Conformal two-dimensional acoustic black hole stealth vibration reduction structure and preparation method thereof
By compatibilizing the two-dimensional acoustic black hole and combining the damping layer design, the problem of excessive additional mass in the two-dimensional acoustic black hole vibration reduction technology is solved, and the multifunctional application of lightweight wide-frequency vibration suppression and bending wave stealth is realized.
Patent Information
- Application Number
- CN202510375343.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-27
- Publication Date
- 2025-06-10
AI Technical Summary
While the existing two-dimensional acoustic black hole vibration reduction technology improves vibration damping performance, it leads to excessive additional mass and makes it difficult to achieve multifunctional applications.
By compatibilizing the ordinary two-dimensional acoustic black hole, a conformal two-dimensional acoustic black hole structure is formed, and combined with the design of the damping layer, a single-directional bending wave stealth and lightweight vibration reduction are achieved.
It realizes the energy-concentrating vibration damping performance without increasing additional mass, and has the bending wave stealth characteristics, which is suitable for lightweight wide-frequency vibration suppression of thin plate structures.
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Figure CN120126434A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of stealth structures and vibration and noise reduction technology, and in particular to a conformal two-dimensional acoustic black hole stealth vibration reduction structure and a preparation method thereof. Background Art
[0002] Conformal transformation refers to mapping points on a virtual space plane to a physical space plane using an analytical function. The mapped points have the invariance of angle preservation and scaling. Conformal transformation belongs to the content of mathematical complex variable functions. It was first applied in the field of optics to design optical invisibility cloaks, and then expanded to fields such as acoustics and mechanics, and can be used in the design of multifunctional devices.
[0003] The vibration problem of thin plate structures is widely present in engineering practice. When subjected to vibration, thin plate structures are not only prone to deformation, affecting equipment operation, but also radiate noise to the outside world, affecting personnel health. The traditional vibration reduction method for thin plate structures is to apply damping materials on the surface, which can achieve a certain vibration reduction effect, but requires laying over a large area, resulting in the problem of excessive additional mass.
[0004] Two-dimensional acoustic black hole is a new type of vibration reduction technology for thin plate structures. Its thickness distribution satisfies power-law variation. After the bending wave propagates to the two-dimensional acoustic black hole, the wave speed gradually decreases and drops to the lowest at the center of the black hole, realizing the energy concentration of the bending wave. Subsequently, it is only necessary to apply damping at the center of the two-dimensional acoustic black hole to achieve vibration reduction performance, which to a certain extent solves the problem of excessive additional mass caused by traditional large-area damping vibration reduction. However, in order to further reduce the additional mass generated by the two-dimensional acoustic black hole vibration reduction technology and realize the multifunctional application of the two-dimensional acoustic black hole, there is an urgent need for a conformal two-dimensional acoustic black hole stealth vibration reduction structure that performs conformal transformation on the two-dimensional acoustic black hole. Summary of the invention
[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a conformal two-dimensional acoustic black hole stealth vibration reduction structure and a preparation method thereof. By conformally transforming an ordinary two-dimensional acoustic black hole, a conformal two-dimensional acoustic black hole structure with unidirectional bending wave stealth is formed. Without affecting the vibration reduction performance, the structure has the two-dimensional acoustic black hole bending wave stealth effect and lightweight vibration reduction performance.
[0006] To achieve the above purpose, the technical solution adopted by the present invention is:
[0007] In a first aspect, a conformal two-dimensional acoustic black hole stealth vibration reduction structure is provided, which includes a substrate, a conformal two-dimensional acoustic black hole is integrally formed on the substrate, a stealth hole is arranged in the middle of the conformal two-dimensional acoustic black hole, the outer side of the inner diameter circle of the conformal two-dimensional acoustic black hole contains two symmetrically distributed bosses, the inner side of the outer diameter circle of the conformal two-dimensional acoustic black hole contains two symmetrically distributed platforms, and a damping layer is pasted on the bottom of the conformal two-dimensional acoustic black hole.
[0008] Furthermore, the thickness distribution of the conformal two-dimensional acoustic black hole is a function of the polar coordinates r and θ, and its functional formula is:
[0009]
[0010] where h z is the thickness inside the conformal two-dimensional acoustic black hole; h 0 is the thickness of the substrate; h 2 is the residual thickness of the acoustic black hole; h 1 is h 0 -h 2； r abh is the radius of the acoustic black hole; a is the radius of the stealth hole; u is the power exponent, and u ≥ 2.
[0011] Furthermore, the two bosses and the two platforms are all located on the same diameter of the outer diameter circle of the conformal two-dimensional acoustic black hole, and the extending direction of this diameter is the effective stealth direction of the conformal two-dimensional acoustic black hole, and the extending direction of the perpendicular line of this diameter is the ineffective stealth direction of the conformal two-dimensional acoustic black hole.
[0012] Furthermore, the two bosses and the two platforms are all flush with the upper surface of the substrate.
[0013] Furthermore, the damping layer is annular, the inner diameter circle of the damping layer coincides and aligns with the lower end of the stealth hole, and the outer diameter circle of the damping layer coincides and aligns with the lower end of the outer diameter circle of the conformal two-dimensional acoustic black hole.
[0014] In a second aspect, a method for preparing a conformal two-dimensional acoustic black hole stealth and vibration damping structure is provided, which includes the following steps:
[0015] S1: Select a rectangular thin plate as the substrate and open a stealth hole on the substrate;
[0016] S2: Integrally form a conformal two-dimensional acoustic black hole on the substrate around the stealth hole, and the thickness distribution of the conformal two-dimensional acoustic black hole is a function of the polar coordinates r and θ, and its functional formula is:
[0017]
[0018] where h z is the thickness inside the conformal two-dimensional acoustic black hole; h 0 is the thickness of the substrate; h 2 is the residual thickness of the acoustic black hole; h 1 is h 0 -h 2； r abh is the radius of the acoustic black hole; a is the radius of the stealth hole; u is the power exponent, and u ≥ 2;
[0019] S3: Paste a ring-shaped damping layer at the bottom of the conformal two-dimensional acoustic black hole, and align the inner diameter circle of the damping layer with the lower end of the stealth hole, and align the outer diameter circle of the damping layer with the lower end of the outer diameter circle of the conformal two-dimensional acoustic black hole.
[0020] Furthermore, the substrate and the conformal two-dimensional acoustic black hole are integrally formed of a metal material or a polymer material, and the damping layer is made of a chemical polymer or a high-damping alloy.
[0021] Furthermore, the substrate and the conformal two-dimensional acoustic black hole are integrally formed of aluminum alloy, with a Young's modulus E of 71 GPa, a density ρ of 2810 kg / m 3 , and a Poisson's ratio υ of 0.33; making it have the characteristics of easy processing, high strength, good wear resistance, etc.
[0022] Furthermore, the damping layer is butyl rubber, with a Young's modulus E of 0.1 Mpa, a density ρ of 1200 kg / m 3 , and a Poisson's ratio υ of 0.48; making it have the characteristics of strong adhesion, good ductility, good damping performance, etc.
[0023] Furthermore, the radius a of the stealth hole is one-fifth of the radius r abh of the acoustic black hole; this aperture ratio can achieve the best stealth effect while having the largest stealth radius.
[0024] The beneficial effects of the present invention are as follows:
[0025] A circular hollow area, that is, a circular stealth hole, is generated at the center of the transformed conformal two-dimensional acoustic black hole in this solution. Compared with the ordinary two-dimensional acoustic black hole, due to the mathematical properties of conformal transformation, the two-dimensional acoustic black holes before and after transformation have almost the same energy-gathering and vibration-damping performance. However, the conformal two-dimensional acoustic black hole uses less damping material, thereby reducing the additional mass. At the same time, the circular stealth hole can be used to achieve vibration immunity in the stealth area and facilitate observing the internal structure of the device. Therefore, this solution not only has the energy-gathering and vibration-damping performance of the ordinary two-dimensional acoustic black hole but also has the bending wave stealth characteristics of the two-dimensional acoustic black hole, and can replace the ordinary two-dimensional acoustic black hole to achieve lightweight wide-band vibration suppression of the thin plate structure. Description of the Drawings
[0026] Figure 1 is a schematic structural diagram of the conformal two-dimensional acoustic black hole.
[0027] Figure 2 is a schematic structural diagram of the effective stealth direction and ineffective stealth direction of the conformal two-dimensional acoustic black hole.
[0028] Figure 3 is a schematic overall diagram of the stealth and vibration-damping structure of the conformal two-dimensional acoustic black hole.
[0029] Figure 4 isFigure 3 Cross-sectional view of the A-A area
[0030] Figure 5 Schematic diagram for verifying the stealth performance of a conformal two-dimensional acoustic black hole
[0031] Figure 6 Scattering measure simulation curve graph
[0032] Figure 7 Schematic diagram for verifying the vibration reduction performance of a conformal two-dimensional acoustic black hole
[0033] Figure 8 Frequency response simulation curve graph
[0034] Figure 9 Frequency response experimental curve graph
[0035] Among them, 1. Substrate, 2. Conformal two-dimensional acoustic black hole, 3. Stealth hole, 4. Boss, 5. Platform, 6. Damping layer Specific implementation manner
[0036] The following describes the specific implementation manner of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation manner. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection
[0037] The stealth and vibration reduction structure of the conformal two-dimensional acoustic black hole 2 in this solution includes a substrate 1. A conformal two-dimensional acoustic black hole 2 is integrally formed on the substrate 1. A stealth hole 3 is provided in the middle of the conformal two-dimensional acoustic black hole 2. There are two symmetrically distributed bosses 4 on the outer side of the inner diameter circle of the conformal two-dimensional acoustic black hole 2. There are two symmetrically distributed platforms 5 on the inner side of the outer diameter circle of the conformal two-dimensional acoustic black hole 2. A damping layer 6 is pasted on the bottom of the conformal two-dimensional acoustic black hole 2
[0038] This solution gives the specific derivation process of the function of the thickness distribution of the conformal two-dimensional acoustic black hole 2
[0039] First, the ordinary two-dimensional acoustic black hole and the conformal two-dimensional acoustic black hole 2 are structurally transformed into each other through conformal transformations z(w) and w(z); in this embodiment, the coordinate space where the ordinary two-dimensional acoustic black hole is located is denoted as the virtual space w, and the coordinate system of the virtual space w is represented by R and ψ; the coordinate space where the conformal two-dimensional acoustic black hole 2 is located is denoted as the physical space z, and the coordinate system of the physical space z is represented by r and θ. The refractive index distributions of the virtual space and the physical space satisfy The conformal transformation selects the Zhukovsky transformation, that is a is the stealth radius
[0040] The thickness distribution function of the ordinary two-dimensional acoustic black hole before transformation in this embodiment is h w (R) is the thickness within the ordinary two-dimensional acoustic black hole region, h 2 is the residual thickness of the acoustic black hole, h 1 is h 0 -h 2 h 0 is the uniform thickness, R b is the radius of the acoustic black hole, u is the exponent, and u is 3.
[0041] The structural refractive index distribution of the ordinary two-dimensional acoustic black hole satisfies From the refractive index distribution relationship between the virtual space and the physical space and the Zhukovsky transformation, the refractive index distribution of the conformal two-dimensional acoustic black hole 2 can be calculated. Since the refractive index distribution of the conformal two-dimensional acoustic black hole 2 also satisfies The thickness of the conformal two-dimensional acoustic black hole 2 can be calculated as follows:
[0042]
[0043] As Figure 1 shown, two thickness singularities (thickness approaching infinity) are symmetrically distributed at the inner diameter of the transformed conformal two-dimensional acoustic black hole 2. The thickness in the region around the singularities is greater than the uniform plate thickness of 6 mm. Two regions with a thickness greater than the uniform plate thickness of 6 mm are symmetrically distributed at the outer diameter. Since the areas of the regions with a thickness greater than the uniform plate thickness of 6 mm at the inner and outer diameters are small, for the convenience of subsequent simulation and experimental processing, the thickness of these regions is smoothed so that the thickness of the conformal two-dimensional acoustic black hole 2 does not exceed the uniform plate thickness; the thickness distribution of the conformal two-dimensional acoustic black hole 2 after thickness smoothing satisfies the function with respect to the polar coordinates r and θ:
[0044]
[0045] where h z is the thickness within the conformal two-dimensional acoustic black hole 2; h 0 is the thickness of the substrate 1; h 2 is the residual thickness of the acoustic black hole; h 1 is h 0 -h 2； r abh is the radius of the acoustic black hole; a is the radius of the stealth hole 3; u is the power exponent, and u≥2; the plane where the polar coordinates are located is the bottom surface of the substrate 1, and the pole of the polar coordinates is the intersection point of the axis of the stealth hole 3 and the bottom surface of the substrate 1.
[0046] As Figure 2As shown, due to the transformation characteristics of the Zhukovsky transformation, the stealth performance is unidirectional. The conformal two-dimensional acoustic black hole 2 is divided into a stealth-effective direction and a stealth-ineffective direction. The stealth-effective direction is the direction in which the convex platform 4 on the outer side of the inner diameter circle and the platform 5 on the inner side of the outer diameter circle of the conformal two-dimensional acoustic black hole 2 are symmetrically distributed. The stealth-ineffective direction is the perpendicular direction of the stealth-effective direction.
[0047] As Figure 3 and Figure 4 shown, the conformal two-dimensional acoustic black hole 2 after smoothing treatment is embedded in the substrate 1, and then the damping layer 6 is pasted on the back of the conformal two-dimensional acoustic black hole 2, which is the conformal two-dimensional acoustic black hole 2 stealth and vibration damping structure described in the present invention. The damping layer 6 is in a ring shape. The inner diameter circle of the damping layer 6 coincides and aligns with the lower end of the stealth hole 3, and the outer diameter circle of the damping layer 6 coincides and aligns with the lower end of the outer diameter circle of the conformal two-dimensional acoustic black hole 2.
[0048] This solution also gives an embodiment of the simulation of the stealth performance verification:
[0049] First, a finite element model of the conformal two-dimensional acoustic black hole plate is established in the finite element analysis software Comsol, as Figure 5 shown; in this simulation, three simulation objects are set, namely an ordinary acoustic black hole plate (the displacement field is denoted as W 1 ), an ordinary acoustic black hole hollow plate (the displacement field is denoted as W 2 ), and a conformal acoustic black hole plate (the displacement field is denoted as W 3 ). In the stealth performance verification simulation, the damping layer 6 is not added to any of the three plates. The geometric dimensions of the simulation geometric model are shown in Table 1 below.
[0050] Table 1 Geometric dimension parameter table of the simulation geometric model
[0051]
[0052] In this embodiment, all three plates use aluminum alloy as the structural material. The material parameters of the simulation geometric model are: Young's modulus E is 71 GPa, density ρ is 2810 kg / m 3 , and Poisson's ratio υ is 0.33; a perfect matching layer is set around the plate, and three acoustic black hole structures are in the center of the plate. A point excitation is set at point a (-300 mm, 0 mm) on the left side of the structure. A trapezoidal area is surrounded by points b (150 mm, 50 mm), c (150 mm, -50 mm), d (250 mm, -150 mm), and e (250 mm, 150 mm) on the right side of the structure for calculating the scattering measure. The calculation formula of the scattering measure is:
[0053]
[0054] W a is the target displacement field (a = 2, 3), Wb is the reference displacement field (b = 1), D is the trapezoidal region, and the smaller the scattering measure value, the better the stealth performance.
[0055] As Figure 6 shown, it gives the comparative curve graphs of the scattering measures ε(w 2 , w 1 , D) and ε(w 3 , w 1 , D). The scattering measure of the conformal acoustic black hole plate is at a low level in the whole frequency band, and there is only a sudden increase at 15KHz, which is caused by local resonance; while the scattering measure of the ordinary acoustic black hole hollow plate is much higher than that of the conformal acoustic black hole plate in the whole frequency band. Thus, it can be shown that the conformal acoustic black hole proposed by the present invention has good stealth performance.
[0056] This solution also gives an embodiment of the simulation of the verification of the vibration damping performance:
[0057] A finite element model of the conformal two-dimensional acoustic black hole plate established in the finite element analysis software Comsol, as Figure 7 shown; three simulation objects are set, namely the equal-thickness plate, the ordinary acoustic black hole plate and the conformal acoustic black hole plate, and the geometric dimensions of the simulation geometric model are as shown in Table 1 above; all three plates use aluminum alloy as the structural material. The equal-thickness plate is not laid with the damping layer 6, and the centers of the ordinary acoustic black hole plate and the conformal acoustic black hole plate are the ordinary acoustic black hole and the conformal acoustic black hole structures. A damping layer 6 made of butyl rubber material is arranged on the back of the structure, and its Young's modulus E is 0.1Mpa, the density ρ is 1200kg / m 3 , and the Poisson's ratio υ is 0.48; a point excitation is set at point a (-300mm, 0mm) on the left side of the structure, and a cut line connected by point b (300mm, 200mm) and point c (300mm, -200mm) is arranged on the right side of the structure for calculating the line average acceleration response. The calculation formula of the line average acceleration response is:
[0058]
[0059] wherein, a i is the acceleration amplitude of any point on the cut line, a re is the reference acceleration, and F is the excitation force.
[0060] As Figure 8As shown, it gives the frequency response curves of the linear average acceleration responses of three simulation objects. It can be found that the frequency response curves of the conformal acoustic black hole plate and the ordinary acoustic black hole plate have good consistency in the full frequency band. The response peaks of both in the middle and high frequency bands are much smaller than those of the equal-thickness plate, indicating that the conformal acoustic black hole structure proposed in the present invention has the same vibration damping performance as the ordinary acoustic black hole. The poor low-frequency vibration damping performance is caused by the cut-off frequency effect of the acoustic black hole, that is, the energy-accumulating vibration damping effect below the cut-off frequency is poor.
[0061] This solution also gives an embodiment of a vibration damping performance verification experiment:
[0062] In this experiment, three experimental samples were set up, namely an equal-thickness plate, an ordinary acoustic black hole plate, and a conformal acoustic black hole plate. The geometric parameters and material parameters of the experimental samples were consistent with the simulation. The experimental samples were suspended by elastic ropes to simulate free boundary conditions. The cross-line average acceleration response was measured by six equally spaced acceleration sensors. The exciter provided point excitation. Since the excitation force of the exciter has frequency response characteristics, the calculation formula for the line average acceleration response was adjusted, that is, the experimental test results are as Figure 9 shown; the experimental results and Figure 6 the simulation results have good consistency. The response peaks of the ordinary acoustic black hole plate and the conformal acoustic black hole plate in the middle and high frequency bands are much smaller than those of the equal-thickness plate, indicating that the conformal acoustic black hole structure proposed in the present invention has the same vibration damping performance as the ordinary acoustic black hole. The poor low-frequency vibration damping performance is caused by the cut-off frequency effect of the acoustic black hole, that is, the energy-accumulating vibration damping effect below the cut-off frequency is poor.
[0063] In summary, when the bending wave propagates from the effective stealth direction to the conformal two-dimensional acoustic black hole 2 region in this solution, the wave speed gradually decreases and finally accumulates on the innermost circle of the conformal two-dimensional acoustic black hole 2 region, cooperating with the damping layer 6 to consume the vibration energy and achieve broadband vibration damping performance. The stealth hole 3 is circular and hollow, which not only reduces the structural weight but also can place other objects or be used to observe the internal situation of the device; compared with the general two-dimensional acoustic black hole, the present invention can simultaneously achieve the bending wave stealth characteristic in the two-dimensional acoustic black hole structure and the lightweight broadband vibration damping performance of the thin plate structure, and has a wider application scenario.
Claims
1. A conformal two-dimensional acoustic black hole stealth vibration reduction structure, characterized in that: It includes a substrate, on which a conformal two-dimensional acoustic black hole is integrally formed, a stealth hole is arranged in the middle of the conformal two-dimensional acoustic black hole, the outer side of the inner diameter circle of the conformal two-dimensional acoustic black hole contains two symmetrically distributed bosses, the inner side of the outer diameter circle of the conformal two-dimensional acoustic black hole contains two symmetrically distributed platforms, and a damping layer is pasted on the bottom of the conformal two-dimensional acoustic black hole.
2. The conformal two-dimensional acoustic black hole stealth vibration reduction structure according to claim 1, characterized in that: The thickness distribution of the conformal two-dimensional acoustic black hole is a function of the polar coordinates r and θ, and the function formula is: Among them, h z is the thickness inside the conformal two-dimensional acoustic black hole; h0 is the thickness of the substrate; h2 is the residual thickness of the acoustic black hole; h1 is h0-h 2； r abh is the radius of the acoustic black hole; a is the radius of the invisible hole; u is the power exponent, and u≥2.
3. The conformal two-dimensional acoustic black hole stealth vibration reduction structure according to claim 2, characterized in that: The two bosses and the two platforms are located on the same diameter of the outer diameter circle of the conformal two-dimensional acoustic black hole, and the extension direction of the diameter is the effective stealth direction of the conformal two-dimensional acoustic black hole, and the extension direction of the perpendicular line of the diameter is the invalid stealth direction of the conformal two-dimensional acoustic black hole.
4. The conformal two-dimensional acoustic black hole stealth vibration reduction structure according to claim 2, characterized in that: The two bosses and the two platforms are flush with the upper surface of the substrate.
5. The conformal two-dimensional acoustic black hole stealth vibration reduction structure according to claim 2, characterized in that: The damping layer is ring-shaped, the inner diameter circle of the damping layer is aligned with the lower end of the stealth hole, and the outer diameter circle of the damping layer is aligned with the lower end of the outer diameter circle of the conformal two-dimensional acoustic black hole.
6. A method for preparing a conformal two-dimensional acoustic black hole stealth vibration reduction structure, characterized in that: The following steps are involved: S1: Select a rectangular thin plate as the substrate and open a stealth hole on the substrate; S2: A conformal two-dimensional acoustic black hole is integrally formed on the substrate around the invisible hole, and the thickness distribution of the conformal two-dimensional acoustic black hole is a function of the polar coordinates r and θ, and the function formula is: Among them, h z is the thickness inside the conformal two-dimensional acoustic black hole; h0 is the thickness of the substrate; h2 is the residual thickness of the acoustic black hole; h1 is h0-h 2； r abh is the radius of the acoustic black hole; a is the radius of the invisible hole; u is the power index, and u≥2; S3: A ring-shaped damping layer is pasted on the bottom of the conformal two-dimensional acoustic black hole, and the inner diameter circle of the damping layer is aligned with the lower end of the stealth hole, and the outer diameter circle of the damping layer is aligned with the lower end of the outer diameter circle of the conformal two-dimensional acoustic black hole.
7. The method for preparing the conformal two-dimensional acoustic black hole stealth vibration reduction structure according to claim 6, characterized in that: The substrate and the conformal two-dimensional acoustic black hole are integrally formed of metal material or polymer material, and the damping layer is made of chemical polymer or high damping alloy.
8. The method for preparing the conformal two-dimensional acoustic black hole stealth vibration reduction structure according to claim 7, characterized in that: The substrate and the conformal two-dimensional acoustic black hole are integrally formed of aluminum alloy, and the Young's modulus E is 71Gpa and the density ρ is 2810kg / m 3 , Poisson's ratio υ is 0.
33.
9. The method for preparing the conformal two-dimensional acoustic black hole stealth vibration reduction structure according to claim 7, characterized in that: The damping layer is butyl rubber, with a Young's modulus E of 0.1 MPa and a density ρ of 1200 kg / m 3 , Poisson's ratio υ is 0.
48.
10. The method for preparing the conformal two-dimensional acoustic black hole stealth vibration reduction structure according to claim 6, characterized in that: The invisible hole radius a is the acoustic black hole radius r abh One fifth of.