and Poisson's ratio of rubber are ρ respectively. The density, loss factor, Young's modulus and Poisson's ratio of rubber are ρ respectively. r =1100kg / m 3 , η r =0.3, E r =10MPa, v r =0.49.

[0058] The acoustic impedance of the water cavity can be expressed as

[0059]

[0060] Where ρ0=1000kg / m 3 and c0 = 1500 m / s are the density of water and the speed of sound waves, V w =S w (h-t3)-2S n (l-t1) is the volume of the water cavity at the spiral neck, S n =πd 2 / 4 is the internal cross-sectional area of ​​the helical neck, d is the helical diameter, and l is the helical length. Finally, the total acoustic impedance of the resonator can be obtained by substituting equations (3) and (4) into (2).

[0061] The acoustic impedance of the embedded neck is given by

[0062]

[0063] in is the perforation ratio of the panel, J n (X) is a first-order Bessel function of order n, is the ratio of the embedded neck radius to the viscous boundary layer thickness, η0 = 1.01 × 10 -5Pa·s is the dynamic viscosity of water. By adjusting the dimensions of the rubber coating and the embedded neck, the acoustic impedance of the metamaterial can be tuned under constant external morphology. Finally, the surface acoustic impedance ratio of the metamaterial is expressed as

[0064] Z s =δZ =δ(Z n +Z c ) / Z0 (6)

[0065] Where Z = (Z n +Z c ) / Z0 is the surface acoustic impedance ratio of the resonator, is the area correction factor used to describe the effect of honeycomb wall thickness on acoustic impedance. By substituting (5) into (1), the sound absorption coefficient of the metamaterial can be predicted theoretically.

[0066] The physical interaction of the rubber coating with the embedded screw neck triggers the Helmholtz resonance, resulting in excellent sound absorption, e.g. Figure 2 As shown in the figure, the theoretical prediction is in good agreement with the finite element simulation results. The proposed double-helix Helmholtz resonator structure cell has an absorption coefficient of 0.91 at 105Hz. At the absorption peak, the acoustic wavelength k is 300 times the thickness H of the metamaterial, which means perfect absorption is achieved at the deep subwavelength scale. By adjusting the internal geometric parameters of the cell, the acoustic properties can be precisely adjusted without changing the external morphology and overall thickness.

[0067] The present invention can effectively absorb low-frequency sound waves in an underwater environment. The metamaterial introduces an embedded double-helix neck and a regular hexagonal rubber coating into a classic Helmholtz resonant cavity. The embedded neck is two hollow spiral tubes, which allow water to flow into (out of) the resonator under acoustic excitation, thereby providing acoustic mass and acoustic resistance for the resonator. The rubber coating provides elasticity and damping, ensures additional acoustic resistance and acoustic capacitance, and triggers quasi-Helmholtz resonance. By adjusting the geometric parameters of the double-helix channel, efficient absorption of low-frequency sound waves can be achieved. The metamaterial can be applied to underwater noise control, acoustic stealth, underwater communications and other fields.

[0068] Example

[0069] The double-helix Helmholtz resonator consists of a double-helix neck and a rubber coating.

[0070] The hexagon side length a = 20 mm, the cavity height h = 48 mm, the rubber coating thickness b = 9.23 mm, the embedded spiral tube diameter d = 2.09 mm, and the spiral tube length l = 39.49 mm. The parametric equation of the spiral line is x = 5cos(s), y = 5sin(s), z = 3s, and s ranges from 3.5 mm to 16.665 mm.

[0071] The density of rubber coating is 1100kg / m 3 , loss factor is 0.3, Young's modulus is 10MPa, Poisson's ratio is 0.49. The density of water is 1000kg / m 3 , the speed of sound is 1500m / s, and the dynamic viscosity is 1.01×10-3Pa·s.

[0072] To further verify the results, Figure 1 The finite element simulation study of the metamaterial structure cell model described above was carried out to obtain its sound absorption performance. The sound absorption coefficient of the double-helix Helmholtz resonator structure was calculated based on the multi-physics field coupling method of the finite element software COMSOL Multiphysics 6.0. The influence of thermoviscous loss in the narrow area was fully considered in the model. The incident area outside the structure was set as the pressure acoustic domain, the internal water area was set as the thermoviscous acoustic domain, and the structural boundary was set as the solid mechanics domain. The incident sound wave was a plane wave with an incident pressure amplitude of 1Pa, incident on the surface of the structure along the negative direction of the z-axis. The structural units were arranged periodically, and the boundary conditions were periodic boundaries.

[0073] Figure 2 for Figure 1 The sound absorption coefficient curve of the model structure shown in the figure shows that the sound absorption coefficient of the structure reaches 0.91 at 105Hz. At the absorption peak, the wavelength k of the sound wave is 300 times the thickness H of the metamaterial, which means that perfect absorption is achieved on a deep subwavelength scale.

[0074] The double-helix underwater acoustic metamaterial of the present invention can achieve efficient absorption of sound waves of a specific frequency by adjusting the geometric parameters of the double-helix channel. This design not only improves the sound absorption performance of the acoustic metamaterial in an underwater environment, but also broadens its application prospects in the fields of underwater acoustic stealth, underwater communications, and underwater structural noise control.

Claims

1. A double helix Helmholtz resonator for low frequency sound absorption, characterized in that: It includes a cavity, the upper cover of the cavity is provided with at least two openings, each opening is embedded with a spiral tube, the spiral tube surrounds downward along the inside of the cavity, the opening above the spiral tube is connected to the water area, a coating is provided in the cavity, the spiral tubes are hollow spiral tubes that do not overlap each other, and the Helmholtz resonance is triggered by the physical interaction between the coating and the embedded spiral tubes.

2. A double helix Helmholtz resonator for low frequency sound absorption according to claim 1, characterized in that: The coating in the cavity is a rubber coating.

3. A double helix Helmholtz resonator for low frequency sound absorption according to claim 2, characterized in that: The rubber coating provides resilience and damping.

4. A double helix Helmholtz resonator for low frequency sound absorption according to claim 2, characterized in that: The hollow spiral tube enables water to flow into or out of the resonator under acoustic excitation.

5. A double helix Helmholtz resonator for low frequency sound absorption according to claim 1, characterized in that: Single Helmholtz resonators are arranged periodically to obtain an underwater acoustic metamaterial that achieves deep wavelength absorption.

6. A double helix Helmholtz resonator for low frequency sound absorption according to claim 5, characterized in that: The process for preparing the hydroacoustic metamaterial comprises the following steps: a. Design the geometric parameters of the double helix channel; b. According to the designed geometric parameters, the double helix channel is manufactured using 3D printing technology or CNC machine tool processing technology; c. Assembling the manufactured double helix channel into a Helmholtz resonator unit; d. Combine multiple Helmholtz resonator units into a metamaterial and cover it with a metal film.

7. A double helix Helmholtz resonator for low frequency sound absorption according to claim 6, characterized in that: The geometric parameters of the double helix channel include the thickness of the helical tube, the diameter of the hole and the pitch of the double helix channel.

8. A double helix Helmholtz resonator for low frequency sound absorption according to claim 5, characterized in that: The calculation process of the sound absorption coefficient of the hydroacoustic metamaterial is as follows: Assuming that the backing condition of the metamaterial is rigid, the sound absorption coefficient of the double-helix Helmholtz resonator is calculated by α=1-|R| 2 =1-|(From s -1) / (From s +1)| 2 (1) Where R is the reflection coefficient and Zs is the surface acoustic impedance ratio of the metamaterial. To determine Zs, the acoustic impedance of the resonant cavity and the embedded neck needs to be calculated. The total acoustic impedance of the resonant cavity is expressed as Among them, Zr and Zw are the acoustic impedances of the rubber coating and the water cavity in the resonant cavity, respectively. The acoustic impedance of the rubber coating is Where j is the imaginary unit, V r =S ch -S w (h-t3) is the volume of the rubber coating, h is the cavity height, are the cross-sectional areas of the resonant cavity and the water cavity, ρ r and c r are the density of rubber and the longitudinal wave velocity, w = 2πf is the angular frequency, f is the frequency, and a is the side length of the hexagon; Introducing complex bulk modulus The longitudinal sound wave velocity is expressed as in, η r and v r are the bulk modulus, loss factor, Young's modulus and Poisson's ratio of rubber respectively; the density, loss factor, Young's modulus and Poisson's ratio of rubber are ρ r =1100kg / m 3 , η r =0.3, E r =10MPa, v r =0.

49. The acoustic impedance of the water cavity is expressed as Where, ρ0=1000kg / m 3 and c0 = 1500 m / s are the density of water and the speed of sound waves, V w =S w (h-t3)-2S n (l-t1) is the volume of the water cavity at the spiral neck, S n =πd 2 / 4 is the internal cross-sectional area of ​​the helical neck, d is the helical tube diameter, l is the helical tube length, and substituting equations (3) and (4) into (2) yields the total acoustic impedance of the resonator; The acoustic impedance of the embedded neck is given by in, is the perforation ratio of the panel, J n (X) is a first-order Bessel function of order n, is the ratio of the embedded neck radius to the viscous boundary layer thickness, η0 = 1.01 × 10 -5 Pa·s is the dynamic viscosity of water. By adjusting the dimensions of the rubber coating and the embedded neck, the acoustic impedance of the metamaterial is adjusted under a constant external morphology. The surface acoustic impedance ratio of the metamaterial is expressed as WITH s =δZ=δ(Z n +Z c ) / Z0 (6) Where Z = (Z n +Z c ) / Z0 is the surface acoustic impedance ratio of the resonator, is the area correction factor used to describe the effect of honeycomb wall thickness on acoustic impedance. By substituting (5) into (1), the sound absorption coefficient of the metamaterial is obtained.

9. A double helix Helmholtz resonator for low frequency sound absorption according to claim 8, characterized in that: The resonant cavity consists of a rubber coating and a water cavity.

10. A double helix Helmholtz resonator for low frequency sound absorption according to claim 9, characterized in that: The acoustic impedances of the rubber coating and the water cavity are connected in parallel.

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