A tube-reinforced negative poisson's ratio honeycomb structure and its ligament-deficient derivatives and applications

Abstract

The present application relates to the technical field of protective functional materials, in particular to a tube-reinforced negative Poisson's ratio honeycomb structure and its lack of ligament derived structure and application, the present application proposes TRAHM as an integrated energy absorption and vibration control general topology design strategy, and derives two types of lack of ligament configurations of ULM-TRAHM and JLM-TRAHM. Through the three-dimensional topology coupling of honeycomb and square tube, a two-stage energy absorption platform and a medium-high frequency elastic wave band gap are formed, and hierarchical energy absorption and medium-high frequency vibration control are realized, breaking the design barrier of mutual exclusion of traditional structure energy absorption and vibration isolation performance, without the need for additional vibration damping resonant components, and under the premise of lightweight, impact protection and medium-high frequency vibration suppression are completed simultaneously, forming a reusable lightweight multifunctional metamaterial, providing an innovative direction for the field of equipment protection.

Description

Technical Field

[0001] This invention relates to the field of protective functional materials technology, and in particular to a tube-reinforced negative Poisson's ratio honeycomb structure and its ligament-deficient derivative structure and applications. Background Technology

[0002] Lightweight, multifunctional structures are an important development direction in the fields of aerospace, automotive, and industrial equipment protection. These fields generally require lightweight construction while also possessing functions such as shock resistance, energy absorption, and elastic wave vibration isolation. Topology is one research direction that aims to meet these multiple requirements.

[0003] Commonly used topological structures, such as negative Poisson's ratio honeycomb structures, thin-walled square tubes, or reinforcements based on these, exhibit superior performance in impact energy absorption due to their unique deformation mechanisms. For example, Chinese patent CN120327033A discloses a symmetrical negative Poisson's ratio vibration damping and energy-absorbing honeycomb sandwich structure, which uses a symmetrical arrow-shaped honeycomb cell arrangement to improve resilience and impact resistance. Wang Xichen, et al. Study on compressive mechanical properties of reinforced concave honeycomb structures [J]. Journal of Ocean University of China, 2026. Through concave honeycomb and double rhomboid reinforcement structures, the platform stress was increased by 75.1% and energy absorption by 45.5%.

[0004] The inventors discovered that conventional negative Poisson's ratio honeycomb and thin-walled square tubes only possess a single energy absorption function and lack effective vibration control capabilities. Simple spliced ​​honeycomb tube composite structures only achieve linear performance superposition, lacking topological coupling effects and failing to simultaneously address energy absorption and vibration isolation. This results in the band gap of existing periodic metamaterials being primarily concentrated in the low-to-mid-frequency range, making it difficult to cover the 100–2000 Hz mid-to-high-frequency vibration range. Furthermore, the energy absorption and vibration isolation functions are mechanistically mutually exclusive; conventional structural optimization can only sacrifice one performance for the improvement of the other. Additionally, material manufacturing introduces processing defects such as wall thickness reduction and modulus attenuation, leading to poor robustness and difficulty in large-scale production of existing metamaterials. Summary of the Invention

[0005] In view of this, the purpose of this invention is to propose a tube-reinforced negative Poisson's ratio honeycomb structure and its ligament-deficient derivative structure and applications, so as to solve the technical problem that existing topologies cannot simultaneously achieve energy absorption and vibration isolation.

[0006] To achieve the above objectives, the present invention provides a tube-reinforced negative Poisson's ratio honeycomb structure, comprising a periodically arrayed unit cell, wherein the unit cell comprises a matrix and an embedded body, and the embedded body is vertically embedded in the matrix in a three-dimensional seamless topology.

[0007] Meanwhile, a ligament-deficient derivative structure of the tube-reinforced negative Poisson's ratio honeycomb structure is provided. The ligament-deficient derivative structure is a single-cell unilateral ligament-deficient configuration. The single-cell unilateral ligament-deficient configuration is achieved by removing the complete connecting ligament on one side of the single cell and introducing local topological defects inside the single cell.

[0008] A ligament-deficient derivative structure of the tube-reinforced negative Poisson's ratio honeycomb structure is also provided. The ligament-deficient derivative structure is a ligament-deficient configuration at the intercellular junction. The ligament-deficient configuration at the intercellular junction is formed by severing the shared intercellular junctional ligament of adjacent cells in a complete periodic array, thereby forming a discontinuous elastic transmission interface between the cells.

[0009] The beneficial effects of this invention are: (1) It provides an integrated multi-functional topology design strategy to achieve graded energy absorption and mid-to-high frequency vibration control in a unified manner, breaking the design barrier of mutually exclusive energy absorption and vibration isolation performance of traditional structures. The tube-reinforced negative Poisson's ratio honeycomb structure of the present invention is not a single component, but a standardized topology design concept. It forms a two-stage energy absorption platform and a mid-to-high frequency elastic wave bandgap through three-dimensional topological coupling of honeycomb and square tube. There is no need to add additional vibration damping resonators. Under the premise of lightweight, it simultaneously completes impact protection and mid-to-high frequency vibration suppression, and can be extended to multiple types of equipment as a general design scheme.

[0010] (2) Two types of ligament-deficient derivative structures are used to segmentally cover the mid-to-high frequency vibration reduction requirements, adapt to the vibration characteristics of different aircraft models, and are used in conjunction with mature mid-to-high frequency vibration isolation systems. Existing low-frequency vibration isolation solutions for UAVs are complete; the single-cell, single-sided ligament-deficient configuration focuses on 400~2000Hz, which is suitable for the vibration of motors in small and medium-sized consumer UAVs; the inter-cell junction ligament-deficient configuration covers a wide frequency range of 100~2000Hz, which is suitable for heavy-duty rotary-wing UAVs. Both types of variants retain complete crash energy absorption capabilities, achieving integrated vibration suppression and impact protection.

[0011] (3) The three structural performance gradients are clearly defined, and the selection is clear, covering multiple equipment operating conditions. The tube-reinforced negative Poisson's ratio honeycomb structure is suitable for general protection of vehicle-mounted and industrial equipment; the single-cell single-sided ligament-deficient configuration is suitable for small and medium-sized consumer drones; the inter-cell junction ligament-deficient configuration is suitable for heavy-duty industrial drones. The frequency bands are clearly defined, and the corresponding configuration can be directly selected according to the equipment vibration frequency.

[0012] (4) A unified dimensionless parameter system combined with multi-objective optimization can improve both performance characteristics simultaneously. The height of the energy absorption platform and the bandgap start and end frequencies are controlled by two sets of dimensionless parameters: beam width ratio and pipe height ratio. Multi-objective optimization is completed by using Latin hypercube sampling, response surface surrogate model and NSGA-II algorithm. The optimal design does not require sacrificing any performance characteristic.

[0013] (5) The structure has high tolerance for manufacturing errors and is suitable for mass additive manufacturing of UAVs. Selective laser sintering integral molding has no assembly interface, which simplifies the processing flow; it has natural robustness against common defects in wall thickness and material modulus in additive manufacturing; the core energy absorption and mid-to-high frequency vibration isolation functions are stable under conventional processing tolerances, and it has the value of large-scale mass production engineering. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a schematic diagram of the three-dimensional topological decomposition of the basic unit cell of TRAHM in an embodiment of the present invention; Among them, (a) is a concave negative Poisson's ratio honeycomb, (b) is a thin-walled square tube, and (c) is a tube-reinforced negative Poisson's ratio honeycomb unit cell; Figure 2 This is a schematic diagram of TRAHM according to an embodiment of the present invention; Among them, 21 is the upper support plate, 22 is the connecting ligament, and 23 is the lower support plate; Figure 3 This is a diagram showing the stress-strain and specific energy absorption curves of TRAHM in an embodiment of the present invention; Figure 4 The diagram shows the TRAHM unit cell band structure and transmission loss of an embodiment of the present invention. Figure 5 These are the RE, ST, and TRAHM stress-strain curves of an embodiment of the present invention; Figure 6 This is a diagram of the RE, ST, and TRAHM band structure according to an embodiment of the present invention; Among them, (a) is a concave negative Poisson's ratio honeycomb, (b) is a thin-walled square tube, and (c) is a tube-reinforced negative Poisson's ratio honeycomb. Figure 7 Schematic diagram of ULM-TRAHM in an embodiment of the present invention; Figure 8 This is a schematic diagram of JLM-TRAHM according to an embodiment of the present invention; Figure 9 This is a diagram of TRAHM deformation under static compression according to an embodiment of the present invention; Wherein, 1 to 8 represent strains of 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7 respectively; Figure 10 This is a transmission loss curve of ULM-TRAHM according to an embodiment of the present invention; Figure 11This is a transmission loss curve diagram of JLM-TRAHM according to an embodiment of the present invention; Figure 12 A comparison of transmission loss curves for three structures in embodiments of the present invention; Figure 13 This is a schematic diagram of the assembly of the ligament-deficient derivative structure and the drone robotic arm according to an embodiment of the present invention; Figure 14 This is a TL curve diagram of the improved robotic arm according to an embodiment of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0017] In this embodiment Figures 3-6 , Figures 10-12 and Figure 14 All results were obtained through finite element simulation, as follows: The static compression model was built using ABAQUS / Explicit, placing the structure between upper and lower rigid plates. The lower plate was completely fixed, while the upper plate was subjected to uniform displacement loads. The thin-walled structure was meshed using shell elements with a mesh size of 0.5~1.0 mm, and each unit cell contained approximately 2000~5000 elements. The nylon material was modeled using an ideal elastoplastic constitutive model with a density of 1.15 g / cm³, an elastic modulus of 2000 MPa, a Poisson's ratio of 0.35, and a yield strength of 40 MPa. The specific energy absorption was obtained by extracting the reaction force and displacement to calculate stress and strain, and then integrating. The band structure was constructed using the COMSOL Multiphysics solid mechanics module, applying Floquet periodic boundary conditions to the unit cells in conjunction with Bloch's theorem. The eigenvalues ​​were solved and plotted by scanning along the irreducible Brillouin zone boundary path of the wave vector. Transmission loss was calculated using the swept harmonic response of a finite periodic structure (8 periods). The formula for calculating transmission loss is TL = 20lg(uo / ui), where ui is the input displacement amplitude at one end of the structure and uo is the output displacement amplitude at the other end. The interval where TL < 0 is the effective vibration isolation interval. The simulation uses the unit cell band structure to define the swept frequency range, employs a conventional mesh discretization model, and applies displacement excitation at the ends to collect the output displacement.

[0018] Research has found that existing honeycomb tubular composite structures lack an integrated topological coupling mechanism, resulting in a single stress plateau during compression, poor graded energy absorption, and an inability to form an effective elastic wave bandgap for vibration control. Furthermore, since energy absorption and vibration isolation properties are inherently mutually exclusive, there is a lack of a unified geometric parameter system that can simultaneously regulate both properties. Moreover, the bandgap of traditional complete lattice metamaterials is concentrated in the mid-to-high frequency range, making them unsuitable for the 100-2000Hz mid-to-high frequency vibration suppression requirements of scenarios such as drones. Existing structures do not consider additive manufacturing defects; errors in wall thickness and material properties can easily lead to the failure of energy absorption and vibration reduction functions, resulting in insufficient engineering applicability.

[0019] To address the aforementioned issues, as one feasible implementation, an integrated topology design strategy for tube-reinforced negative Poisson's ratio (TRAHM) honeycomb structures was constructed. Based on the TRAHM fundamental topology, two ligament-deficient variants were designed: a single-cell unilateral ligament-deficient configuration (ULM-TRAHM) and a cell-intercellular junction ligament-deficient configuration (JLM-TRAHM). In TRAHM, the internal structure of a single cell is continuous and integrated, with adjacent cells sharing ligaments during array arrangement. In ULM-TRAHM, only the ligament on one side of a single cell is broken, while the external lattice remains intact. In JLM-TRAHM, all intercellular junction ligaments are uniformly broken. All three structures are integrally formed using a three-dimensional periodic array of single cells, as detailed below: (1) TRAHM: Tube-reinforced negative Poisson's ratio honeycomb, a universal multifunctional substrate structure; (2) ULM-TRAHM: Single-cell unilateral ligament-deficient configuration, oriented towards mid-to-high frequency vibration isolation of 400~2000Hz; (3) JLM-TRAHM: The intercellular junction lacks ligament configuration, which is used for vibration isolation of UAVs in a wide range of 100~2000Hz. Example 1

[0020] A tube-reinforced negative Poisson's ratio honeycomb structure includes a periodically arrayed unit cell, each unit cell comprising a matrix and an embedded body, wherein the embedded body is vertically embedded within the matrix in a three-dimensional seamless topology.

[0021] Preferably, the three-dimensional seamless topology means that the four corners of the built-in body and the interior corners of the base body are geometrically continuous without assembly gaps.

[0022] Preferably, the substrate is a concave-angle negative Poisson's ratio honeycomb (RE), and the inner body is a thin-walled square tube (ST).

[0023] Preferably, the beam width ratio of the unit cell is... The value range is 0.2~0.8, pipe height ratio The value range is 0.5 to 0.8.

[0024] Preferably, the beam width ratio The pipe height ratio ,in, Let be the length of the RE oblique ligament, and b be the width of a single cell. denoted as ST, and h as the height of a single cell.

[0025] Specifically, such as Figure 1As shown, the TRAHM provided in this embodiment is composed of unit cells arranged in a three-dimensional periodic array. Each unit cell consists of two parts: an RE matrix and a vertically embedded ST. The RE matrix is ​​composed of multiple oblique ligaments and vertical ligaments forming a concave corner configuration. The embedded ST has a square cross-section and a wall thickness of t2. The two are combined to form a unit cell through a three-dimensional seamless topological fusion method. The embedded ST is vertically embedded in the central region of the matrix. The four corners of the ST are geometrically continuous with the interior corners of the RE, without any assembly gaps.

[0026] Basic unit cell dimensions: s=22mm, h=18mm, b=15mm, RE wall thickness t1, ST wall thickness t2, concave angle. Define two dimensionless control parameters: beam width ratio. The value ranges from 0.2 to 0.8, and the pipe height ratio is... The value ranges from 0.5 to 0.8. The benchmark combination is... .

[0027] The main body is made of nylon material with a density of 1.15 g / cm³. 3 With an elastic modulus of 2000MPa, it can replace metal and resin composite materials according to load-bearing requirements.

[0028] By relying on the three-dimensional fusion coupling of RE and built-in ST, a two-stage stable energy absorption platform and a mid-to-high frequency elastic wave bandgap are realized simultaneously, opening up a design path that combines impact protection and mid-to-high frequency vibration control in a single structure.

[0029] like Figure 2 As shown, in the periodic array of the tube-reinforced negative Poisson's ratio honeycomb structure, adjacent unit cells are connected by connecting ligaments 22. The top of the array is provided with an upper support plate 21 and the bottom is provided with a lower support plate 23. The upper support plate 21 and the lower support plate 23 are fixedly connected to the upper and lower ends of each unit cell, respectively, for bearing external loads and transmitting impact forces.

[0030] 1. Analysis of Function Implementation (1) Staged energy absorption function like Figure 3 As shown, the TRAHM structure maintains a negative Poisson's ratio characteristic throughout the entire strain range, and forms a two-stage stable stress plateau during the compression process; under low strain, the RE ligament undergoes plastic deformation to absorb micro-impacts, while under high strain, the lower tube gradually crushes to resist high-intensity impacts, and the dual-plateau deformation mechanism remains stable under dynamic impacts of 10~100m / s.

[0031] like Figure 5 As shown, compared with RE and pure thin-walled square tube ST, RE and ST both exhibit only a single and relatively low stress plateau, while TRAHM exhibits a unique dual-plateau characteristic, verifying the synergistic energy absorption gain effect generated by the three-dimensional fusion of RE and ST.

[0032] The RE and ST in this structure have no assembly gaps, and the load can be continuously transferred in both directions. In the low strain stage, the RE ligament preferentially buckles and absorbs energy, while the ST simultaneously constrains the RE to prevent local instability and fracture. After the strain enters the transition range, the RE expands laterally to open the sidewall of the ST tube, changing the buckling wavelength of the square tube and extending the high-stress bearing platform. In the high strain stage, the lower tube dominates the dissipation of high-intensity impact energy. The deformation modes of the two are mutually constrained and mutually amplified, naturally forming two independent stable energy absorption platforms, which cannot be achieved by linear superposition of a single structure.

[0033] (2) Vibration control function like Figure 4 As shown, a complete elastic wave bandgap is formed at mid-to-high frequencies by relying on the Bragg scattering effect of a periodic lattice, achieving mid-to-high frequency vibration isolation in conventional equipment. This serves as a basic design strategy to provide a mechanical and bandgap-based underlying framework for variants. The vibration isolation effect is evaluated by calculating the transmission loss (TL). TL < 0 indicates that there is a vibration isolation effect within this frequency range; the smaller the TL, the better the vibration isolation effect.

[0034] At the same time, such as Figure 6 The comparison shows that pure ST has no complete elastic wave bandgap, while pure RE has only a narrow mid-to-high frequency bandgap. TRAHM unit cells can form broadband elastic wave bandgap, a result of the combined effect of periodic Bragg scattering and intracellular local resonance. The seamless connection between RE and ST within the unit cell forms a continuous interface with differences in stiffness and mass. When elastic waves propagate to this interface, interface mode transitions occur, transforming the bending wave that originally propagated along the RE ligament into radial expansion and contraction vibrations of the square tube cavity. These two types of vibration modes couple and dissipate vibrational energy. Complete periodic arrays rely on geometric periodicity to achieve coherent interference of elastic waves, forming a basic bandgap. The embedded ST can also serve as a rigid oscillator, forming a resonant unit with the surrounding flexible RE, further broadening the damping frequency band.

[0035] (3) Synergistic effect of TRAHM three-dimensional topological coupling The RE and the built-in ST are seamlessly integrated in three dimensions without any interface gaps. Mechanical and vibrational energy can be completely coupled and transferred within the unit cell. This is a necessary structural condition for generating nonlinear synergistic gain and a core feature that distinguishes it from existing simple spliced ​​composite structures. Example 2

[0036] A ligament-deficient derivative structure of the tube-reinforced negative Poisson's ratio honeycomb structure, wherein the ligament-deficient derivative structure is a single-cell unilateral ligament-deficient configuration, wherein the single-cell unilateral ligament-deficient configuration is achieved by removing the intact connecting ligament on one side of the single cell and introducing local topological defects inside the single cell.

[0037] Preferably, the single-cell unilateral ligament-deficient configuration is characterized by retaining the thin-walled features and not scaling the thickness, while the entire single cell is scaled by a factor of 1.5, and the vibration isolation frequency band of the configuration is 400~2000Hz.

[0038] Specifically, such as Figure 7 As shown: ULM-TRAHM uses TRAHM unit cells as a base, removing the intact connecting ligaments on one side of the unit cell and introducing only local topological defects within the cell. The overall array period remains unchanged. While preserving the thin-walled characteristics and maintaining the thickness without scaling, the unit cell is uniformly scaled by 1.5 times to adapt to the lightweight size requirements of UAVs. The baseline parameters are adjusted to α=0.2 and β=0.8.

[0039] This variant retains TRAHM's original dual-platform graded energy absorption capability, which can withstand the impact of drone crashes. Intracellular local stiffness mutations create an effective vibration reduction range of 400~2000Hz, covering the typical mid-to-high frequency vibrations of small and medium-sized drone motors on the basis of mature low-frequency vibration isolation for drones, and is suitable for general vibration reduction protection for consumer-grade drones.

[0040] See Figure 10 The transmission loss curve of ULM-TRAHM shows a significant decrease in the TL value (TL<0) within the 400~2000Hz frequency band, indicating that elastic wave propagation is effectively suppressed in this frequency band. This variant can cover the typical mid-to-high frequency vibration of small and medium-sized drone motors based on mature mid-to-high frequency vibration isolation solutions for drones, and is suitable for the general vibration reduction and protection needs of consumer-grade drones. Example 3

[0041] A ligament-deficient derivative structure of the tube-reinforced negative Poisson's ratio honeycomb structure, wherein the ligament-deficient derivative structure is a ligament-deficient configuration at the intercellular junction, wherein the intercellular junction-deficient configuration is formed by severing the shared junctional ligament of adjacent cells in a complete periodic array, thereby forming a discontinuous elastic transmission interface between the cells.

[0042] Preferably, the intercellular junction ligament-deficient configuration is characterized by retaining the thin-walled features and not scaling the thickness, while the entire single cell is scaled by a factor of 1.5, and the vibration isolation frequency band of the configuration is 100~2000Hz.

[0043] For details, see Figure 8 JLM-TRAHM uniformly severs the shared junctional ligaments of adjacent cells within a complete TRAHM array, forming a discontinuous elastic transfer interface between cells. While preserving thin-wall characteristics and maintaining the same thickness, the cell can be scaled 1.5 times to adapt to lightweight UAVs, with baseline parameters of α=0.2 and β=0.8.

[0044] This variant maintains a stable two-stage energy absorption platform, meeting protection requirements. The intercellular disconnection interface significantly weakens the transcellular transmission capability of elastic waves, effectively broadening the vibration isolation frequency band to 100~2000Hz, with a lower low-frequency oscillation threshold, providing optimal suppression of mid-to-high frequency vibrations across a wide range for heavy-duty UAV rotors.

[0045] See Figure 11The transmission loss curves show that the JLM-TRAHM effectively widens the vibration isolation frequency band to 100~2000Hz, with a lower mid-to-high frequency vibration initiation threshold. Compared to the ULM variant, JLM not only extends to higher frequency bands, but more importantly, it lowers the vibration isolation initiation frequency from 400Hz to 100Hz, covering a wider range of mid-to-high frequency vibrations generated by heavy-duty UAV rotors. A comparison of the TL curves of the two variants is shown below. Figure 12 As shown, the performance gradient is clear, and the appropriate model can be selected based on the specific vibration spectrum characteristics of the equipment.

[0046] Based on the TRAHM basic topology, two ligament-deficient variants, ULM-TRAHM and JLM-TRAHM, were designed. By introducing intracellular and intercellular topological defects, the vibration reduction range of 100~2000Hz in the mid-to-high frequency range was expanded to adapt to the vibration conditions of UAVs. A dimensionless collaborative parameter control system was established, and a multi-objective optimization algorithm was used to simultaneously improve the structural specific energy absorption and relative bandgap width, eliminating the mutual contradiction between energy absorption and vibration isolation performance.

[0047] In all three structures, the honeycomb ligaments preferentially buckle and deform in the low-strain range, forming the first low-stress plateau, absorbing minor impact loads, compressing the structure to expand laterally, and avoiding local stress concentration and fracture. In the transition range, the honeycomb matrix gradually collapses, and the built-in square tubes begin to participate in the main load-bearing. In the high-strain range, the thin-walled square tubes steadily and progressively collapse, forming the second high-stress plateau, dissipating a large amount of high-intensity impact energy from the crash and collision. In the dense range, the internal pores are completely compacted, the stress rises rapidly, and the energy absorption process tends to saturate. Dynamic impact conditions only increase the stress amplitude of the plateau, the two-stage progressive collapse mechanism remains unchanged, and the specific energy absorption increases synchronously with the impact velocity.

[0048] Meanwhile, the TRAHM basic topology relies on a complete periodic lattice to generate multi-band elastic wave band gaps, making it suitable for mid-to-high frequency vibration control. The ULM-TRAHM variant uses intracellular local defects to form a vibration reduction range of 400~2000Hz, which, combined with existing mature low-frequency vibration isolation solutions for UAVs, covers the vibration of motors in small and medium-sized UAVs; the JLM-TRAHM variant uses intercellular disconnected interfaces to widen the effective vibration isolation to 100~2000Hz, and can also synchronously attenuate mid-to-low frequency vibrations down to 100Hz, making it suitable for broadband vibration scenarios of heavy-duty UAV rotors. Example 4

[0049] The three provided structures are integrally formed using selective laser sintering (SLS), and these structures are used as energy-absorbing and vibration-damping connectors between the drone's arms and motors.

[0050] Specifically, (1) Additive manufacturing scheme: The entire structure is integrally formed using SLS technology. In the SLS process, the unsintered powder can self-support complex thin-walled structures without the need for additional support structures, which is suitable for the complex configuration of RE and ST fusion in this invention. Standard tensile test specimens are printed simultaneously with the molding process to complete the calibration of material mechanical properties and ensure quality control.

[0051] (2) Defect tolerance verification All three structures can withstand two main manufacturing defects: wall thickness reduction (0.8 mm, 0.6 mm) and matrix elastic modulus decay (1.8 GPa, 1.6 GPa). Under defective operating conditions, the dual-platform energy absorption mechanism remains intact, and the core frequency band vibration isolation function does not fail. This robustness stems from the topological coupling synergistic enhancement mechanism of this invention—functionality depends on the coupling relationship between the RE and ST, rather than the absolute size or modulus of a single component. For the two types of ligament-deficient configurations, the unit cell reference size of this invention is on the order of millimeters; therefore, millimeters are used as the geometric adjustment reference unit. When only the length and width of the missing ligament are slightly altered at the millimeter level without completely destroying the basic ligament-deficient topology, the dual-stage energy absorption mechanism and the target vibration isolation frequency band will not experience failure shift.

[0052] (3) Typical assembly applications See Figure 13 The ULM-TRAHM and JLM-TRAHM models can be pre-drilled with through-holes for the drone's robotic arm to pass through and be fitted at the connection point between the brushless motor and the robotic arm. The perforated structure does not compromise the overall vibration isolation performance; see [link to documentation]. Figure 14 The improved TL curve of the robotic arm shows no significant degradation in the core frequency band vibration isolation function after the opening. Without completely losing the structural configuration, and using millimeters as the geometric adjustment reference unit, adjusting the missing ligament length and width does not degrade the structural energy absorption and vibration isolation core effects. When the through-hole is opened in the central area of ​​the structure without damaging the thin-walled structure, the vibration isolation and energy absorption performance will not fail. If large-diameter assembly is required, the overall geometric dimensions can be simultaneously enlarged to offset stiffness loss, or an assembly method that does not damage the structure can be adopted.

[0053] The TRAHM basic topology can be attached to automotive crash barriers and industrial equipment bases for general impact protection and mid-to-high frequency vibration control. ULM-TRAHM is suitable for small and medium-sized consumer drones, while JLM-TRAHM is suitable for heavy-duty industrial drones. The three configurations have clear performance gradients, allowing users to directly select the appropriate configuration based on the equipment's vibration frequency characteristics.

[0054] (4) Structural parameter optimization methods This invention establishes a dimensionless synergistic parameter control system, using the beam width ratio α and tube height ratio β as design variables, and specific energy absorption (SEA) and relative bandgap width as optimization objectives. The specific optimization process is as follows: ① Initial sample points are generated within the design space using Latin hypercube sampling; ② Calculate the SEA and bandgap width of each sample point using finite element simulation; ③ Construct a response surface surrogate model to fit the mapping relationship between design variables and performance indicators; ④ The NSGA-II multi-objective genetic algorithm is used for Pareto front optimization.

[0055] Simulation results show that there are several Pareto optimal solution sets that can achieve synchronous improvement of SEA and relative bandgap width, effectively eliminating the mutual contradiction between energy absorption and vibration isolation performance.

[0056] Table 1 Performance Comparison between Optimized and Baseline Configurations

[0057] Beam width ratio This represents the proportion of the cellular oblique ligament relative to the width of the unit cell. As the diameter increases, the honeycomb ligaments become thicker and longer, increasing the buckling capacity in the low-strain zone, but simultaneously increasing the structural equivalent density. (Pipe height ratio) This indicates the percentage of the built-in ST relative to the unit cell height. When the ST is increased, its vertical extension is better, and its axial load-bearing efficiency is improved. SEA for and The response of the elastic wave bandgap is sluggish; the elastic wave bandgap is more sensitive to the response of structural parameters. Increase the periodic impedance of the reinforced honeycomb matrix. Increasing the size of the ST and RE enables the formation of more efficient local resonant units. The two mechanisms generate a coupling effect under specific parameter combinations, resulting in a nonlinear increase in the relative bandwidth.

[0058] Table 1 shows that the optimized configuration only improves the SEA by 5.12%, while the relative bandwidth jumps by 82.02%. The difference in the magnitude of these changes stems from their different sensitivities to structural parameters. SEA depends on the overall progressive failure path and equivalent density of the structure. and The change in [the force] increases the platform stress while simultaneously increasing the structural mass; the positive and negative effects partially offset each other, hence the slow change characteristic. The relative bandwidth depends on the wave dynamics conditions of the periodic structure—when [the force]... At that time, the impedance comparison between RE and ST is insufficient to generate a wide bandgap; while when At this point, the stiffness ratio and mass ratio cross critical values, enabling frequency coupling between Bragg scattering and local resonance mechanisms, resulting in a nonlinear abrupt change in the bandgap width. This discovery has direct guiding significance for the design of engineering materials: under different vibration reduction requirements, the optimal configuration can be quickly determined based on the parameter control system established by this technical solution, eliminating the need to make a difficult trade-off between energy absorption and vibration isolation.

[0059] The tube-reinforced negative Poisson's ratio honeycomb structure and its ligament-deficient derivative configuration, which combine energy absorption and vibration control, can be integrally molded using SLS additive manufacturing technology. It is suitable for impact protection and broadband vibration suppression in various scenarios such as aviation drones, automotive equipment, and industrial equipment. At the same time, the three structures have clear performance gradients, allowing direct selection based on the specific vibration spectrum characteristics and protection requirements of the equipment, and have good engineering applicability and large-scale mass production value.

[0060] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention (including the claims) is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in the details for the sake of brevity.

[0061] This invention is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A tube-reinforced negative Poisson's ratio honeycomb structure, characterized in that, The invention comprises a periodically arrayed unit cell, the unit cell comprising a matrix and an embedded body, the embedded body being vertically embedded within the matrix in a three-dimensional seamless topology.

2. The structure according to claim 1, characterized in that, The three-dimensional seamless topology means that the four corners of the built-in body and the interior corners of the base body are geometrically continuous without assembly gaps.

3. The structure according to claim 1, characterized in that, The substrate is a concave-angle negative Poisson's ratio honeycomb, and the inner body is a thin-walled square tube.

4. The structure according to claim 1, characterized in that, The beam width ratio of the unit cell The value range is 0.2~0.8, pipe height ratio The value range is 0.5 to 0.

8.

5. The structure according to claim 4, characterized in that, The beam width ratio The pipe height ratio ,in, denoted as , where is the length of the concave-angle negative Poisson's ratio honeycomb oblique ligament, and b is the width of a single cell. denoted as , where h is the height of the thin-walled square tube, and h is the height of the unit cell.

6. A ligament-deficient derivative structure of the tube-reinforced negative Poisson's ratio honeycomb structure according to any one of claims 1 to 5, characterized in that, The ligament-deficient derivative structure is a single-cell unilateral ligament-deficient configuration, which is formed by removing the intact connecting ligament on one side of the single cell and introducing local topological defects inside the single cell.

7. The ligament-deficient derivative structure according to claim 6, characterized in that, The single-cell unilateral ligament-deficient configuration is constructed by scaling the single cell by a factor of 1.5 while retaining the thin-walled characteristics and without scaling the thickness. The vibration isolation frequency band of the configuration is 400~2000Hz.

8. A ligament-deficient derivative structure of the tube-reinforced negative Poisson's ratio honeycomb structure according to any one of claims 1 to 5, characterized in that, The ligament-deficient derivative structure is a ligament-deficient configuration at the intercellular junction, which is formed by severing the shared intercellular junctional ligament in adjacent cells within a complete periodic array, thereby creating a discontinuous elastic transmission interface between the cells.

9. The ligament-deficient derivative structure according to claim 8, characterized in that, The intercellular junction ligament-deficient configuration is characterized by retaining thin-walled features and not scaling the thickness, while the entire unit cell is scaled up by a factor of 1.5, and the vibration isolation frequency band of the configuration is 100~2000Hz.

10. The structure according to claim 1, 6, or 8, characterized in that, The structure is integrally formed by selective laser sintering and is used as an energy-absorbing and vibration-damping connector between the drone arm and the motor.

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