Design method of multifunctional superstructure capable of customizing low-frequency vibration reduction and bearing capacity

Abstract

The invention provides a design method of a multifunctional superstructure capable of customizing low-frequency vibration reduction and bearing capacity, and relates to the technical field of structural engineering.The design method comprises the following steps that firstly, a size parameter (T), a thickness parameter (delta) and cutting parameters (a, b, c and d) are set, and a unit cell main body structure is generated based on a P-type three-period minimal curved surface (TPMS) equation; a solid area is generated through expansion of the external TPMS, a hollowed area is defined by the internal TPMS, and difference set operation is executed to form a hollowed structure; further defining a tailoring pattern, and tailoring in xy, xz and yz directions; and finally, mass blocks are arranged on six planes inside. According to the technical scheme, the problems that in the prior art, a traditional vibration reduction structure is single in function, and low-frequency vibration reduction and high-bearing-capacity requirements are difficult to consider are solved.

Description

Technical Field

[0001] This invention relates to the technical field of structural engineering, and more particularly to a multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity. Background Technology

[0002] In fields such as mechanical engineering, aerospace, and precision instruments, structural components are often affected by low-frequency vibrations caused by various excitation sources during use. If these vibrations are not controlled, they can easily lead to system performance degradation, fatigue damage, or even functional failure. Therefore, under the premise of ensuring structural strength and stiffness, achieving effective suppression of low-frequency vibrations has become an important problem that urgently needs to be solved in engineering structural design.

[0003] Achieving this goal faces numerous challenges: on the one hand, controlling low-frequency waves is difficult, and traditional damping methods struggle to create an effective bandgap in the low-frequency range; on the other hand, vibration reduction and load-bearing capacity often conflict in design, making it difficult to optimize both using traditional methods. Currently widely used traditional vibration reduction technologies, such as spring-damped systems, rubber isolators, and mass-tuned dampers, offer advantages like simple structure, mature design, and high repeatability, and remain the preferred choice in engineering practice. However, these technologies are mostly based on fixed configurations, making it difficult to simultaneously achieve multiple design goals such as lightweighting, low-frequency vibration reduction, and load-bearing performance, especially in terms of adaptability to complex working conditions and structural customization capabilities.

[0004] To overcome the aforementioned limitations, researchers have recently shifted towards utilizing lightweight metastructures to achieve integrated functional and structural design. Through structural design, wave propagation can be guided or suppressed within the structure, thereby achieving low-frequency vibration reduction and stiffness control. Among these, the three-period minimal surface (TPMS) structure has attracted widespread attention in metastructure design due to its natural spatial periodicity, continuity, and superior mechanical properties, and has become one of the typical configurations that combines low-frequency bandgap characteristics with lightweight load-bearing capacity.

[0005] However, existing TPMS superstructures still face challenges such as limited low-frequency band gap, inflexible adjustment of structural stiffness and dimensions, and difficulty in balancing load-bearing capacity and vibration reduction performance, which restrict their engineering applications. Therefore, there is an urgent need to propose a customizable structural design method based on TPMS structures with parametric adjustment capabilities. Through flexible configuration of structural parameters, integrated control of low-frequency vibration reduction performance and load-bearing capacity can be achieved, enabling the customization of multifunctional and highly adaptable superstructures to meet the comprehensive performance requirements of complex engineering environments. Summary of the Invention

[0006] To address the technical problems mentioned in the background section, this invention provides a multifunctional superstructure design method that allows for customizable low-frequency vibration reduction and load-bearing capacity. Through parametric modeling, the invention flexibly adjusts the geometry and dimensions of the superstructure to achieve coordinated control of vibration reduction performance and structural stiffness, thus meeting the comprehensive performance requirements of complex engineering environments.

[0007] The technical means employed in this invention are as follows: A multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity includes the following steps: Step 1: Set the structural parameters of the unit cell, including dimensional parameters. T Thickness parameters δ With cutting pattern parameters a , b , c , d ; Step 2: Define a three-period minimal surface TPMS function with the origin of the xyz coordinate axes as the center, and construct the main body structure of the unit cell based on the TPMS equation; Step 3: Generate a solid region by extending the external TPMS and a hollow region by defining the internal TPMS, and perform a difference operation to form a hollow structure; Step 4: Define the clipping region in the first quadrant; extend it symmetrically to other quadrants based on the origin; use the clipping pattern to complete the clipping in the xy, xz, and yz directions; Step 5: Arrange mass blocks in six symmetrical planes inside the hollowed-out unit cell. Step 6: Complete rapid molding using photosensitive resin and / or thermoplastic polymer.

[0008] Furthermore, the main body of the unit cell is a P-type minimal curved surface structure.

[0009] Furthermore, in step 2, a three-period minimum surface function is defined with the origin of the xyz coordinate axes as the center; a TPMS unit cell structure is generated based on the function, wherein... T Define the unit cell size; TPMS function: .

[0010] Furthermore, in step 3, the minimal curved surface is extended inward to form a solid structural region: ; The internal minimum surface function is defined as: ; The excavated area is: ; The hollowed-out structure formed by performing a difference operation is as follows: .

[0011] Furthermore, in step 4, the cutting pattern parameters... a , b , c , d The six boundary positions of the hexagonal cutting pattern are defined respectively, and the cutting conditions in the first quadrant are: ; The remaining quadrants are obtained by symmetry about the origin: ; ; The clipping region in the xy plane is: ; The clipping regions in the xz and yz planes are similar to those in the xy plane: ; ; The final model is trimmed as follows: .

[0012] Furthermore, the mass block is connected to the unit cell body by adhesive or bolts.

[0013] Compared with the prior art, the present invention has the following advantages: (1) High customizability: By adjusting mathematical equations and design parameters, multiple design dimensions such as structural size, thickness, cutting pattern and additional mass block can be customized, which is suitable for different application scenarios.

[0014] (2) Integration of vibration reduction and load-bearing performance: The structure has both good low-frequency vibration reduction characteristics and load-bearing capacity while maintaining a lightweight design.

[0015] (3) Wideband vibration reduction effect: Based on the natural periodicity and continuity of the TPMS structure, the vibration reduction bandwidth is effectively expanded.

[0016] (4) High efficiency of parameter-driven modeling: The present invention adopts a parameterized modeling method driven by mathematical equations, which can quickly generate structural models and make automatic adjustments in programming software (such as Wolfram Mathematica), greatly improving design efficiency and reducing the traditional process of relying on experience design and repeated trial and error.

[0017] In summary, this invention provides an efficient and practical multifunctional superstructure design method, which has significant application value and broad market prospects in the field of vibration reduction technology. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating the method of the present invention. Figure 2 This is a schematic diagram of the unit cell body generated by the programming software Wolfram Mathematica in this invention; Figure 3 This is a schematic diagram of the unit cell structure of the present invention; Figure 4 The graph shows the dispersion curve and transmissibility curve of a single cell. Figure 5 Transmission rate curves for different array configurations of a single cell; Figure 6 This is a schematic diagram illustrating the load-bearing capacity of the original unit cell and the new unit cell.

[0020] Among them, 1. Unit cell body; 2. Unit cell body size; 3. Unit cell body thickness; 4. Cutting pattern; 5. Mass block. Detailed Implementation

[0021] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0022] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0023] like Figure 1-6 As shown, this invention provides a multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity, comprising the following steps: Step 1: Set the structural parameters of the unit cell, including dimensional parameters. T Thickness parameters δ With cutting pattern parameters a , b , c , d The main body of the unit cell is a P-type minimal curved surface structure. Step 2: Define a three-period minimum surface (TPMS) function centered at the origin of the xyz coordinate axes, and construct the main unit cell structure based on the TPMS equations; in Step 2, a three-period minimum surface function is defined centered at the origin of the xyz coordinate axes; the TPMS unit cell structure is generated based on the function, wherein... T Define the unit cell size; TPMS function: .

[0024] Step 3: Generate a solid region by extending the external TPMS and a hollowed-out region by defining the internal TPMS, and perform a difference operation to form a hollowed-out structure; in step 3, the minimal surface is extended inward to form a solid structure region: ; The internal minimum surface function is defined as: ; The excavated area is: ; The hollowed-out structure formed by performing a difference operation is as follows: .

[0025] Step 4: Define the clipping region in the first quadrant; extend it symmetrically to other quadrants based on the origin; use the clipping pattern to complete the clipping in the xy, xz, and yz directions; in Step 4, the clipping pattern parameters... a , b , c , d The six boundary positions of the hexagonal cutting pattern are defined respectively, and the cutting conditions in the first quadrant are: ; The remaining quadrants are obtained by symmetry about the origin: ; ; The clipping region in the xy plane is: ; The clipping regions in the xz and yz planes are similar to those in the xy plane: ; ; The final model is trimmed as follows: .

[0026] In a preferred embodiment, the mass block is connected to the unit cell body by adhesive or bolts.

[0027] Step 5: Arrange mass blocks in six symmetrical planes inside the hollowed-out unit cell. Step 6: Complete rapid molding using photosensitive resin and / or thermoplastic polymer.

[0028] Example 1 like Figure 1-6 As shown, this invention provides a multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity.

[0029] The structure designed by this method is highly customizable. By adjusting the equations and parameters, the dimensions 2, thickness 3, cutting pattern 4, and geometric parameters of the mass block 5 of the unit cell 1 can be customized, thereby controlling its vibration reduction effect and load-bearing performance.

[0030] The technical solution of this patent is clearly and completely described below through specific embodiments and in conjunction with the accompanying drawings. It should be particularly noted that this embodiment is only used to exemplify the feasibility of the multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity described in this patent. In practical applications, structural parameters (such as dimensions) may vary. T ,thickness δ The selection of materials (such as pattern cutting, mass block configuration, etc.) and materials (such as photosensitive resin, steel) can be adjusted according to specific needs.

[0031] First, set the parameter values, and then edit the code in Wolfram Mathematica based on the equations and parameters to generate a unit cell model for preview. Figure 2 As shown, the parameters are adjusted based on the preview results to optimize structural performance.

[0032] Given the parameters, we can create the dimensions. T It is 50 mm thick. δ The diameter is 2 mm, and the pattern is cut into hexagons. a It is 2 mm. b It is 24 mm. c It is 31.7 mm. dThe mass block is a 16.8 mm thick cylindrical steel unit cell with a diameter of 20 mm and a thickness of 5 mm. It can be fabricated according to the equations and parameters, such as... Figure 3 As shown, the main material of the unit cell is photosensitive resin, with a Young's modulus of 563 MPa, a Poisson's ratio of 0.3, and a density of 1600 kg / m³. 3 The allowable stress is approximately 14 MPa; the mass block is made of steel with a Young's modulus of 210 GPa, a Poisson's ratio of 0.33, and a density of 0.70850 kg / m³. 3 Its dispersion curve and transfer rate curve can be obtained through simulation, as shown in the figure. Figure 4 As shown in the figure, this structure exhibits a significant bandgap in the frequency ranges of 400 Hz-3800 Hz, 3900 Hz-4600 Hz, and 4800 Hz-6500 Hz, demonstrating excellent broadband vibration suppression capabilities. The transmissibility curves for four different array configurations are shown in the figure. Figure 5 As shown, simulation calculations show that the unit cell can withstand a maximum pressure of 42,769 Pa. After optimizing the cutting pattern, it can withstand a maximum pressure of 464,913 Pa, increasing the load-bearing capacity by an order of magnitude. Figure 6 As shown in the figure, the simulation results show that the superstructure based on the three-period minimal surface constructed using this customizable low-frequency vibration reduction and load-bearing capacity multifunctional superstructure design method exhibits good vibration suppression effect in the low-frequency range. At the same time, the load-bearing capacity can be adjusted over a wide range by changing the cutting pattern, verifying the effectiveness of this customizable design method.

[0033] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In the above embodiments of the present invention, the descriptions of each embodiment have their own emphasis; parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments. It should be understood that the disclosed technical content in the several embodiments provided in this application can be implemented in other ways.

[0034] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity, characterized in that, Includes the following steps: Step 1: Set the structural parameters of the unit cell, including dimensional parameters. T Thickness parameters δ With cutting pattern parameters a , b , c , d ; Step 2: Define a three-period minimal surface TPMS function with the origin of the xyz coordinate axes as the center, and construct the main body structure of the unit cell based on the TPMS equation; Step 3: Generate a solid region by extending the external TPMS and a hollow region by defining the internal TPMS, and perform a difference operation to form a hollow structure; Step 4: Define the clipping region in the first quadrant; Based on the symmetry of the origin, it extends to other quadrants; Use the cutting pattern to complete the cutting in the xy, xz, and yz directions; Step 5: Arrange mass blocks in six symmetrical planes inside the hollowed-out unit cell. Step 6: Complete rapid molding using photosensitive resin and / or thermoplastic polymer.

2. The multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity according to claim 1, characterized in that, The main body of the unit cell is a P-type minimal curved surface structure.

3. The multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity according to claim 1, characterized in that, In step 2, a three-period minimal surface function is defined with the origin of the xyz coordinate axes as the center. TPMS unit cell structures are generated based on functions, where T Define the unit cell size; TPMS function: 。 4. The multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity according to claim 1, characterized in that, In step 3, the minimal curved surface is extended inward to form a solid structural region: ； The internal minimum surface function is defined as: ； The excavated area is: ； The hollowed-out structure formed by performing a difference operation is as follows: 。 5. The multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity according to claim 1, characterized in that, In step 4, the pattern parameters are cut. a , b , c , d The six boundary positions of the hexagonal cutting pattern are defined respectively, and the cutting conditions in the first quadrant are: ； The remaining quadrants are obtained by symmetry about the origin: ； ； The clipping region in the xy plane is: ； The clipping regions in the xz and yz planes are similar to those in the xy plane: ； ； The final model is trimmed as follows: 。 6. The multifunctional superstructure design method with customizable low-frequency vibration reduction and load-bearing capacity according to claim 1, characterized in that, The mass block is connected to the unit cell body by adhesive or bolts.

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