Lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration reduction and design method thereof

Abstract

The invention discloses a lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration reduction and a design method thereof, and belongs to the technical field of low-frequency vibration reduction structures.The lattice structure is formed by a cell element array, and cell elements belong to a two-dimensional phonon crystal structure; each cell element comprises a scatterer, a coating layer and a connecting layer; the coating layer sleeves the middle position of the outer side of the scatterer, and the connecting layer sleeves the outer side of the coating layer; a local resonance band gap exists in the lattice structure, the effect of large-range frequency vibration reduction and suppression can be achieved by regulating and controlling the band gap, and compared with a traditional low-frequency vibration reduction structure, the lattice structure is lighter.

Description

Technical Field

[0001] The present invention belongs to the technical field of low-frequency vibration damping structures, and particularly relates to a lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping and a design method thereof. Background Art

[0002] In the aerospace field, key components such as precision instrument cabins, power system brackets, and lightweight load-bearing structures of aircraft and spaceborne equipment have long faced severe vibration environment challenges. Low-frequency vibration, due to its long wavelength, high energy, and easy resonance with structures, seriously threatens the stability of precision instruments and the service life of equipment, and may even cause catastrophic failures.

[0003] In advanced technology fields such as precision instruments and compact aerospace equipment, vibration damping structures often face the challenge of extreme space constraints, requiring vibration damping units to be integrated within a limited design space of millimeters or even sub-millimeters, forcing a significant reduction in the size of a single cell of the lattice structure (typical characteristic scale <10 mm). However, traditional vibration damping lattice design faces a fundamental contradiction: according to the elastic wave propagation theory, the starting frequency of the bandgap of the lattice structure is usually inversely proportional to the cell size - miniaturization of the cell will cause the bandgap to shift to higher frequencies, making it difficult to cover the low-frequency vibration range.

[0004] There are mainly two mechanisms for the formation of the bandgap: the Bragg scattering mechanism and the local resonance mechanism. When elastic waves propagate in this locally resonant phononic crystal, a low-frequency bandgap can also be obtained when the cell size is small, achieving small-size control of large wavelengths. The construction of traditional low-frequency local resonance structures generally uses relatively dense precious metals such as gold, lead, and tungsten as scatterers, and materials with relatively small elastic moduli such as rubber as the coating structure. The softer material forms a coating structure around the relatively dense scatterer structure and is periodically embedded in the matrix material to form a local resonance structure, which has significant low-frequency bandgap characteristics. However, to obtain a high-quality local resonance bandgap, the density of the scatterer should be as large as possible, but using materials with a large density for the scatterer structure of the lattice structure will greatly increase the weight of the lattice structure, which is contrary to the lightweight characteristic. In addition, for low-frequency vibration damping, the stiffness needs to be further reduced to match the natural frequency of the system, and the structural optimization method under multi-physical field coupling still needs to be further studied to balance lightweight and strength.

[0005] Therefore, there is an urgent need to innovate the lattice structure design to comprehensively improve low-frequency broadband vibration damping, multi-directional vibration damping and vibration suppression, and environmental tolerance on the basis of miniaturization and lightweight, so as to meet the stringent requirements of high-end aerospace equipment. Summary of the Invention

[0006] The present invention provides a lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping and its design method. There is a local resonance band gap in the structure. By regulating the band gap, the effect of vibration damping and vibration suppression in a wide range of frequencies can be achieved, and it is lighter than traditional low-frequency vibration damping structures.

[0007] To achieve the above objectives, the present invention adopts the following technical solutions: A lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping is formed by arranging unit cells in a circumferential array manner. The unit cells belong to a two-dimensional phononic crystal structure; a single unit cell includes: a scatterer, a coating layer, and a connecting layer; the coating layer is sleeved at the middle position outside the scatterer, and the connecting layer is sleeved outside the coating layer; the connecting layer is used for connecting adjacent unit cells. Preferably, the scatterer is cylindrical, and the coating layer is cylindrical; the connecting layer is circular, and there are small short plates around the outside for connecting with adjacent unit cells. The scatterer is made of a lightweight material, preferably aluminum; the coating layer is made of a silicone rubber material with oxidation resistance and corrosion resistance. The scatterer and the coating layer are fixedly connected using a special glue, and the coating layer and the connecting layer are fixedly connected by a card slot connection.

[0008] A design method for a lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping includes the following steps: S1: Determine the frequency range of the band gap and the size of the design space according to the usage scenario; the frequency range of the band gap needs to meet low-frequency broadband, and the design space of the lattice structure is an annular shape (inner diameter is 15 mm, outer diameter is 30 mm, and height is 15 mm).

[0009] S2: Based on the design of the lattice structure for traditional low-frequency vibration damping, select the basic unit cell structure and the materials of each part. The unit cell structure belongs to a local resonance structure. Select a two-dimensional hollow scatterer lattice unit cell structure. Common choices for the hollow shape design of the scatterer include circular rings, square rings, hexagonal rings, etc. After calculation and comparison, the lower limit frequency of the first complete band gap of the circular ring is lower than that of other shapes.

[0010] S3: Select the materials of each part of the unit cell structure. The scatterer structure needs to select a metal material with a relatively large density (the unit cell structure needs to meet the lightweight condition, and here aluminum material is selected), the coating layer structure selects a material with a relatively small elastic modulus (here a silicone rubber material with oxidation resistance and corrosion resistance is selected), and the connecting layer structure selects a common 3D printing material (here an epoxy resin material is selected).

[0011] S4: Adjust the structure and size of the unit cell according to the required bandgap frequency range and the size of the design space. Since the design space is small and meets the lightweight requirement (the scatterer material is aluminum with a relatively low density), the bandgap generated by the unit cell structure is in a relatively high frequency band. Therefore, it is necessary to optimize and adjust the structure and size of the unit cell. The unit cell adopts a double-sided cylindrical connection plate structure (according to the influence law of the upper and lower limit frequencies and the width of the first complete bandgap by the single-sided and double-sided cylindrical connection plate structures, the double-sided cylindrical connection plate structure can enhance the coupling between the resonance mode and the Lamb wave compared with the single-sided cylindrical connection plate structure, and the generated bandgap frequency range is wider and the lower limit frequency is lower).

[0012] S5: Conduct parameter optimization and sensitivity analysis on the size of a single unit cell structure. There are a total of 11 size parameters for the unit cell structure. By performing single-parameter calculations for each parameter, it is determined that 7 size parameters are relatively sensitive to the bandgap frequency range. Refer to Figure 8 as the frequency variation diagram of the inner diameter r of the scatterer structure, and then perform response surface optimization on the sensitivity parameters to obtain the unit cell structure with a bandgap in the required frequency range.

[0013] The above lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping can be used for low-frequency broadband vibration damping and isolation in a micro space.

[0014] Beneficial effects: The present invention provides a lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping and its design method. The lattice structure is formed by an array of unit cells. A single unit cell includes a scatterer, a coating layer, and a connection layer. The scatterer uses a relatively lightweight aluminum material, and the coating layer structure uses a silicone rubber material with oxidation resistance and corrosion resistance. The unit cell structure adopts a double-sided cylindrical connection plate structure to enhance the coupling between the resonance mode and the Lamb wave (Lamb wave), and the generated bandgap frequency range is wider and the lower limit frequency is lower. After optimizing and adjusting the size parameters of the unit cell structure, compared with the unit cell structure without size optimization, the lower limit cut-off frequency of the generated bandgap is greatly reduced, and the bandgap width also increases to a certain extent, thus meeting the requirements of low-frequency broadband vibration damping and suppression, small design space, and lightweight. Description of the Drawings

[0015] Figure 1 is the overall view of the unit cell structure of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention.

[0016] Figure 2 is the top view of the unit cell structure of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention.

[0017] Figure 3 is the front view of the unit cell structure of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention.

[0018] Figure 4 It is the sectional view of the unit cell structure of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention.

[0019] Figure 5 It is the energy band structure diagram of the unit cell structure of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention.

[0020] Figure 6 It is the array diagram of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention.

[0021] Figure 7 It is the circumferential array diagram of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention.

[0022] Figure 8 It is the frequency variation diagram of the inner diameter r of the scatterer structure of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention.

[0023] Figure 9 It is the energy band structure diagram of the unit cell structure of the single- and double-sided cylindrical connecting plate lattice structure in the embodiment of the present invention.

[0024] Figure 10 It is the vibration mode comparison of the single- and double-sided cylindrical connecting plate lattice structure in the embodiment of the present invention.

[0025] Figure 11 It is the vibration mode of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping in the embodiment of the present invention, where (a) is Figure 5 the vibration mode at point A on the upper edge of the first complete forbidden band in Figure 5 , (b) is Figure 5 the vibration mode at point B on the upper edge of the first complete forbidden band in Figure 5 , (c) is

[0026] Figure 12 the vibration mode at point C on the lower edge of the first complete forbidden band in

[0027] Figure 13 It is the vibration mode at point D on the upper edge of the first complete forbidden band in

[0028] Figure 14 It is the schematic diagram of the unit cell structure based on

[0029] In the figure: 1 - Scatterer structure; 2 - Connection plate; 3 - Coating layer structure; 4 - Card slot. Detailed implementation manner

[0030] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments: As Figure 6 shown in the design method of a lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping, specifically including the following steps: The first step: Determine the frequency range of the bandgap and the size of the design space according to the usage scenario; the frequency range of the bandgap needs to meet the requirements of low-frequency broadband, and the design space of the lattice structure is an annular shape (inner diameter is 15 mm, outer diameter is 30 mm, and height is 15 mm).

[0031] The second step: Based on the design of the lattice structure for traditional low-frequency vibration damping, select the basic unit cell structure and the materials of each part. The unit cell structure belongs to the local resonance structure. Select the two-dimensional hollow scatterer lattice unit cell structure (basic unit cell structure) as Figure 14 shown. The common choices for the hollow shape design of the scatterer include circular rings, square rings, regular hexagonal rings, etc. After calculation and comparison, under the condition of the same porosity, ensuring that the volume and mass of the middle scatterer are the same. As shown in Table 1, the lower limit frequency of the first complete bandgap of the circular ring is lower and the bandgap width is wider than that of other shapes.

[0032] Table 1 Influence of different hollow shapes of scatterers on the energy band structure Scatterer hollow shape Upper limit frequency of band gap (HZ) Lower limit frequency of band gap (HZ) Band gap width (HZ) Porosity (%) Circle 1831.3 633.3 1198 47.9 Regular hexagon 1968.1 821.86 1146.24 47.9 Square 1967.8 822 1145.8 47.9 The third step: Select the materials of each part of the unit cell structure. The scatterer structure needs to use a metal material with a relatively large density (the unit cell structure needs to meet the lightweight condition, and aluminum material is selected in this embodiment). The coating layer structure uses a material with a relatively small elastic modulus (silicone rubber material with oxidation resistance and corrosion resistance is selected in this embodiment). The connection layer structure uses a common 3D printing material (epoxy resin material is selected in this embodiment).

[0033] The fourth step: Adjust the structure and size of the unit cell according to the required bandgap frequency range and the size of the design space; since the design space is small and meets the lightweight requirement (aluminum with a relatively small density is selected for the scatterer material), the bandgap generated by the unit cell structure is in a relatively high frequency band. Therefore, it is necessary to optimize and adjust the structure and size of the unit cell.

[0034] As Figure 11As shown, the upper cut-off frequency (point A) of the first complete band gap is caused by the vibration of the cladding structure 3 and the connecting plate 2 of the unit cell, while the lower cut-off frequency (point B) of the first complete band gap is caused by the vibration of the hollow scatterer structure 1 and the cladding structure 3 of the unit cell. It can be seen that local resonance occurs to achieve the effect of vibration reduction and suppression. The vibration occurring at the edge of the lower limit frequency (point C) is caused by the torsion of the intermediate scatterer structure 1 and the cladding structure 3 together, and the vibration occurring at the edge of the upper limit frequency (point D) is similar to the vibration at point A and is caused by the vibration of the cladding structure 3 and the connecting plate 2 of the unit cell. As Figure 9 and Figure 10 shown, for the single-sided cylindrical connecting plate structure, the first complete band gap (the gray band in the figure) is narrower than that of the double-sided cylindrical connecting plate. This is due to the in-phase coupling effect. The in-phase vibration of the double-sided cylindrical connecting plate structure enhances the interaction with Lamb waves, and the "tensile-compressive" coupling mode ( Figure 9 the mode at point A in Figure 9 ) of the double-sided cylindrical connecting plate structure significantly enhances the vertical vibration. The symmetric vibration of the double-sided cylindrical connecting plate structure results in a larger in-plane displacement at the base surface (comparing the modes at points B and D in ), which expands the band gap. Therefore, the first complete band gap of the double-sided cylindrical connecting plate structure is wider than that of the single-sided cylindrical connecting plate structure. So, according to the influence rules of the upper and lower cut-off frequencies and the width of the first complete band gap on the single-sided and double-sided cylindrical connecting plate structures, the double-sided cylindrical connecting plate structure can enhance the coupling of the resonance mode and Lamb waves compared with the single-sided cylindrical connecting plate structure. The generated band gap frequency range is wider and the lower limit frequency is lower. Therefore, the unit cell of this embodiment adopts the double-sided cylindrical connecting plate structure; Figure 5 Step 5: Calculate the characteristic frequencies of a single unit cell by finite element simulation to obtain the energy band structure diagram of the unit cell. As shown, multiple complete band gaps can be seen in the figure. The width of the first complete band gap reaches 1198 Hz, and the frequency range is 633.3 - 1831.3 Hz, that is, elastic waves within this frequency range will be inhibited from propagating in this structure. The width of the first complete band gap (the gray band in the figure) is determined by the upper and lower cut-off frequencies of the band gap. The lower edge frequency band of the first complete band gap is caused by the local resonance of the scatterer structure, while the upper edge frequency band is caused by the vibration of the connecting plate structure. The vibrations of the two are completely independent and no coupling occurs. The regulation of the band gap can be achieved by adjusting the structural dimensions of each part of the unit cell.

[0035] Carry out parameter optimization and sensitivity analysis on the size of a single cell structure, and analyze the influence law of each parameter on the bandgap frequency range. Among them, there are 11 cell structure size parameters, including the inner diameter and outer diameter of the scatterer structure plate, the height of the scatterer structure, the outer diameter and height of the cladding layer structure, the outer diameter and thickness of the connecting plate, the width of the connecting plate, the thickness and depth of the card slot, and the lattice constant of the cell. Conduct a single-factor experiment for each parameter (predetermine the approximate range of each parameter, take evenly spaced points according to the range of each parameter, keep other parameters unchanged, perform simulation calculations, select the parameters that change significantly for the lower bandgap frequency and the bandgap width as each size parameter changes, and determine the value range of each parameter based on the frequency change diagram of each parameter), as Figure 8 Shown is the frequency change diagram of the inner diameter r of the scatterer. It is determined that there are 7 size parameters that are relatively sensitive to the bandgap frequency range, namely the inner diameter and outer diameter of the scatterer structure, the outer diameter and height of the cladding layer structure, the width and thickness of the connecting plate, and the height of the scatterer structure. Then, perform response surface optimization on the 7 sensitivity parameters. Use the bandgap width, the upper bandgap cut-off frequency, and the lower bandgap cut-off frequency as the final evaluation factors, use the 7 sensitive parameters as the response surface factors, use the value range of the sensitive parameters obtained from the above single-factor experiment as the response surface level, then perform simulation calculations based on the experimental data given by the BBD response surface method, then conduct BBD response surface analysis, give the predicted values of each sensitive parameter, and finally calculate and verify the predicted values to obtain the cell structure size with the bandgap in the required frequency range. Compared with the lower bandgap cut-off frequency generated by the cell structure before optimization, there is a significant reduction, and the bandgap width also increases to a certain extent. Refer to Table 2.

[0036] Table 2 Changes in the bandgap frequency range before and after optimization Unit cell structure before / after optimization Upper limit frequency of band gap (HZ) Lower limit frequency of band gap (HZ) Band gap width (HZ) Before optimization 1925.7 1028 897.7 After optimization 1831.3 633.3 1198 The lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping obtained through the above design is formed by a cell array as shown in Figures 1 - 4 Shown. A single cell is connected from the inside to the outside by three parts: a scatterer structure 1, a cladding layer structure 3, and a connecting plate 2. The scatterer structure 1 is made of aluminum material and is cylindrical. The cladding layer structure 3 is made of oxidation-resistant and corrosion-resistant silicone rubber material and is cylindrical. The connecting plate 2 is made of 3D printing material epoxy resin and is circular. Use double-sided cylindrical connecting plates to expand the range of the complete bandgap, enhance the coupling between the resonance mode and Lamb waves, thereby significantly expanding the bandgap bandwidth and reducing the lower bandgap cut-off frequency, so that the structure can meet low-frequency broadband vibration damping. The material parameters of the lattice structure are shown in Table 3.

[0037] Table 3 Material parameter table for each part of the cell Material name Density (kg / m3) Young's modulus (Mpa) Poisson's ratio Aluminum 2702 70900 0.33 Epoxy resin 1180 4350 0.369 Silicone rubber 1300 0.1175 0.469 The scatterer structure 1 and the coating layer structure 3 are fixedly connected by a special glue, while the coating layer structure 3 and the connecting plate are fixedly connected through an intermediate card slot 4, because it is difficult to complete the fixation and connection of the 3D printing material and the material of the coating layer structure 3 by bonding.

[0038] As shown, each cell is connected to four adjacent cells through four short connecting plates on the outer side of the connecting plate 2 to form the final lattice structure. As Figure 6 shown, in a circumferential array manner, the connected lattice structure ( Figure 7 shown) is circumferentially arrayed along the middle circle to form a lattice structure, so as to achieve the effect of vibration reduction and suppression in multiple directions.

[0039] Perform finite element frequency domain calculation on the obtained lattice structure above. As Figure 6 shown, apply an acceleration response at its left end. The right end of the structure is the output end. Periodic boundary conditions are applied to the left and right of the structure. Finally, the transmission loss ratio diagram of the lattice structure as Figure 12 Figure 13 shown is obtained. Near the frequency where the band gap is located in the band structure diagram, obvious transmission peaks and valleys appear in the frequency response curve, indicating that the above lattice structure has low-frequency broadband vibration isolation effect.

[0040] The above is only the preferred embodiment of the present invention. It should be pointed out that those skilled in the art can make corresponding changes and adjustments to the technology of the present invention without departing from the basic principle of the present invention, and these changes and adjustments all fall within the protection scope of the present invention.

Claims

1. A lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping, characterized in that, Formed by a cell array; a single cell includes: a scatterer, a cladding layer, and a connection layer; the cladding layer is sleeved at the middle position on the outer side of the scatterer, the connection layer is sleeved on the outer side of the cladding layer, and there are small short plates around the outer side of the connection layer for connecting with adjacent cells.

2. The lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping according to claim 1, wherein The scatterer is cylindrical, and the cladding layer is cylindrical; the connection layer is annular.

3. The lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping according to claim 1 or 2, characterized in that, The material of the scatterer is a lightweight material, the material of the cladding layer is a material with a small elastic modulus, and the material of the connection layer is a 3D printing material.

4. The lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping according to claim 3, characterized in that, The scatterer is made of aluminum material, the cladding layer is made of silicone rubber material, and the connection layer is made of epoxy resin.

5. The lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping according to claim 1 or 2, characterized in that The scatterer and the cladding layer are fixedly connected using a special glue, and the cladding layer and the connection layer are fixedly connected using a slot connection.

6. A design method for a lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping, characterized in that, It includes the following steps: S1: Determine the frequency range of the bandgap and the size of the design space according to the usage scenario; S2: Based on the lattice structure design of traditional low-frequency vibration damping, select the basic cell structure and the materials of each part, and calculate and compare to select the scatterer shape according to the frequency range; S3: Select the materials of each part of the cell structure according to the requirements; S4: Adjust the structure of the cell according to the required bandgap frequency range; S5: According to the required bandgap frequency range and the size of the design space, perform parameter optimization and sensitivity analysis on the dimensions of the cell structure to obtain a cell structure with a bandgap in the required frequency range; S6: According to different vibration damping requirements, select different array methods to form a lattice structure with a cell array.

7. The design method of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping according to claim 6, characterized in that, In S2, the selected scatterer shape is a circular ring.

8. The design method of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping according to claim 6 or 7, characterized in that In the cell structure, the scatterer is made of aluminum material, the cladding layer is made of silicone rubber material, and the connection layer is made of epoxy resin material.

9. The design method of the lightweight three-dimensional hollow scatterer lattice structure for low-frequency vibration damping according to claim 6, characterized in that, S5 specifically includes the following steps: Perform parameter optimization and sensitivity analysis on the dimensions of a single cell structure, analyze the influence law of each parameter on the bandgap frequency range, conduct single-factor tests on each parameter respectively to determine the value range of each parameter, determine that the size parameters more sensitive to the bandgap frequency range are the inner diameter and outer diameter of the scatterer structure, the outer diameter and height of the cladding layer structure, the width and thickness of the connection plate, and the height of the scatterer structure. Then perform response surface optimization on the sensitive parameters, use the bandgap width, the upper cut-off frequency of the bandgap, and the lower cut-off frequency of the bandgap as the final evaluation factors, use the sensitive parameters as the response surface factors, use the value range of the sensitive parameters as the response surface levels, perform simulation calculations based on the experimental data given by the BBD response surface method, conduct BBD response surface analysis, give the predicted values of each sensitive parameter, and finally calculate and verify the predicted values to obtain the cell structure dimensions with a bandgap in the required frequency range.

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