A vibration reduction structure based on a dot matrix metamaterial and a design method thereof

Abstract

The application discloses a kind of based on dot matrix metamaterial vibration reduction structure and its design method, it is related to the field of vibration reduction technology, to solve how to realize the vibration suppression or weaken vibration of pipeline structure problem.The based on dot matrix metamaterial vibration reduction structure includes: at least two vibration reduction components.Each vibration reduction component includes: first panel, second panel, damping layer and multiple core units.Second panel is opposited and spaced apart with first panel, and the two ends of core unit are connected with first panel and second panel respectively.Core unit includes: at least four cores, and the core is enclosed to form a three-dimensional hollow body, the damping layer is arranged on the side of second panel away from first panel, and the first panel included in multiple vibration reduction components is sequentially fixedly connected to form a first annular member, and the second panel included in multiple vibration reduction components is enclosed to form a second annular member;Second annular member is located in first annular member.

Description

Technical Field

[0001] This invention relates to the field of vibration reduction technology, and in particular to a vibration reduction structure based on lattice metamaterials and its design method. Background Technology

[0002] Liquid rocket engines are high-power-density devices. High-speed mechanical rotation, propellant flow, and unstable combustion all contribute to engine structural vibrations, which severely impact the engine's safe and reliable operation. Piping structures are typical weak points in engine components subjected to vibration loads, and vibration-induced fractures are a significant source of engine failure. Large-scale vibrations can cause instantaneous pipe fractures under impact loads, while moderate-scale vibrations can become a source of cumulative fatigue damage, affecting the engine's lifespan and the number of times it can be reused.

[0003] Therefore, how to suppress or reduce vibration in pipeline structures is a technical problem that the industry urgently needs to solve. Summary of the Invention

[0004] The purpose of this invention is to provide a vibration reduction structure based on lattice metamaterials and its design method, for use in suppressing or reducing vibration in pipeline structures.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a vibration damping structure based on lattice metamaterials. This vibration damping structure includes at least two damping components. Each damping component includes a first panel, a second panel, a damping layer, and multiple core units. The second panel is opposite to and spaced apart from the first panel, and the two ends of the core units are respectively connected to the first panel and the second panel. Each core unit includes at least four cores, which enclose to form a three-dimensional hollow body. The damping layer is disposed on the side of the second panel facing away from the first panel. The first panels included in the multiple damping components are sequentially fixedly connected end-to-end to form a first annular member, and the second panels included in the multiple damping components enclose to form a second annular member; the second annular member is located within the first annular member.

[0006] Compared with the prior art, the beneficial effects of this application are as follows: In the vibration damping structure based on lattice metamaterials provided by this invention, during practical use, the vibration damping structure is fitted onto the outer wall of the pipeline, with the inner wall of the second annular member abutting against the outer wall of the pipeline. When the pipeline vibrates, the vibration damping structure generates a force opposite to the direction of pipeline vibration, and the vibration damping structure can generate a wide bandwidth, thereby suppressing or reducing pipeline vibration. It should be noted that the specific design parameters of the above-mentioned vibration damping structure are designed according to the pipeline to be damped, and are not specifically limited here.

[0007] Secondly, the present invention also provides a design method for a vibration damping structure based on lattice metamaterials. This design method is used to design the vibration damping structure based on lattice metamaterials described above; the vibration damping structure is sleeved on the outer wall of the pipeline; the first panels of multiple vibration damping components are sequentially connected end-to-end and fixed with screws to form a first annular member; the first panels and screws are equivalent to oscillators.

[0008] Design methods for vibration reduction structures based on lattice metamaterials include: Based on the vibration frequency response characteristics of the pipeline to be vibration-damped, determine the amplitude and / or frequency band of the pipeline that needs vibration reduction. Based on the amplitude and / or frequency band of the pipeline that needs to be reduced, determine the preset vibration attenuation frequency band of the vibration reduction structure so that the amplitude and / or frequency band of the pipeline that needs to be reduced are located in the central area of ​​the preset vibration attenuation frequency band. The equivalent mass method was used to obtain preliminary relevant parameters of the vibration reduction structure; Dispersion analysis was performed on the preliminary relevant parameters to obtain the first vibration attenuation frequency band; Based on the first vibration attenuation frequency band and the preset vibration attenuation frequency band, the preliminary relevant parameters of the vibration reduction structure are optimized to obtain the optimized relevant parameters. The preliminary and optimized related parameters both include the equivalent stiffness of the core unit and the mass of the oscillator. The optimized related parameters are subjected to dispersion analysis to obtain the second vibration attenuation frequency band. The difference between the second vibration attenuation frequency band and the preset vibration attenuation frequency band meets the preset error requirements.

[0009] Compared with the prior art, the beneficial effects of this application are as follows: In the design method of the vibration reduction structure based on lattice metamaterials provided by this invention, the relevant parameters of the vibration reduction structure provided in the first aspect are optimized so that the difference between the second vibration attenuation frequency band obtained by dispersion analysis of the optimized relevant parameters and the preset vibration attenuation frequency band meets the preset error requirement. At this time, the vibration reduction effect of the vibration reduction structure on the pipeline can be further improved. Attached Figure Description

[0010] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the vibration reduction structure based on lattice metamaterials before assembly in an embodiment of the present invention; Figure 2 As described in the embodiments of the present invention Figure 1 Partial structural diagram; Figure 3This is a schematic diagram of the vibration reduction structure based on lattice metamaterials and the assembled pipeline structure in an embodiment of the present invention; Figure 4 As described in the embodiments of the present invention Figure 3 The right view; Figure 5 As described in the embodiments of the present invention Figure 3 The front view; Figure 6 This is a flowchart illustrating the design method of a vibration reduction structure based on lattice metamaterials in an embodiment of the present invention. Figure 7 This is a schematic diagram of the theoretical model of the pipeline in an embodiment of the present invention; Figure 8 This is a comparison chart of the bandgap effects obtained by simulation dispersion analysis and theoretically derived dispersion relationships in embodiments of the present invention; Figure 9 This is a schematic diagram showing the frequencies and corresponding vibration modes of the upper and lower limits of the bending wave bandgap in an embodiment of the present invention; Figure 10 This is a comparison diagram of the sinusoidal vibration test acceleration response before and after installing three vibration damping structures on the pipeline in this embodiment of the invention; Figure 11 This is a comparison diagram of the acceleration response of a narrow-band random vibration test before and after the installation of the vibration damping structure in the pipeline, as shown in this embodiment of the invention. Figure 12 This is a comparison diagram of the acceleration response of a broadband random vibration test before and after the installation of the vibration reduction structure in the pipeline, as shown in this embodiment of the invention.

[0011] Figure label: 1-Vibration damping component, 10-First panel, 11-Second panel, 12-Damping layer, 13-Core unit, 130-Core, 131-First part, 132-Second part, 14-Screw; 2-Pipeline, 3-Vibration damping structure. Detailed Implementation

[0012] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0013] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0014] In this invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can represent: a, b, c, a combination of a and b, a combination of a and c, a combination of b and c, or a, b, and c, where a, b, and c can be single or multiple.

[0015] In conjunction with the background technology section, current technologies for enhancing the vibration resistance of engine piping structures in engine engineering applications include the following approaches: First, increasing the strength margin of the piping structure, such as replacing materials with better performance. Second, altering the spatial orientation or topological configuration of the piping structure, thereby changing its natural frequency. Third, installing dynamic vibration absorbers outside the piping. These methods either increase the structural mass, severely affecting the engine's thrust-to-weight ratio; or increase the manufacturing process or cost, impacting the product's cost-effectiveness; or alter the original structural form, potentially leading to re-coupling with other components of the complex power system; or result in a narrow vibration reduction frequency band, making engineering applications more challenging.

[0016] Furthermore, some systems currently employ solid sheathing structures for pipeline vibration reduction. However, these solid sheathing structures have a large mass, significantly impacting the structural quality of the aircraft. Alternatively, lattice structures can be used for pipeline vibration reduction, but this is only suitable for suppressing the vibration transmission of block structures themselves and is difficult to apply to the vibration reduction of other pipeline structures. Another option is to use a double-layer pyramid-shaped lightweight vibration-damping metamaterial lattice structure for pipeline vibration reduction, but this is mainly used for the vibration reduction of flat plate structures and is also insufficient for reducing the vibration of pipeline structures.

[0017] To address at least some of the aforementioned technical problems, in a first aspect, the present invention provides a vibration reduction structure based on lattice metamaterials. See also... Figures 1 to 3The vibration damping structure based on lattice metamaterials includes at least two vibration damping components 1. Each vibration damping component 1 includes a first panel 10, a second panel 11, a damping layer 12, and multiple core units 13. The second panel 11 is opposite to and spaced apart from the first panel 10, and the two ends of the core unit 13 are respectively connected to the first panel 10 and the second panel 11. The core unit 13 includes at least four cores 130, which are arranged to form a three-dimensional hollow body. The damping layer 12 is disposed on the side of the second panel 11 facing away from the first panel 10. The first panels 10 included in the multiple vibration damping components 1 are sequentially fixedly connected end to end to form a first annular member, and the second panels 11 included in the multiple vibration damping components 1 are arranged to form a second annular member, which is located inside the first annular member.

[0018] Compared with the prior art, the beneficial effects of this application are as follows: See Figures 1 to 3 In the vibration damping structure based on lattice metamaterials provided by this invention, during actual use, the vibration damping structure 3 is sleeved on the outer wall of the pipe 2, and the inner wall of the second annular member abuts against the outer wall of the pipe 2. When the pipe 2 vibrates, the vibration damping structure 3 generates a force opposite to the vibration direction of the pipe 2, and the vibration damping structure 3 can generate a wide bandwidth, thereby suppressing or weakening the vibration of the pipe 2. It should be noted that the specific design parameters of the above-mentioned vibration damping structure are designed according to the pipe to be damped, and are not specifically limited here.

[0019] As one possible implementation, see Figure 1 and Figure 2 The first ends of multiple cores 130 are all connected to the first panel 10, and the second ends of multiple cores 130 are all connected to the second panel 11. The first ends of all cores 130 included in each core unit 13 abut against each other, and the second ends of all cores 130 included in each core unit 13 abut against each other.

[0020] The aforementioned multiple cores 130 are assembled to form a skeleton structure. Each core unit 13 can be considered equivalent to an elastic element, and the core unit has a certain stiffness.

[0021] In one alternative approach, see Figure 1 and Figure 2 The core 130 includes a first part 131 and a second part 132. A first end of the first part 131 is connected to a first panel 10, a second end of the first part 131 is connected to a first end of the second part 132, and a second end of the second part 132 is connected to a second panel 11. The first part 131 and the second part 132 are not on the same straight line. The same core unit 13 includes multiple intersection points of the first part 131 and the second part 132, and these intersection points are coplanar.

[0022] For example, each core unit 13 includes four cores 130, and the intersection of the four cores 130 is located on the same circumference.

[0023] There is an angle between the first part and the second part mentioned above, which is neither equal to 180° nor 360°.

[0024] As one possible implementation, see Figures 1 to 3 The aforementioned multiple first panels 10 can be fixedly connected by screws 14 or glued together. In this application, the first panels 10 included in the multiple vibration damping components 1 are connected end to end in sequence and fixed by screws 14 to form a first annular member. The screws 14 can be made of steel and are constraint screws.

[0025] The number and shape of the first and second panels mentioned above are not specifically limited here, as long as they can meet the actual needs.

[0026] For example, the vibration damping structure 3 includes two vibration damping components 1, each vibration damping component 1 including a first panel 10 and a second panel 11. The two first panels 10 together form a ring shape, and the two second panels 11 together form a ring shape.

[0027] As one possible implementation, the first panel has an elastic modulus of 3 GPa to 3.5 GPa, a Poisson's ratio of 0.3 to 0.4, and a density of 1200 kg / m³. 3 Up to 1400 kg / m 3 The first panel is made of lightweight and tough nylon, and its melting point is 280°C to 320°C.

[0028] For example, the elastic modulus of the first panel can be 3 GPa, 3.1 GPa, 3.2 GPa, 3.3 GPa, 3.4 GPa, 3.45 GPa, or 3.5 GPa, etc. The Poisson's ratio can be 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, or 0.4, etc. The density can be 1200 kg / m³. 3 1250kg / m 3 1280kg / m 3 1300kg / m 3 1350kg / m 3 1380kg / m 3 Or 1400 kg / m 3 The melting point of the first panel can be 280℃, 285℃, 290℃, 295℃, 300℃, 305℃, 310℃, 315℃, or 320℃, etc.

[0029] The second panel has an elastic modulus of 3 GPa to 3.5 GPa, a Poisson's ratio of 0.3 to 0.4, and a density of 1200 kg / m³. 3Up to 1400 kg / m 3 The second panel is made of lightweight, tough nylon, with a melting point of 280°C to 320°C. The thickness of the second panel is t. in It is 1mm.

[0030] For example, the elastic modulus of the second panel can be 3 GPa, 3.1 GPa, 3.2 GPa, 3.3 GPa, 3.4 GPa, 3.45 GPa, or 3.5 GPa, etc. The Poisson's ratio can be 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, or 0.4, etc. The density can be 1200 kg / m³. 3 1250kg / m 3 1280kg / m 3 1300kg / m 3 1350kg / m 3 1380kg / m 3 Or 1400 kg / m 3 The melting point of the second panel can be 280℃, 285℃, 290℃, 295℃, 300℃, 305℃, 310℃, 315℃, or 320℃, etc.

[0031] The core unit has an elastic modulus of 3 GPa to 3.5 GPa, a Poisson's ratio of 0.3 to 0.4, and a density of 1200 kg / m³. 3 Up to 1400 kg / m 3 The core unit is made of lightweight and tough nylon, and its melting point is 280°C to 320°C.

[0032] For example, the elastic modulus of the core unit can be 3 GPa, 3.1 GPa, 3.2 GPa, 3.3 GPa, 3.4 GPa, 3.45 GPa, or 3.5 GPa, etc. The Poisson's ratio can be 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, or 0.4, etc. The density can be 1200 kg / m³. 3 1250kg / m 3 1280kg / m 3 1300kg / m 3 1350kg / m 3 1380kg / m 3 Or 1400 kg / m 3 The melting point of the core unit can be 280℃, 285℃, 290℃, 295℃, 300℃, 305℃, 310℃, 315℃ or 320℃, etc.

[0033] The damping layer has an elastic modulus of 3 GPa to 4 GPa, a Poisson's ratio of 0.3 to 0.4, and a density of 1380 kg / m³. 3 Up to 1430kg / m 3 The damping layer is made of polyimide polymer. The thickness of the damping layer is 0.2 mm.

[0034] For example, the elastic modulus of the damping layer can be 3 GPa, 3.1 GPa, 3.2 GPa, 3.3 GPa, 3.4 GPa, 3.45 GPa, 3.5 GPa, 3.6 GPa, 3.7 GPa, 3.8 GPa, 3.9 GPa, or 4 GPa, etc. The Poisson's ratio can be 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, or 0.4, etc. The density can be 1380 kg / m³. 3 1390kg / m 3 1400kg / m 3 1410kg / m 3 1420kg / m 3 1425kg / m 3 Or 1430kg / m 3 wait.

[0035] It should be noted that the relevant parameters of the first panel, the second panel, and the core unit mentioned above may or may not be equal. No specific restrictions are imposed here, and they can be set according to the actual situation.

[0036] The length L0 of the vibration damping structure is 4.9 mm.

[0037] As one possible implementation, vibration-damping structures are fabricated using additive manufacturing techniques. For example, vibration-damping structures are fabricated using selective laser sintering (SLS).

[0038] In summary, the vibration damping structure in this application is based on a body-centered cubic lattice structure design. This structure offers numerous advantages, including lightweight construction, a wide vibration damping frequency band, ease of installation and manufacturing, preservation of the original pipeline geometry, a wide range of adjustable parameters, and simple adjustment methods. Therefore, it can meet the engineering application requirements of liquid rocket engine structures. Specifically, the vibration damping structure in this application primarily targets the suppression of bending vibrations in the pipeline.

[0039] Secondly, embodiments of the present invention also provide a design method for vibration reduction structures based on lattice metamaterials. See [link to related document]. Figures 1 to 7 The design method for vibration reduction structures based on lattice metamaterials is used to design the vibration reduction structures based on lattice metamaterials described above. The vibration reduction structure is sleeved on the outer wall of the pipeline. The first panels of multiple vibration reduction components are connected end to end in sequence and fixed with screws to form a first annular member. The first panels and screws are equivalent to oscillators.

[0040] Please see Figure 6 , Figure 6 This is a flowchart illustrating the design method of a vibration reduction structure based on lattice metamaterials in an embodiment of the present invention. The executing entity is a terminal device equipped with the embodiments disclosed in this specification. For example, the terminal device may be a tablet computer or a PDA, etc.

[0041] Design methods for vibration reduction structures based on lattice metamaterials include: Step 101: Based on the vibration frequency response characteristics of the pipeline to be vibration-damped, determine the amplitude and / or frequency band of the pipeline that needs vibration reduction. As one possible approach, before determining the amplitude and / or frequency band requiring vibration reduction based on the vibration frequency response characteristics of the pipeline to be reduced, the design method for vibration reduction structures based on lattice metamaterials includes: Step S1: Obtain the propagation of the bending wave in the pipeline to be vibration-damped; Step S2: Determine the vibration frequency response characteristics of the pipeline to be vibration-damped based on the propagation of the bending wave.

[0042] In one alternative approach, step S2: determining the vibration frequency response characteristics of the pipeline to be vibration-damped based on the propagation of the bending wave includes: Step S2.1: Equivalently represent the pipeline as a Timoshenko beam to obtain the vibration control equation of the pipeline; the specific method of equivalence can be found in the prior art, and will not be described in detail here.

[0043] The vibration control equation for the pipeline is (defined as Equation 1 for ease of subsequent description): in, ; ; ; ; This indicates the Young's modulus of the pipeline; Indicates the j-th segment of the pipeline; Indicates the lateral displacement of the pipeline. Let represent the x-coordinate of the j-th pipe segment, t represent time, and μ represent the Poisson's ratio of the material used to manufacture the pipe. Indicates the density of the pipeline; This indicates the shear modulus of the material used to make the pipes. The shear coefficient of the Timoshenko beam is represented by ; S represents the radial cross-sectional area of ​​the pipeline. The moment of inertia of the pipeline section; Indicates the outer diameter length of the pipe. Indicates the inner diameter length of the pipe; It is a mathematical symbol.

[0044] Step S2.2: Based on the vibration control equation of the pipeline, the lateral displacement of the pipeline is determined; Based on the vibration control equation of the pipeline, the lateral displacement of the pipeline is determined by the following formula: in, Indicates the j-th segment of the pipeline; Indicates the lateral displacement of the pipeline. Let represent the x-coordinate of the j-th pipeline segment, t represent time, and i represent the imaginary unit. Indicates the vibration frequency. The modal shape function represents the pipeline.

[0045] Step S2.3: Based on the lateral displacement of the pipeline, determine the modal shape function of the pipeline; Based on the lateral displacement of the pipeline, the modal shape function of the pipeline is determined by the following formula (for ease of subsequent description, it is defined as Formula 2): in, The modal shape function of the pipeline is represented by i, which represents the imaginary unit. Represents the undetermined coefficients (n=1,2,3,4); k n Indicates the number of the first wave. Represents the x-coordinate of the j-th pipeline segment; When no vibration damping structure is installed on the Timoshenko beam, the first wave number can be determined based on the boundary conditions of the Timoshenko beam under free boundary conditions. in, , ; ; Indicates the density of the pipeline; The value represents the vibration frequency, and E represents the Young's modulus of the pipeline. This indicates the shear modulus of the material used to make the pipes. denoted by , μ represents the shear coefficient of the Timoshenko beam; μ represents the Poisson's ratio of the material used to manufacture the pipe; and S represents the radial cross-sectional area of ​​the pipe. This represents the moment of inertia of the pipeline section. For ease of subsequent description, this will be used to determine the first wave number. The formula is defined as Formula 3.

[0046] Step S2.4: Obtain the vibration frequency response characteristics of the pipeline based on the modal shape function and the first wave number under the boundary conditions. Note that for details on how to obtain the vibration frequency response characteristics of the pipeline based on the modal shape function and the first wave number under the boundary conditions in step S2.4, please refer to the prior art, which will not be described in detail here.

[0047] The boundary conditions are: the boundary conditions of the Timoshenko beam under the free boundary when no vibration damping structure is installed on the Timoshenko beam.

[0048] Step 102: Determine the preset vibration attenuation frequency band of the vibration reduction structure according to the amplitude and / or frequency band of the pipeline that needs to be reduced, so that the amplitude and / or frequency band of the pipeline that needs to be reduced are located in the central area of ​​the preset vibration attenuation frequency band. For example, if the amplitude and / or frequency band of the pipeline that needs vibration reduction is 5, then the value of the center region of the preset vibration attenuation frequency band is 5. In this case, the preset vibration attenuation frequency band can be 2-8, or 1 to 9, etc. This part can be set according to the actual situation and is not limited to the above description.

[0049] Furthermore, the frequency bands with larger pipeline amplitudes or those requiring vibration reduction should be contained within the central area of ​​the preset vibration attenuation frequency band as much as possible.

[0050] Step 103: Use the equivalent mass method to obtain preliminary relevant parameters of the vibration reduction structure; As one possible implementation, multiple core units are represented as equivalent springs. The pipeline is divided into multiple segments along its length, and a vibration-damping structure is fitted onto the outer wall of the j-th segment. For ease of understanding... Figure 7 The diagram shows the (j-1)th, jth, and (j+1)th pipe segments. This represents the x-coordinate of the j-th pipe segment. This represents the ordinate of the j-th pipeline segment.

[0051] The equivalent mass method is used to obtain preliminary relevant parameters of the vibration reduction structure, including the following formula (defined as Formula 4 for ease of subsequent description): in, , Indicates the mass of the initial oscillator; Indicates the displacement of the initial oscillator; This represents time, and 'i' represents the imaginary unit. Indicates the vibration frequency. This represents the equivalent stiffness of the initial core element. This represents the length of the j-th pipe segment; This represents the displacement at the end of the j-th pipe segment. It should be noted that the preliminary relevant parameters include the displacement of the preliminary oscillator and the equivalent stiffness of the preliminary core element.

[0052] Combining formulas one through four, we obtain formula five: in, Indicates the vibration frequency. This represents the equivalent stiffness of the initial core element. This indicates the mass of the initial oscillator. This indicates the initial displacement amplitude of the oscillator. This represents the value of the modal shape function of the pipeline at the installation point.

[0053] Step 104: Perform dispersion analysis on the preliminary relevant parameters to obtain the first vibration attenuation frequency band; As one possible approach, dispersion analysis is performed on preliminary relevant parameters to obtain the first vibration attenuation frequency band, including: Step 104.1: Perform dispersion analysis on the preliminary correlation parameters to obtain the second wavenumber. ; Step 104.1 uses the following formula: ; in, Indicates the j-th segment of the pipeline. Indicates the first Pipeline section; This represents the bending moment of the j-th pipe segment. This represents the bending moment of the (j+1)th pipe segment. This represents the force in the j-th pipe segment. This represents the force in the (j+1)th segment of the pipeline. Indicates time, It is a mathematical symbol. Indicates the displacement of the initial oscillator; This represents the displacement of the j-th pipe segment. This represents the displacement of the (j+1)th pipe segment. This represents the angle of the j-th pipe segment. This indicates the angle of the (j+1)th segment of the pipeline; Let j represent the length of the j-th pipe segment; for ease of subsequent description, the above formula is defined as Formula Six.

[0054] Combining formulas two through six, we can obtain... ; in, , ; ; ; ; in, Represents the transfer matrix. It is a symbol for matrix operations. This represents the length of the j-th pipe segment; Indicates the second wave number; This represents the coefficients to be determined (n=1,2,3,4); Represents the undetermined coefficients (n=1,2,3,4); k n Indicates the first wave number; Represents the identity matrix.

[0055] Step 104.2: Based on the second wave number to learn about the second wave Corresponding vibration frequency ; Step 104.2 uses the following formula: =0; When the second wave When it is a complex number, it is related to the second wave number. Corresponding vibration frequency Here, H represents the bandgap frequency in the first vibration attenuation band; it should be noted that since H and K in the above formula depend on the first wavenumber, and the first wavenumber and... Therefore, based on the above formula, the second wave number can be obtained. Corresponding vibration frequency .

[0056] Step 104.3: Based on multiple second wave numbers that are complex numbers Corresponding vibration frequency Thus, the first vibration attenuation frequency band was determined.

[0057] Step 105: Optimize the preliminary relevant parameters of the vibration reduction structure based on the first vibration attenuation frequency band and the preset vibration attenuation frequency band to obtain the optimized relevant parameters; Step 105 includes: If the lower limit frequency in the first vibration attenuation frequency band is greater than the upper limit frequency or lower limit frequency in the preset vibration attenuation frequency band, then increase the mass of the oscillator or decrease the equivalent stiffness of the core unit to obtain the optimized relevant parameters. If the upper limit frequency in the first vibration attenuation frequency band is less than the upper limit frequency or lower limit frequency in the preset vibration attenuation frequency band, then the mass of the oscillator is reduced or the equivalent stiffness of the core unit is increased to obtain the optimized relevant parameters.

[0058] For example, in the actual design process, dispersion analysis is performed on the adjusted relevant parameters, and the process is iterated repeatedly until the final optimized relevant parameters are obtained. At this point, dispersion analysis is performed on the optimized relevant parameters to obtain the second vibration attenuation frequency band, and the difference between the second vibration attenuation frequency band and the preset vibration attenuation frequency band meets the preset error requirement.

[0059] The preliminary and optimized parameters both include the equivalent stiffness of the core element and the mass of the oscillator.

[0060] Compared with the prior art, the beneficial effects of this application are as follows: In the design method of the vibration reduction structure based on lattice metamaterials provided in the embodiments of the present invention, by optimizing the relevant parameters of the vibration reduction structure provided in the first aspect, the difference between the second vibration attenuation frequency band obtained by the dispersion analysis of the optimized relevant parameters and the preset vibration attenuation frequency band meets the preset error requirements. At this time, the vibration reduction effect of the vibration reduction structure on the pipeline can be further improved. Furthermore, the above-mentioned vibration reduction structure has good practicality and reliability. The vibration reduction structure can be printed with high precision through additive manufacturing technology (such as selective laser sintering technology). Theoretical, experimental and simulation analysis studies show that the designed vibration reduction structure can produce good elastic wave suppression effect in the designed frequency band. In addition, the vibration reduction structure has the advantages of easy installation and simple use. Compared with traditional dynamic vibration absorbers and vibration isolation metastructures, the designed vibration reduction structure is made of a single material and uses simple screw and adhesive connection methods, reducing the cumbersome manufacturing process and installation method brought about by traditional multi-material preparation methods, so the reliability is also higher. Moreover, the structural mass of the vibration reduction structure is small, and its equivalent density is less than 1g / cm³. 3 .

[0061] As one possible approach, the correlation frequency of the vibration attenuation band is related to the local resonance of the vibration damping structure. For a pipeline, the amplitude of vibration attenuation can be adjusted by changing the number of vibration damping structures, the spacing between them, and the material of the damping layer within the structure.

[0062] In this application, an equivalent mass method is used to approximately obtain a vibration attenuation frequency band, while a dispersion analysis method can be used to obtain a vibration attenuation frequency band more accurately.

[0063] When using the equivalent mass method, the equivalent mass can be obtained in the equivalent mass model through theoretical or simulation methods. The vibration damping structure is equivalent to a mass spring model, and the frequency range corresponding to a negative equivalent mass of the vibration damping structure is calculated. Within this frequency range, when the pipeline vibrates, the vibration damping structure generates a force opposite to the direction of pipeline vibration, thereby suppressing the vibration amplitude of the pipeline.

[0064] When using the dispersion analysis method, Bloch boundary conditions are set at both ends of the pipeline in the dispersion analysis model, and the second wave number q is... The band is swept to calculate the characteristic frequencies corresponding to different second wave numbers q. When the second wave number q has a real solution, the corresponding vibration frequency is the frequency band where the vibration wave can propagate. When the second wave number q has no real solution, the corresponding vibration frequency is the frequency band where the vibration wave cannot propagate, i.e., the vibration attenuation band. Furthermore, a simplified theoretical calculation can be used to determine the characteristic frequencies corresponding to different second wave numbers q. When the corresponding vibration frequency is calculated, it is the upper limit of the vibration attenuation frequency band. When the second wave number When the vibration frequency is calculated, the lower limit of the vibration attenuation frequency band is determined. The vibration attenuation frequency band is thus obtained.

[0065] The following description uses one possible scenario as an example. It should be noted that the following description is for understanding purposes only and is not intended to limit the specific situation.

[0066] The dimensions of the above-mentioned pipeline are: outer diameter r of the pipeline out It is 28 mm thick, and the wall thickness is t. p The diameter is 1.5mm, and the inner diameter of the pipe is r. p r out =r p +t p The pipeline is made of 45 steel, with a Young's modulus of E = 170 GPa, a Poisson's ratio of μ = 0.3, and a density of ρ = 7850 kg / m³. 3 The resonant frequency of the pipeline is around 1110 Hz (i.e., the frequency band requiring vibration reduction is around 1110 Hz). Based on the design parameters, the core diameter d0 is set to 1 mm, and the thickness t of the first panel is... out The thickness of the second panel is 5mm. in When the shortest straight-line distance h between the first and second panels is 20mm, the length L0 of the vibration damping structure is 10mm, and the length L of the j-th pipe segment is 20mm, the dispersion relationship obtained through simulation dispersion analysis (finite element software calculation) and theoretical derivation (i.e., dispersion analysis method) is compared. The comparison results are as follows: Figure 8 As shown. It should be noted that the above parameters are related to the equivalent stiffness of the core element and the mass of the oscillator. The equivalent stiffness of the core element and the mass of the oscillator can be calculated from these parameters. For example, finite element software can be used to calculate... , g.

[0067] Depend on Figure 8It can be seen that the theoretical bandgap frequency obtained through theoretical derivation is 1057-1585Hz. The theoretical bandgap obtained from the simulation dispersion analysis and the theoretical derivation are in good agreement with the simulated bandgap, indicating that the bandgap frequency and dispersion relationship are basically consistent, verifying the accuracy of the theoretical model. The theoretically calculated bandgap width is slightly smaller than the simulation result, which may be due to the inaccuracy of the spring-lumped mass model used in the theoretical calculation. In addition, at the lower boundary of the bandgap frequency (around 1057Hz), the second wavenumber increases rapidly. Figure 9 This is a schematic diagram showing the frequencies and corresponding vibration modes of the upper and lower limits of the flexural wave bandgap, where, Figure 9 The lower boundary frequency of the bandgap corresponding to figure (1) is 1082 Hz. Figure 9 The upper boundary frequency of the bandgap in the diagram corresponding to (2) is 1536 Hz. Figure 9 It can be seen that at the upper and lower frequency limits, the vibration damping structure generates a reaction force in the direction of the pipeline's vibration displacement, thereby achieving the effect of vibration suppression. Figure 10 This is a comparison diagram of the acceleration response of a sinusoidal vibration test before and after installing three vibration damping structures on the pipeline in an embodiment of the present invention. Figure 10 It can be seen that after the vibration damping structure was installed on the pipeline, the peak vibration acceleration of the pipeline joint was 25.22 g, corresponding to a frequency of 918 Hz. Comparing the joint vibration response before and after the installation of the vibration damping structure, the peak vibration value decreased significantly by 78.2%, and the corresponding peak frequency decreased by 195 Hz. If we compare the change in vibration acceleration amplitude at the original pipeline's resonant frequency, the amplitude at 1113 Hz after the installation of the vibration damping structure was only 4.6 g, a decrease of 96% compared to the pipeline without the structure. Furthermore, before the installation of the vibration damping structure, the pipeline without it had only one relatively high resonant peak, while after the installation, multiple peaks appeared in the frequency range near that resonant peak, but the amplitudes of these multiple peaks were significantly reduced compared to the pipeline without the structure.

[0068] To further investigate the effects of installing vibration damping structures on the vibration acceleration response and energy distribution in the pipeline, a narrowband random vibration test was conducted with the peak frequency as the center frequency and a bandwidth of 100 Hz. The random vibration test conditions were: root mean square vibration acceleration of 3g and excitation time of 5 min. Figure 11 This is a comparison of the acceleration response of a narrowband random vibration test before and after installing a vibration damping structure on a pipeline in this frequency band (e.g., with the peak frequency as the center frequency, a bandwidth of 100Hz, and the frequency band approximately 1063Hz to 1163Hz). Figure 11As can be seen, compared with the pipeline without vibration damping structure, the peak power spectral density decreased by 97.6% and the root mean square (RMS) value of vibration acceleration decreased by 80.97% after the vibration damping structure was installed. Therefore, the effectiveness of the designed vibration damping structure was also verified through narrowband random vibration tests.

[0069] To gain a more comprehensive understanding of the vibration energy distribution at pipe joints before and after the installation of vibration damping structures, a broadband random vibration test was conducted. The frequency range was 5-3000Hz, the root mean square value of the vibration acceleration was 6g, and the excitation time was 5min. Figure 12 This is a comparison diagram of the acceleration response of a broadband random vibration test before and after the installation of the vibration damping structure in the pipeline, as shown in this embodiment of the invention. Figure 12 It can be seen that the peak power spectral density before the vibration damping structure was installed on the pipeline was 305.98g. 2 / Hz, RMS value 68.52g. After installing the vibration damping structure on the pipeline, the peak power spectral density was 10.62g² / Hz, and the RMS value was 21.11g. Compared with the pipeline without the vibration damping structure, the peak power spectral density decreased by 96.5%, and the RMS value decreased by 69.2%. Comparing the random vibration frequency response curves before and after the installation of the vibration damping structure, it can be seen that without the vibration damping structure, there is only one resonance peak near the peak frequency, and the energy is mainly concentrated in this frequency band. After the installation of the vibration damping structure, three obvious peaks appear in this frequency band, dispersing the energy. In addition, the curve without the vibration damping structure is relatively smooth, while multiple spikes appear after the installation of the vibration damping structure. In other frequency bands, it fluctuates around the curve without the vibration damping structure, and no obvious vibration amplification phenomenon is observed.

[0070] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely exemplary descriptions of the invention as defined by the appended claims, and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A vibration reduction structure based on lattice metamaterials, characterized in that, include: At least two vibration damping components; Each of the vibration damping components includes: First panel; The second panel is positioned opposite to and spaced apart from the first panel; Multiple core units, each core unit having its two ends connected to the first panel and the second panel respectively; each core unit includes at least four cores, which together form a three-dimensional hollow body; A damping layer is disposed on the side of the second panel opposite to the first panel; The first panels of the plurality of vibration damping components are sequentially fixedly connected end to end to form a first annular member, and the second panels of the plurality of vibration damping components are enclosed to form a second annular member; the second annular member is located inside the first annular member.

2. The vibration reduction structure based on lattice metamaterials according to claim 1, characterized in that, The first ends of the plurality of cores are all connected to the first panel, and the second ends of the plurality of cores are all connected to the second panel; The first ends of all the cores included in each said core unit abut against each other, and the second ends of all the cores included in each said core unit abut against each other.

3. The vibration reduction structure based on lattice metamaterials according to claim 2, characterized in that, The core includes a first part and a second part; a first end of the first part is connected to the first panel, a second end of the first part is connected to the first end of the second part, and a second end of the second part is connected to the second panel; the first part and the second part are not on the same straight line. The same core unit includes multiple intersection points of the first part and the second part, and the multiple intersection points are coplanar.

4. The vibration reduction structure based on lattice metamaterials according to claim 1, characterized in that, The first panel has an elastic modulus of 3 GPa to 3.5 GPa, a Poisson's ratio of 0.3 to 0.4, and a density of 1200 kg / m³. 3 Up to 1400 kg / m 3 The first panel is made of lightweight and tough nylon, and the melting point of the first panel is 280°C to 320°C. The second panel has an elastic modulus of 3 GPa to 3.5 GPa, a Poisson's ratio of 0.3 to 0.4, and a density of 1200 kg / m³. 3 Up to 1400 kg / m 3 The second panel is made of lightweight and tough nylon, and its melting point is 280°C to 320°C. The core unit has an elastic modulus of 3 GPa to 3.5 GPa, a Poisson's ratio of 0.3 to 0.4, and a density of 1200 kg / m³. 3 Up to 1400 kg / m 3 The core unit is made of lightweight and tough nylon, and the melting point of the core unit is 280°C to 320°C. The damping layer has an elastic modulus of 3 GPa to 4 GPa, a Poisson's ratio of 0.3 to 0.4, and a density of 1380 kg / m³. 3 Up to 1430kg / m 3 The damping layer is made of polyimide polymer material.

5. A design method for vibration reduction structures based on lattice metamaterials, characterized in that, Used to design a vibration reduction structure based on lattice metamaterials as described in any one of claims 1 to 4; the vibration reduction structure is sleeved on the outer wall of the pipeline; the first panels included in the plurality of vibration reduction components are connected end to end in sequence and fixed with screws to form a first annular member; The first panel and the screw are considered equivalent to oscillators; the design method of the vibration reduction structure based on lattice metamaterials includes: Based on the vibration frequency response characteristics of the pipeline to be vibration-damped, determine the amplitude and / or frequency band of the pipeline that needs vibration reduction. Based on the amplitude and / or frequency band of the pipeline that needs vibration reduction, a preset vibration attenuation frequency band of the vibration reduction structure is determined so that the amplitude and / or frequency band of the pipeline that needs vibration reduction are located in the central region of the preset vibration attenuation frequency band. The equivalent mass method is used to obtain the preliminary relevant parameters of the vibration reduction structure; Dispersion analysis is performed on the preliminary relevant parameters to obtain the first vibration attenuation frequency band; Based on the first vibration attenuation frequency band and the preset vibration attenuation frequency band, the preliminary relevant parameters of the vibration reduction structure are optimized to obtain the optimized relevant parameters. The preliminary and optimized related parameters both include the equivalent stiffness of the core unit and the mass of the oscillator; the optimized related parameters are subjected to dispersion analysis to obtain a second vibration attenuation frequency band, and the difference between the second vibration attenuation frequency band and the preset vibration attenuation frequency band meets the preset error requirement.

6. The design method for vibration reduction structures based on lattice metamaterials according to claim 5, characterized in that, Before determining the amplitude and / or frequency band requiring vibration reduction based on the vibration frequency response characteristics of the pipeline to be vibration-damped, the design method of the vibration reduction structure based on lattice metamaterials includes: Obtain information on the propagation of bending waves in the pipeline to be vibration-damped; Based on the propagation of the bending wave, the vibration frequency response characteristics of the pipeline to be vibration-damped are determined.

7. The design method for vibration reduction structures based on lattice metamaterials according to claim 6, characterized in that, Based on the propagation of the bending wave, the vibration frequency response characteristics of the pipeline to be vibration-damped are determined as follows: The pipeline is equivalent to a Timoshenko beam to obtain the vibration control equation of the pipeline; The lateral displacement of the pipeline is determined based on the vibration control equation of the pipeline. Based on the lateral displacement of the pipeline, the modal shape function of the pipeline can be obtained; The vibration frequency response characteristics of the pipeline are obtained based on the modal shape function and the first wave number under the boundary conditions. The boundary condition is defined as the boundary condition of the Timoshenko beam under the free boundary when the vibration damping structure is not installed on the Timoshenko beam.

8. The design method for vibration reduction structures based on lattice metamaterials according to claim 7, characterized in that, The vibration control equation for the pipeline is: in, ; ; ; ; This indicates the Young's modulus of the pipeline; Indicates the j-th segment of the pipeline; This indicates the lateral displacement of the pipeline. Let represent the x-coordinate of the j-th pipe segment, t represent time, and μ represent the Poisson's ratio of the material used to manufacture the pipe. This indicates the density of the pipeline; This indicates the shear modulus of the material used to manufacture the pipeline. The shear coefficient of the Timoshenko beam is represented by ; S represents the radial cross-sectional area of ​​the pipeline. The moment of inertia of the cross section of the pipeline is represented; This indicates the outer diameter length of the pipeline. This indicates the inner diameter length of the pipeline; According to the vibration control equation of the pipeline, the lateral displacement of the pipeline includes: Formula used: in, Indicates the j-th segment of the pipeline; This indicates the lateral displacement of the pipeline. Let represent the x-coordinate of the j-th pipeline segment, t represent time, and i represent the imaginary unit. Indicates the vibration frequency. Represents the modal shape function of the pipeline; Based on the lateral displacement of the pipeline, the modal shape functions of the pipeline are determined to include: Formula used: in, The modal shape function of the pipeline is represented by i, where i represents the imaginary unit. Represents the undetermined coefficients (n=1,2,3,4); k n Indicates the number of the first wave. Represents the x-coordinate of the j-th pipeline segment; When the vibration damping structure is not installed on the Timoshenko beam, the first wave number is obtained based on the boundary conditions of the Timoshenko beam under free boundary conditions. in, , ; ; This indicates the density of the pipeline; The frequency of vibration is represented by E, and the Young's modulus of the pipeline is represented by E. This indicates the shear modulus of the material used to manufacture the pipeline. The shear coefficient of the Timoshenko beam is represented by μ; the Poisson's ratio of the material used to manufacture the pipeline is represented by μ; and the radial cross-sectional area of ​​the pipeline is represented by S. This represents the moment of inertia of the cross section of the pipeline.

9. The design method for vibration reduction structures based on lattice metamaterials according to claim 8, characterized in that, The multiple core units are equivalent to springs; the pipeline is divided into multiple segments along its length; the vibration damping structure is sleeved on the outer wall of the j-th segment of the pipeline; The preliminary relevant parameters of the vibration reduction structure are obtained using the equivalent mass method, including: Formula used: in, , This indicates the mass of the oscillator initially described; This indicates the displacement of the oscillator as initially described; This represents time, and 'i' represents the imaginary unit. Indicates the vibration frequency. This represents the equivalent stiffness of the initially described core unit. This represents the length of the j-th pipe segment; This represents the displacement at the end of the j-th pipeline segment; Dispersion analysis is performed on the preliminary correlation parameters to obtain the first vibration attenuation frequency band, including: Dispersion analysis was performed on the preliminary correlation parameters to obtain the second wavenumber. ; According to the second wave number to know the second wave number Corresponding vibration frequency ; When the second wave number When it is a complex number, it is related to the second wave number. The corresponding vibration frequency The bandgap frequency in the first vibration attenuation frequency band; Based on multiple second wave numbers that are complex The corresponding vibration frequency The first vibration attenuation frequency band is known; Dispersion analysis was performed on the preliminary correlation parameters to obtain the second wavenumber. include: Formula used: ； in, Indicates the j-th segment of the pipeline. Indicates the first Pipeline section; This represents the bending moment of the j-th pipe segment. This represents the bending moment of the (j+1)th pipe segment. This represents the force in the j-th pipe segment. This represents the force in the (j+1)th segment of the pipeline. Indicates time, This indicates the displacement of the oscillator as initially described; This represents the displacement of the j-th pipe segment. This represents the displacement of the (j+1)th pipe segment. Indicates the angle of the j-th pipe segment. This indicates the angle of the (j+1)th segment of the pipeline; This represents the length of the j-th pipe segment; formula: ； And the formula: ； in, Represents the transfer matrix. This represents the length of the j-th pipe segment; This indicates the second wave number.

10. The design method for vibration reduction structures based on lattice metamaterials according to claim 5, characterized in that, Based on the first vibration attenuation frequency band and the preset vibration attenuation frequency band, the preliminary relevant parameters of the vibration reduction structure are optimized to obtain the optimized relevant parameters, including: If the lower limit frequency in the first vibration attenuation frequency band is greater than the upper limit frequency or lower limit frequency in the preset vibration attenuation frequency band, then the mass of the oscillator is increased or the equivalent stiffness of the core unit is decreased to obtain the optimized relevant parameters. If the upper limit frequency in the first vibration attenuation frequency band is less than the upper limit frequency or lower limit frequency in the preset vibration attenuation frequency band, then the mass of the oscillator is reduced or the equivalent stiffness of the core unit is increased to obtain the optimized relevant parameters.

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