Acoustic black hole metamaterial with load bearing and vibration suppression and design method

Abstract

This invention proposes an acoustic black hole metamaterial and its design method that combines load-bearing and vibration suppression. It is composed of multiple periodically arranged unit cells interconnected. Each unit cell integrates six three-dimensional acoustic black hole units formed by rotating a power-law thickness-gradient structure. Through the synergistic effect of the three-dimensional acoustic black hole units and lattice topology design, a significant elastic wave bandgap is achieved in an ultra-wide frequency range, effectively suppressing structural vibration while maintaining excellent static load-bearing capacity. This invention overcomes the inherent contradiction between vibration reduction performance and load-bearing capacity. While achieving lightweight miniaturization, it has advantages such as simple manufacturing process, compact structure, and easy integration, making it suitable for fields with high requirements for load-bearing and vibration suppression.

Description

Technical Field

[0001] This invention relates to the technical field of acoustic metastructures, specifically to an acoustic black hole metamaterial and its design method that combines load-bearing and vibration suppression. Background Technology

[0002] In critical engineering fields such as shipbuilding, high-speed rail, aerospace, and precision manufacturing, effectively suppressing low-to-mid-frequency vibrations in the 10–1000 Hz range is a core technical challenge for ensuring equipment operational accuracy, extending structural service life, and improving overall system reliability. It is also one of the key bottlenecks that urgently need to be overcome. Typical examples include critical components such as ship propulsion shafts, high-speed rail bogies, and precision machine tool bases, which inevitably generate continuous mechanical vibrations during operation. Such vibrations not only easily cause structural fatigue damage and reduce measurement and machining accuracy, but in severe cases, they may also lead to subsystem resonance or even systemic failure, threatening operational safety.

[0003] Traditional vibration isolation technologies primarily rely on the damping properties of materials, employing rubber isolators, metal springs, or viscoelastic damping materials to achieve vibration attenuation. However, these methods are limited by the material stiffness-damping trade-off, making it difficult to create an effective isolation bandgap in the low-to-mid frequency range, resulting in a significant decrease in isolation performance. Furthermore, while lightweight materials such as honeycomb sandwich structures and porous metals possess certain load-bearing capacity, they generally suffer from narrow local bandgaps, limited frequency reduction ranges, and singular damping mechanisms. These limitations make it difficult to simultaneously address the demands for wide-frequency vibration reduction and high specific strength load-bearing capacity, failing to meet the growing requirements of modern engineering for "wide-frequency, lightweight, and integrated" vibration control systems.

[0004] In recent years, acoustic metamaterials have attracted widespread attention due to their ability to control the propagation behavior of elastic waves through artificially designed unit structures. Among them, locally resonant acoustic metamaterials typically consist of a rigid frame, a pre-tensioned elastic membrane, and additional mass blocks: the elastic membrane is tensioned and fixed within a rigid frame, and concentrated mass blocks are attached to its surface. Through a locally resonant mechanism, efficient absorption of low-frequency waves is achieved in a specific frequency band, exhibiting good vibration reduction potential in the 100–1000 Hz range. However, this type of structure still has significant limitations: firstly, the reliance on a rigid frame results in poor overall flexibility and weak adaptability; secondly, the inherent bandwidth of the resonance mechanism is narrow, making it difficult to cover broadband vibration sources; and thirdly, the manufacturing process is complex, requiring precise pre-tensioning of the membrane and assembly of mass blocks, resulting in a large structural weight, which is not conducive to lightweight applications, especially in high-end equipment platforms such as aerospace where mass is sensitive.

[0005] In summary, existing vibration isolation solutions still face significant challenges in areas such as low-to-mid-frequency broadband vibration reduction, structural lightweighting, and integrated load-bearing functions. Therefore, there is an urgent need to develop a novel multifunctional structural material that can achieve broadband vibration suppression while possessing excellent mechanical load-bearing capacity, structural compactness, and manufacturability. Developing lightweight lattice metamaterials based on the acoustic black hole effect, and achieving integrated design of efficient vibration energy dissipation and structural load-bearing function through wave propagation modulation mechanisms, has significant engineering implications and application prospects. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide an acoustic black hole metamaterial and design method that combines load-bearing and vibration suppression, which can achieve a significant elastic wave bandgap in an ultra-wide frequency range, effectively suppress structural vibration, maintain excellent static load-bearing capacity, and is small in size, easy to manufacture, and conducive to practical applications.

[0007] The embodiments of this application are implemented as follows: This application provides an acoustic black hole metamaterial that combines load-bearing and vibration suppression. The metamaterial is characterized by being composed of multiple periodically arranged and interconnected unit cells, each of which integrates multiple three-dimensional acoustic black hole units formed by rotating a power-law thickness-gradient structure.

[0008] In some alternative implementations, the three-dimensional acoustic black hole unit is based on a power-law type thickness-gradient three-dimensional acoustic black hole thin plate, which is rotated around the bottom axis to form a three-dimensional solid structure with spatial rotational symmetry.

[0009] In some alternative implementations, the unit cell is a cubic configuration, integrally formed by 3D printing, with the 3D printing material being nylon, resin, thermoplastic polyurethane, or polylactic acid.

[0010] In some alternative implementations, the unit cell adopts a face-centered cubic lattice topology, with the lattice constant being consistent with the side length of the unit cell.

[0011] In some alternative implementations, the unit cell is composed of six of the three-dimensional acoustic black hole units arranged symmetrically along the principal axes of ±X, ±Y, and ±Z space, forming a three-dimensional orthogonal support network structure.

[0012] In some alternative implementations, the three-dimensional acoustic black hole unit rotates at an angle of 360° to form a closed rotating structure; or partially rotates at an angle of 90°–270° to form an open rotating structure.

[0013] In some alternative implementations, the size of the unit cell is 50–100 mm.

[0014] In some alternative implementations, the surface of the three-dimensional acoustic black hole unit is coated with a damping coating, which is a rubber-like viscoelastic material.

[0015] A design method for an acoustic black hole metamaterial that combines load-bearing and vibration suppression, characterized in that the three-dimensional acoustic black hole thin plate follows a power-law function in its thickness direction as follows: h(x) = h0 + (h1) h0) / l m ·x 2 x∈[0,l) Where x represents the distance coordinate along the length of the three-dimensional acoustic black hole plate, with the starting point located in the central region of the three-dimensional acoustic black hole unit; h(x) represents the local plate thickness at position x; h0 represents the truncated thickness of the three-dimensional acoustic black hole plate; h1 represents the original thickness of the initial uniform region of the three-dimensional acoustic black hole plate; l is the length of the gradient region of the three-dimensional acoustic black hole unit; and m is the power law exponent, m≥2.

[0016] In some alternative implementations, the size of h0 is no more than 10% of h1.

[0017] The beneficial effects of this application are as follows: This application provides an acoustic black hole metamaterial and design method that combines load-bearing and vibration suppression. It integrates the energy focusing mechanism of acoustic black holes with a face-centered cubic lightweight lattice structure. Through a three-dimensional solid gradient design, it achieves an ultra-wide elastic wave bandgap of 379.8Hz–3516.0Hz while possessing excellent static strength and buckling resistance, effectively solving the technical problem of balancing vibration reduction and load-bearing functions in traditional vibration isolation structures. The three-dimensional acoustic black hole... The structure of the Hole (ABH) unit requires no additional mass blocks, pre-tightening membranes, or complex assemblies; it achieves broadband vibration suppression solely through power-law gradient geometry and periodic topology. The entire unit is a solid continuum, which can be integrally formed using additive manufacturing technologies such as 3D printing. This process is simple, lightweight, and highly repeatable, significantly improving its engineering applicability in high-end fields such as aerospace and rail transportation. The orthogonal support network, composed of six-way symmetrical ABH units, provides omnidirectional vibration suppression capabilities. By adjusting parameters such as the power-law exponent m, cutoff thickness h0, and gradient length l, the bandgap and mechanical properties can be flexibly controlled within a density range of 30%–60%, adapting to various operating conditions. Additionally, a damping coating can be optionally applied to the surface to enhance energy dissipation and improve adaptability to environmental disturbances such as temperature and boundary changes, supporting customized applications in multiple scenarios. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the acoustic black hole metamaterial according to an embodiment of this application; Figure 2 This is a schematic diagram of the structure of the power-law type thickness-gradient ABH thin plate according to an embodiment of this application; Figure 3 This is a schematic diagram of the structure of a single cell according to an embodiment of this application; Figure 4 This is a front view of a unit cell according to an embodiment of this application; Figure 5 This is the band structure obtained from finite element analysis in the embodiments of this application; Figure 6 This is a frequency response curve obtained from finite element calculation in the embodiments of this application. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0021] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0022] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0023] The features and performance of this application will be further described in detail below with reference to the embodiments.

[0024] like Figures 1-4As shown, this application provides an acoustic black hole metamaterial and design method that combines load-bearing and vibration suppression. The metamaterial is composed of multiple periodically arranged unit cells 1 interconnected with each other, and each unit cell integrates six three-dimensional acoustic black hole units 2 formed by rotating a power-law thickness-gradient structure.

[0025] Furthermore, based on the coupling mechanism of local resonance and acoustic black hole effect, this invention achieves gradient propagation control and localized energy dissipation of elastic waves in space through geometric topology design, thereby achieving efficient vibration suppression over a wide frequency range.

[0026] Specifically, the three-dimensional acoustic black hole unit is based on a power-law type thickness-gradient structure, whose local stiffness continuously varies with position, forming a significant wave impedance gradient field. When an elastic wave propagates along the ABH unit from the thick end to the thin end, its group velocity gradually decreases with decreasing thickness and tends to zero, causing the wavefront to accumulate and linger at the end of the structure, producing a "black hole"-like energy trapping phenomenon. Although the ideal infinitely slow wave state cannot be achieved due to the truncated thickness h0 caused by manufacturing limitations, high-intensity vibration modes still accumulate in this region. Combined with the material's own damping characteristics, efficient energy dissipation can be achieved, significantly weakening the intensity of reflected waves and suppressing the overall vibration response of the structure.

[0027] Furthermore, each unit cell consists of six ABH units symmetrically arranged along three orthogonal directions (±X, ±Y, ±Z), forming a three-dimensional lattice structure with face-centered cubic periodicity. This periodic arrangement induces Bragg scattering: when the wavelength of the incident elastic wave is comparable to or a multiple of the lattice constant, the scattered waves between different unit cells undergo destructive interference, forming a frequency range that prohibits propagation—the Bragg bandgap. In addition, the non-uniform mass-stiffness distribution of the ABH units themselves excites local resonant responses, inducing strong local modes in the lower frequency range and opening a local resonant bandgap.

[0028] The two mechanisms described above do not operate independently, but rather achieve bandgap splicing and overlap through appropriate parameter matching, ultimately constructing an ultra-wide complete bandgap (379.8Hz–3516.0Hz) spanning nearly three octaves. Specifically, in the low-to-mid frequency range (<1000Hz), traditional Bragg structures are difficult to apply due to the need for large-sized periods, while this invention effectively solves this problem by utilizing the energy absorption mechanism dominated by the ABH effect; in the mid-to-high frequency range, the Bragg mechanism dominated by the periodic structure provides stable suppression capability. The synergistic effect of these two mechanisms overcomes the bandgap width bottleneck caused by a single physical mechanism.

[0029] Furthermore, this structure achieves an integrated design of vibration reduction performance and mechanical load-bearing capacity. The face-centered cubic lattice has a highly symmetrical force transmission path. Under external static or dynamic compressive loads, stress can be uniformly distributed to adjacent nodes through the six ABH elements, avoiding local stress concentration. Although the ABH elements have a thickness gradient, the overall structure is a solid continuous structure without weak connections or cavity defects, possessing excellent buckling resistance and specific stiffness advantages.

[0030] Furthermore, this metamaterial does not require additional concentrated mass blocks, pre-tensioned films, or complex assembly processes. All functions are integrated into a single material system, and it can be molded as a single unit through additive manufacturing technology, making it simple to manufacture, highly precise, and highly adaptable.

[0031] In summary, this invention integrates the energy focusing characteristics of acoustic black holes into a three-dimensional periodic lightweight lattice structure, constructing a multifunctional metamaterial that combines ultra-wideband vibration isolation performance, high specific strength load-bearing capacity, lightweight characteristics, and good manufacturability. Its working mechanism stems from the synergistic effect of multiple physical mechanisms: local resonance induced by geometric gradient design, Bragg scattering effect excited by the periodic topological structure, and vibration energy dissipation mechanism involving intrinsic material damping. These multi-scale wave modulation mechanisms are coupled together, significantly expanding the elastic wave bandgap in the low-frequency to mid-high frequency range, achieving effective suppression of broadband vibrations. Simultaneously, while maintaining excellent vibration reduction performance, this structure possesses good mechanical load-bearing capacity, successfully overcoming the inherent contradiction between broadband vibration reduction and structural load-bearing function in traditional vibration isolation systems. This provides a new technical path and structural solution for engineering fields with stringent requirements for multifunctional integrated structures, such as shipbuilding, rail transportation, aerospace, and precision instrument platforms.

[0032] In some alternative implementations, the unit cell has a cubic configuration with geometric dimensions of a×a×a, where a ranges from 50 mm to 100 mm. This configuration is suitable for lightweight, high-load-bearing structural designs and facilitates integrated manufacturing via additive manufacturing technology. The unit cell dimensions can be adjusted appropriately while maintaining structural performance. The lattice constant, the cutoff thickness h0 of the acoustic black hole, the original thickness h1 of the initial uniform region of the thin plate, and the power exponent m can all be varied within a certain range to meet the requirements of load-bearing capacity and vibration suppression in different scenarios.

[0033] The ABH unit is based on a power-law type thickness-gradient ABH thin plate. Through rotation around the bottom axis, a three-dimensional solid structure with spatial rotational symmetry is formed. The ABH thin plate follows a power-law function in its thickness direction, which can be expressed as: where x represents the distance coordinate along the length of the thin plate, starting at the center region of the acoustic black hole; h(x) is the local plate thickness at position x; h0 represents the truncated thickness of the acoustic black hole; h1 represents the original thickness of the initial uniform region of the thin plate; l is the length of the gradient region of the acoustic black hole; and m is the power-law exponent (m≥2).

[0034] Six three-dimensional acoustic black hole units are arranged symmetrically in pairs along the three orthogonal directions of the cubic unit cell, corresponding to the x, y, and z axes respectively. Each pair of units is arranged back-to-back to form a bidirectional gradient structure, which can exhibit efficient vibration suppression capability in any excitation direction.

[0035] Furthermore, the three-dimensional acoustic black hole unit is modeled based on a cylindrical coordinate system. Its bottom is fixed on the unit cell skeleton frame, and its top is suspended freely, forming a non-uniform cantilever resonant structure. By utilizing the continuous change in thickness to induce the bending wave velocity to gradually decrease and energy focusing, broadband elastic wave attenuation can be achieved without introducing additional mass.

[0036] In some alternative implementations, the overall relative density of the metamaterial is controlled between 30% and 60%, which ensures sufficient specific stiffness and specific strength to meet load-bearing requirements, while retaining rich internal dynamic properties to support the formation of low-frequency broadband bandgap.

[0037] Furthermore, by performing multi-objective optimization design on the unit cell topology and power-law parameters, and based on finite element simulation, the elastic wave bandgap width can be further widened, and the robustness to environmental factors such as temperature changes and boundary condition disturbances can be enhanced, thereby improving engineering applicability.

[0038] Example 1 In this embodiment, the surface of the three-dimensional acoustic black hole unit can be coated with a damping coating, such as a rubber-like viscoelastic material, to enhance the local energy dissipation capability and further improve the vibration suppression effect, especially the response attenuation near the resonance peak is more significant.

[0039] Example 2 In this embodiment, selective laser sintering (SLS) is used for 3D printing, and the material is TPU (thermoplastic polyurethane) with an elastic modulus of 61 MPa, a Poisson's ratio of 0.47, and a density of 1100 kg / m³. 3 The lattice constant of the unit cell is 50 mm, the cutoff thickness h0 of the acoustic black hole is 1 mm, the original thickness h1 of the initial uniform region of the thin plate is 24 mm, the length l of the gradient region of the acoustic black hole is 25 mm, and the power exponent m is 2.

[0040] The bandgap characteristics of this structure were obtained through numerical simulation using the finite element method combined with three-dimensional periodic boundary conditions. In the calculation, periodic boundary conditions were applied to the unit cell, and wave vector scanning was performed along the highly symmetric path of its Brillouin zone to obtain the complete bandgap structure. Figure 5 As shown, the metamaterial exhibits a distinct fully elastic wave bandgap in the frequency range of 379.8 Hz to 3516.0 Hz, with a relative bandwidth of 1.61, indicating that elastic waves propagating in this frequency band will be significantly suppressed. This result confirms that the structure possesses excellent ultra-wideband vibration suppression capabilities, effectively covering the widely existing mid-to-low frequency vibration sources in engineering.

[0041] By applying a rightward surface excitation to the left side of the instance and picking the displacement amplitudes of the excitation surface and the right side of the instance, the transmission loss curve of the instance can be obtained, as shown below. Figure 6 As shown, near the frequency of the complete bandgap in the band structure diagram, the transmission loss curve shows obvious transmission peaks and valleys, indicating that the structure can effectively block the propagation path of elastic waves and has a vibration isolation effect.

Claims

1. An acoustic black hole metamaterial that combines load-bearing and vibration suppression, characterized in that, It consists of multiple periodically arranged and interconnected unit cells, each of which integrates multiple three-dimensional acoustic black hole units formed by rotating a power-law thickness gradient structure.

2. The acoustic black hole metamaterial with both load-bearing and vibration-suppressing properties as described in claim 1, characterized in that, The aforementioned three-dimensional acoustic black hole unit is based on a three-dimensional acoustic black hole thin plate with a power-law type thickness gradient, and is formed by rotating around the bottom axis to form a three-dimensional solid structure with spatial rotational symmetry.

3. The acoustic black hole metamaterial with both load-bearing and vibration suppression properties as described in claim 2, characterized in that, The unit cell is cubic in shape and is integrally formed by 3D printing. The 3D printing material is nylon, resin, thermoplastic polyurethane, or polylactic acid.

4. The acoustic black hole metamaterial with both load-bearing and vibration-suppressing properties as described in claim 3, characterized in that, The unit cell adopts a face-centered cubic lattice topology, and the lattice constant is consistent with the side length of the unit cell.

5. The acoustic black hole metamaterial with both load-bearing and vibration-suppressing properties as described in claim 4, characterized in that, The unit cell is composed of six three-dimensional acoustic black hole units arranged symmetrically along the spatial principal axes of ±X, ±Y, and ±Z, forming a three-dimensional orthogonal support network structure.

6. An acoustic black hole metamaterial combining load-bearing and vibration suppression as described in claim 2 or 5, characterized in that, The three-dimensional acoustic black hole unit rotates at an angle of 360°, forming a closed rotating structure; or partially rotates at an angle of 90°–270°, forming an open rotating structure.

7. The acoustic black hole metamaterial with both load-bearing and vibration-suppressing properties as described in claim 4, characterized in that, The size of the unit cell is 50–100 mm.

8. The acoustic black hole metamaterial with both load-bearing and vibration-suppressing properties as described in claim 7, characterized in that, The surface of the three-dimensional acoustic black hole unit is coated with a damping coating, which is a rubber-like viscoelastic material.

9. A design method for an acoustic black hole metamaterial that combines load-bearing and vibration suppression as described in claim 2 or 5, characterized in that, The three-dimensional acoustic black hole thin plate, in its thickness direction, follows a power-law function as follows: h(x)=h0+(h1 h0) / l m ·x 2 ,x∈[0,l) Where x represents the distance coordinate along the length of the three-dimensional acoustic black hole plate, with the starting point located in the central region of the three-dimensional acoustic black hole unit; h(x) represents the local plate thickness at position x; h0 represents the truncated thickness of the three-dimensional acoustic black hole plate; h1 represents the original thickness of the initial uniform region of the three-dimensional acoustic black hole plate; l is the length of the gradient region of the three-dimensional acoustic black hole unit; and m is the power law exponent, m≥2.

10. The design method of an acoustic black hole metamaterial that combines load-bearing and vibration suppression as described in claim 9, characterized in that, The size of h0 is no more than 10% of h1.

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