Reusable honeycomb material, vibration isolation characteristic prediction method and energy absorption characteristic analysis method

Abstract

The invention belongs to the technical field of reusable materials, and relates to a reusable honeycomb material, a vibration isolation characteristic prediction method and an energy absorption characteristic analysis method. The reusable honeycomb-shaped material is constructed by the following method: low-carbon steel is distributed on six corners of a regular hexagon in a concentrated mass manner and is connected by rubber rod pieces, and half rubber rod pieces are connected to the outer parts of two corners positioned in the middle horizontal position to form rectangular unit cells; and the rectangular unit cells are periodically arranged to form a flexible honeycomb structure. Repeatable use of two functions of variable vibration isolation characteristic and energy absorption of the oscillator string is realized. Compared with a single-vibrator acoustic metamaterial, the multi-vibrator design enriches the band gap types and expands the band gap width; and a repeatable energy absorption effect is realized through recoverable elastic deformation of the flexible rod piece and mass movement of the vibrator. The method has very important significance on the design of impact-resistant, vibration-damping and noise-reducing materials of aerospace equipment structures.

Description

Technical Field

[0001] The invention belongs to the technical field of reusable materials, and relates to a reusable honeycomb material, a vibration isolation characteristic prediction method, and an energy absorption characteristic analysis method. Background Art

[0002] Random shocks are common in industrial environments and difficult to eliminate. Shocks with high mechanical energy pose a significant risk to the accuracy, service life, and safety of instruments. The design of energy-absorbing structures is crucial to preventing irreversible damage to equipment. At the same time, as large-scale, high-end equipment develops towards larger sizes, higher speeds, higher precision, heavier loads, lighter weight, and greater flexibility, mechanical vibration and noise issues are also common and increasingly prominent, seriously affecting the performance and efficiency of major equipment. This makes the development of vibration reduction and noise reduction technologies both important and urgent. The presence of random shocks and low-frequency noise in complex service environments has led to a demand for the development of multifunctional, lightweight engineering materials for high-end equipment.

[0003] By designing the microstructure of phononic crystals, it is possible to prevent the propagation of elastic waves within a certain frequency range. The causes of band gaps are Bragg scattering and local resonance. Bragg scattering means that when the wavelength of the incident wave is close to the lattice constant, the elastic wave will be strongly scattered by the structure. The mechanism of local resonance acoustic metamaterials is that when the elastic wave passes through the phononic crystal, the local resonance unit and the elastic wave are strongly coupled, which suppresses the vibration of the matrix and leads to the generation of band gaps. The unit cells of existing low-frequency vibration isolation metamaterials are mostly single oscillator designs. The connecting rod between the matrix and the resonant mass in the structure only plays a connecting role, and its oscillator effect is not considered. In addition, the energy absorption effect of the oscillator under impact load has not been addressed.

[0004] Research on structural energy absorption performance focuses on the energy absorption characteristics of lattice structures of varying configurations. By improving the specific energy absorption of structures through structural design, theoretical models for structural energy absorption are derived and validated through experimental and numerical experiments. Existing energy-absorbing metamaterials mostly absorb energy by converting impact energy into irreversible plastic deformation energy of the metal, without considering the energy absorption effect of moving mass. Furthermore, the potential vibration isolation and band gap effects of moving mass as an oscillator are not considered. Summary of the Invention

[0005] The purpose of the present invention is to provide a reusable honeycomb material and a method for predicting vibration isolation characteristics and an energy absorption characteristic analysis method, which solves the problem of predicting the vibration isolation mode and vibration isolation range of the honeycomb arrangement structure, breaks the energy absorption mode of converting impact energy into irreversible plastic deformation of the metal lattice structure, and realizes the reusability of the energy absorption structure.

[0006] The present invention is achieved through the following technical solutions: The present invention discloses a reusable honeycomb material, which is constructed by the following method: The concentrated mass of low-carbon steel is distributed on the six corners of a regular hexagon and connected with rubber rods. Half a rubber rod is also connected to the outside of the two corners located in the middle horizontal position to form a rectangular unit cell; the rectangular unit cells are periodically arranged to form a flexible honeycomb structure.

[0007] Furthermore, the flexible honeycomb metamaterial has a shear wave band gap between 37-148 Hz and a compression wave band gap between 273-310 Hz.

[0008] The present invention discloses a method for predicting vibration isolation characteristics of a reusable honeycomb material, comprising the following steps: S1. Equivalently transform the rectangular unit cell into a mass-spring system; S2. Set the degrees of freedom of motion of the concentrated mass within the unit cell according to the motion mode of the mass point when different waves pass through the unit cell. Determine the initial frequency of the band gap and its corresponding theoretical vibration mode when shear waves and compression waves pass through. Calculate the negative effective mass interval based on the theoretical vibration mode to obtain the solution to the vibration isolation performance of the oscillator string variable.

[0009] Furthermore, S1 is specifically: The six corners of the regular hexagon represent six mass points, and the rubber rod is equivalent to a spring; There are two mass points connected with half a rubber rod on the outside, and the mass of a low carbon steel concentrated mass and three half rubber rods is equivalent to For the remaining 4 mass points, the mass of a low-carbon steel concentrated mass and two half rubber rods are equivalent to , .

[0010] Furthermore, in S2, when the shear wave passes through the unit cell, the particle moves Movement in the same direction The particle motion mode at the same location is the same; the boundary conditions of the vibration mode corresponding to the initial frequency of the band gap are: the output boundary displacement is equal to the source boundary displacement; Assume that the degree of freedom of motion of the mass point is , an equivalent dynamic model of the unit cell is established for the motion degrees of freedom of mass points at different positions: The degrees of freedom of the M1 point on one side are Y1 and Y5, and the degrees of freedom of the M1 point on the other side are Y4 and Y5, located at the same position The degree of freedom of the two M2 points at the same position is Y2. The degree of freedom of the two M2 points at is Y3; The two horizontal rubber rods are marked as , the four inclined rubber rods are all recorded as , the two half inclined rubber rods are recorded as ; set up Same direction, when When tilting the rubber rod The equivalent stiffness is ;when When tilting the rubber rod The equivalent stiffness is ;Horizontal rubber rod , half an inclined rubber rod The equivalent stiffnesses are ; The initial frequency of the band gap when the shear wave passes through is 41.7 Hz; the corresponding theoretical vibration mode is: .

[0011] Furthermore, based on the theoretical vibration mode, the effective mass of the unit cell system is obtained, which is expressed as: ; in, represents the angular frequency of the propagation wave in the reusable honeycomb material, and the frequency The relationship is ; The effective mass curve is obtained based on the angular frequency and the effective mass of the unit cell system, where the frequency range corresponding to the negative effective mass is the vibration isolation range.

[0012] Furthermore, in S2, when the compression wave passes through the unit cell, the particle moves Movement in the same direction The particle motion mode at the same location is the same; the boundary condition of the vibration mode corresponding to the initial frequency of the band gap is that the output boundary displacement is equal to the source boundary displacement; Assume that the degree of freedom of motion of the mass point in the system is , an equivalent dynamic model of the unit cell is established for the motion degrees of freedom of mass points at different positions: The degrees of freedom of the M1 point on one side are X1 and X5, and the degrees of freedom of the M1 point on the other side are X4 and X5, located at the same position The degrees of freedom of the two M2 points at the same position are X2. The degrees of freedom of the two M2 points at is X3; The two horizontal rubber rods are marked as , the four inclined rubber rods are all recorded as , the two half inclined rubber rods are recorded as , rubber rod The equivalent stiffnesses are ; The initial frequency of the band gap when the compression wave passes through is 272.13 Hz; the corresponding theoretical vibration mode is: .

[0013] Furthermore, based on the theoretical vibration mode, the effective mass of the unit cell system is obtained, which is expressed as: The effective mass of the unit cell system is:

[0014] in, , represents the angular frequency of the propagation wave in the reusable honeycomb material, and the frequency The relationship is ; The effective mass curve is obtained based on the angular frequency and the effective mass of the unit cell system, where the frequency range corresponding to the negative effective mass is the vibration isolation range.

[0015] The present invention also discloses a method for analyzing the energy absorption characteristics of the reusable honeycomb material, comprising the following steps: S1. deriving an equivalent propagation velocity of elastic waves in the reusable honeycomb material; S2. As the loading speed increases, the energy absorption characteristics of the reusable honeycomb material gradually improve; When the loading velocity is close to the equivalent propagation velocity, the energy absorption characteristics of the reusable honeycomb material reach the optimum.

[0016] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention discloses a reusable honeycomb material, the micro-configuration of which is: multiple concentrated masses are distributed on the six corners of a regular hexagon, and the concentrated masses are connected by rods of flexible superelastic rubber material. The design of the micro-configuration enables the reusable honeycomb material to have the dual functions of vibrator string variable vibration isolation characteristics and energy absorption. The flexible honeycomb metamaterial design of the present invention has multiple vibrators, which can realize the reusability of the two functions of material vibrator string variable vibration isolation characteristics and energy absorption. Compared with the single vibrator structure, the band gap types are enriched and the band gap width is expanded; and the energy absorption mode of converting impact energy into irreversible plastic deformation of the metal lattice structure is broken, and the reusable energy absorption effect of the metamaterial is realized through the reversible deformation of the flexible connector and the mass movement of the vibrator. The reusable honeycomb material of the present invention has a simple structure and is easy to prepare, and provides a new solution for the impact resistance and vibration reduction and noise reduction design of large-scale equipment structures.

[0017] The present invention also discloses a method for predicting the vibration isolation characteristics of the reusable honeycomb material. For vibration isolation, a multi-lumped-mass equivalent dynamics theoretical model of a periodic unit cell is established. By using different mass points as different types of elastic wave oscillators, the corresponding bandgap initial frequencies and vibration modes are obtained. Based on the corresponding vibration modes, the negative effective mass interval is solved, resulting in a solution for the vibration isolation characteristics of the metamaterial oscillator. Numerical analysis of the unit cell's band structure and the metamaterial's transmission characteristic curve verifies its low-frequency bandgap vibration isolation performance.

[0018] The present invention also discloses a method for analyzing the energy absorption characteristics of the reusable honeycomb material. Regarding energy absorption, the presence of concentrated masses within the material and the design of flexible, hyperelastic rubber connecting rods between these concentrated masses result in significant differences in the material's dynamic and quasi-static behaviors at varying loading speeds, influenced by the presence or absence of internal kinetic energy. Furthermore, the absorption method, which converts impact energy into recoverable elastic strain energy of the flexible rubber connecting rods and the kinetic energy of the concentrated masses, disrupts the energy absorption behavior associated with irreversible plastic deformation of the metal lattice structure, resulting in the material's repeatable energy absorption. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A schematic diagram of a reusable dual-function honeycomb material and a unit cell thereof according to the present invention; Figure 2 The equivalent mass-spring system of the reusable honeycomb material unit cell provided by the present invention; Figure a shows the mass distribution inside the unit cell; Figure b shows the equivalent mass-spring system; Figure 3 The equivalent dynamic model and vibration isolation mode of a unit cell when the shear wave passes through the material provided by the present invention; Figure a shows the equivalent dynamic model of the unit cell and the degrees of freedom of motion of each mass point; Figure b shows the corresponding vibration mode of the theoretical band gap initial frequency of the equivalent mass-spring system; Figure 4 A simplified equivalent dynamic model of the theoretical vibration mode corresponding to the initial frequency of the shear wave band gap provided by the present invention; Figure 5 Comparison of the theoretical and numerical solutions for the negative effective mass interval of the matrix when the shear wave passes through provided by the present invention; Figure 6 The equivalent dynamic model and vibration isolation mode of the unit cell when the compression wave passes through the material provided by the present invention; Figure a shows the equivalent dynamic model of the unit cell and the degrees of freedom of motion of each mass point; Figure b shows the corresponding vibration mode of the theoretical band gap initial frequency of the equivalent mass-spring system; Figure 7A simplified equivalent dynamic model of the theoretical vibration mode corresponding to the initial frequency of the compression wave band gap provided by the present invention; Figure 8 Comparison of the theoretical and numerical solutions for the negative effective mass interval of the matrix when the compression wave passes through the present invention; Figure 9 The band structure curve of the unit cell provided by the present invention; the vertical axis represents different frequencies, and the horizontal axis represents different directions; Figure 10 Characteristic vibration modes corresponding to different points in the energy band structure diagram provided by the present invention; Figure 11 Transmission characteristic curves of different types of elastic waves passing through materials provided by the present invention; Figure a is a shear wave transmission characteristic curve, and Figure b is a compression wave transmission characteristic curve; Figure 12 A microelement load diagram when one end of the uniform slender rod provided by the present invention is subjected to an impact load; Figure 13 The strain rate provided by the present invention is (That is, the compression speed is ) when the material's stress-strain response curve and internal energy change diagram; Figure a is the stress-strain curve, and Figure b is the material's internal energy conversion diagram; Figure 14 The strain rate provided by the present invention is Stress distribution cloud diagram of the material under different strains; Figure 15 The strain rate provided by the present invention is (That is, the compression speed is ) when the material's stress-strain response curve and internal energy change diagram; Figure a is the stress-strain curve, and Figure b is the material's internal energy conversion diagram; Figure 16 The strain rate provided by the present invention is Stress distribution cloud diagram of the material under different strains; Figure 17 The strain rate provided by the present invention is (That is, the compression speed is ) when the material's stress-strain response curve and internal energy change diagram; Figure a is the stress-strain curve, and Figure b is the material's internal energy conversion diagram; Figure 18 The strain rate provided by the present invention is Stress distribution cloud diagram of the material under different strains; Figure 19 The material strain rate provided by the present invention is 、 、 Comparison of stress-strain response curves; Figure 20This is a comparison diagram of the stress-strain response curves of the material provided by the present invention during quasi-static compression. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solutions and advantages of the present invention more clear, the following is a further detailed description with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. That is, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments.

[0021] The components described and illustrated in the drawings and embodiments of the present invention may be arranged and designed in a variety of different configurations. Therefore, the detailed description of the embodiments of the present invention provided in the following drawings is not intended to limit the scope of the claimed invention, but merely represents a selected embodiment of the present invention. All other embodiments derived by those skilled in the art based on the drawings and embodiments of the present invention without inventive effort shall fall within the scope of protection of the present invention.

[0022] It should be noted that the terms "comprises", "includes" or any other variations are intended to cover non-exclusive inclusion, so that a process, element, method, article or apparatus that includes a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to the process, element, method, article or apparatus.

[0023] The present invention discloses a reusable honeycomb material, which is constructed by the following method: The concentrated mass of low-carbon steel is distributed on the six corners of a regular hexagon and connected with rubber rods. Half a rubber rod is also connected to the outside of the two corners located in the middle horizontal position to form a rectangular unit cell; the rectangular unit cells are periodically arranged to form a flexible honeycomb structure.

[0024] The features and performance of the present invention are further described in detail below with reference to the embodiments.

[0025] Step 1: If Figure 1 As shown, the concentrated mass of mild steel is distributed at the six corners of a regular hexagon and connected by rubber rods. Rectangular unit cells are taken from the material and arranged periodically to form a flexible honeycomb structure, so its performance can represent the performance of the entire material.

[0026] Step 2: Equivalent unit cell to Figure 2 The mass-spring model shown in the figure has 6 mass points. Among them, two mass points are connected to the outside of half a rubber rod, and the mass of a low-carbon steel concentrated mass and three half rubber rods is equivalent to For the remaining 4 mass points, the mass of a low-carbon steel concentrated mass and two half rubber rods are equivalent to , .

[0027] Step 3: Explain in terms of shear waves and compression waves When the shear wave passes through the unit cell, the particle moves Movement in the same direction and position The particle motion mode at the same location is the same; the boundary condition of the vibration mode corresponding to the initial frequency of the band gap is: the output boundary displacement is equal to the source boundary displacement, that is, Therefore, the degree of freedom of motion of the mass point in the system can be set as , the degrees of freedom of motion of mass points at different positions are as follows Figure 3 The equivalent dynamic model of the unit cell shown in a, the degrees of freedom of the M1 point on the left are Y1 and Y5, and the degrees of freedom of the M1 point on the right are Y4 and Y5, located at the same position The degree of freedom of the two M2 points at the same position is Y2. The degrees of freedom of the two M2 points at the same location are Y3. The two horizontal rubber rods are denoted as , the four inclined rubber rods are all recorded as , the two half inclined rubber rods are recorded as ,set up Same direction, when When tilting the rubber rod The equivalent stiffness is ;when When tilting the rubber rod The equivalent stiffness is Horizontal rubber rod , half an inclined rubber rod The equivalent stiffnesses are .

[0028] At this time, the kinetic energy T of the equivalent mass-spring system of the unit cell is: (1) in, Represents the velocity of each mass point.

[0029] The potential energy V is: (2) From formula (1) and formula (2), we can see that the Lagrangian of the unit cell system is L for: (3) The Lagrange equation is: (4) in, represents the displacement and velocity of each mass point, .

[0030] Substituting Equation (3) into Equation (4), the differential motion equation of the system is obtained as follows: (5) in, Represents the acceleration of each mass point.

[0031] Formula (5) can be simplified as: (6) Formula (6) is transformed into: (7) in, K represents the stiffness matrix after the differential equation of motion (5) is written in matrix form, M represents the mass matrix, U Represents the displacement matrix of the equivalent dynamic system.

[0032] Substituting the Young's modulus, density, mass and other parameters of the material into Equation (6), solving the determinant, we can get the initial frequency of the band gap when the shear wave passes through is 41.7 Hz. Solving Equation (7), we can get the corresponding vibration mode: (8) The initial frequency of the shear wave band gap corresponds to the vibration mode as follows Figure 3 As shown in b.

[0033] Next, the theoretical negative effective mass interval is solved based on the vibration mode corresponding to the initial frequency of the shear wave band gap: According to formula (8), we can know that: (9) (10) At this time, the unit cell can be simplified to three degrees of freedom As shown shown.

[0034] From formulas (5), (9), and (10), the differential equation of motion of the system at this time can be obtained as: (11) Where F represents the harmonic excitation applied to the edge of the unit cell.

[0035] Since the motion pattern of the oscillator at the original position satisfies 、 , combined with formula (11), the effective mass of the system can be obtained as: (12) in, , represents the angular frequency of the propagation wave in the reusable honeycomb material, and the frequency The relationship is ; Based on angular frequency The effective mass curve is obtained by combining the effective mass of the unit cell system, where the frequency range corresponding to the negative effective mass is the vibration isolation range of the shear wave.

[0036] The comparison between the theoretical solution and the numerical solution of the negative effective mass of the unit cell when the shear wave passes through is as follows Figure 5 shown.

[0037] When the compression wave passes through the unit cell, the particle moves Movement in the same direction and position The particle motion mode at the same location is the same; the boundary condition of the vibration mode corresponding to the initial frequency of the band gap is that the output boundary displacement is equal to the source boundary displacement, that is, Therefore, the degree of freedom of motion of the mass point in the system can be set as , the degrees of freedom of motion of mass points at different positions are as follows Figure 6 The equivalent dynamic model of the unit cell shown in a, the degrees of freedom of the M1 point on the left are X1 and X5, and the degrees of freedom of the M1 point on the right are X4 and X5, located at the same position The degrees of freedom of the two M2 points at the same position are X2. The degrees of freedom of the two M2 points at the same location are X3. The two horizontal rubber rods are denoted as , the four inclined rubber rods are all recorded as , the two half inclined rubber rods are recorded as , rubber rod The equivalent stiffnesses are .

[0038] At this time, the kinetic energy of the equivalent mass-spring system of the unit cell is: (13) in, Represents the velocity of each mass point.

[0039] The potential energy of the system is: (14) From equations (13) and (14), we can see that the Lagrangian of the system is: (15) in l is the length of the entire rubber rod.

[0040] The Lagrange equation is: (16) in, represents the displacement and velocity of each mass point, .

[0041] Substituting formula (15) into formula (16) yields: (17) in, Represents the acceleration of each mass point.

[0042] From Equations (16) and (17), we can obtain that the initial frequency of the band gap when the compression wave passes through is 272.13 Hz, and the corresponding vibration mode is: (18) The vibration mode corresponding to the initial frequency of the compression wave band gap is as follows Figure 6 As shown in b.

[0043] Next, the theoretical negative effective mass interval is solved based on the vibration mode corresponding to the initial frequency of the compression wave band gap: According to formula (18), we can know that: (19) (20) At this time, the equivalent mass-spring system can be simplified to two degrees of freedom ,like Figure 7 shown.

[0044] The differential equation of motion of the system at this time can be obtained as: (twenty one) (twenty two) After a series of calculations, the effective mass of the system can be obtained as: (twenty three) The comparison between the theoretical solution and the numerical solution of the negative effective mass of the unit cell when the compression wave passes through is as follows: Figure 8 shown.

[0045] in, , Represents the angular frequency of the wave transmitted in the material, which is different from the frequency The relationship is .

[0046] Based on angular frequency The effective mass curve is obtained by combining the effective mass of the unit cell system, where the frequency range corresponding to the negative effective mass is the vibration isolation range of the compression wave.

[0047] The following is a specific verification of the vibration isolation characteristics of the reusable honeycomb material of the present invention.

[0048] Set up reusable honeycomb material ( Figure 1 ) are shown in Table 1. Figure 1 The red part is made of mild steel and the grey part is made of rubber. Direction Settings Floquent Periodic boundary conditions, in y Set continuous periodic boundaries in the direction. x When propagating in the direction, the band structure of the honeycomb material and the characteristic vibration modes corresponding to different points can be reused, as shown in Figure 9 、 Figure 10 shown.

[0049] Table 1 Material parameters of flexible honeycomb structure

[0050] Figure 11 and Figure 12 The transmission characteristic curves of shear wave and compression wave are respectively Figure 5 、 Figure 8 Compared with the negative effective mass range, the flexible honeycomb metamaterial has a shear wave band gap between 37-148 Hz and a compression wave band gap between 273-310 Hz.

[0051] Will Figure 4 The initial frequency of the shear wave band gap corresponds to the vibration mode Figure 10 Comparing the characteristic vibration modes of point A in the figure, we can see that the vibration modes corresponding to the initial frequency of the shear wave band gap derived theoretically are similar to those of the numerical solution. Figure 5 It can be seen that when the shear wave passes through, the theoretical negative effective mass interval deduced based on the vibration mode corresponding to the theoretical band gap initial frequency is in good agreement with the numerical solution.

[0052] Similarly, comparison Figure 7 and Figure 10 From the characteristic vibration mode of point D, it can be seen that the vibration mode corresponding to the initial frequency of the compression wave band gap derived theoretically is similar to the numerical solution.

[0053] Depend on Figure 8 It can be seen that when the compression wave passes, the theoretical negative effective mass interval deduced based on the vibration mode corresponding to the theoretical band gap initial frequency is in good agreement with the numerical solution.

[0054] The vibration modes corresponding to the initial frequencies of the shear wave and compression wave band gaps show that different parts of the unit cell act as local oscillators when blocking the passage of different types of elastic waves. That is, the present invention theoretically obtains a solution to the serial vibration isolation characteristics of the flexible honeycomb metamaterial oscillator, and the theoretical solution of the vibration isolation performance is in good agreement with the numerical solution.

[0055] The following describes a method for analyzing the energy absorption characteristics of the reusable honeycomb material: The force analysis of the internal microelement of a uniform slender rod when one end is subjected to an impact load is as follows: Figure 12 As shown, Newton's second law gives: (twenty four) in, is the rod density, is the cross-sectional area of the rod, is the length of the microelement, When the rod is subjected to impact load, the microelement AB The compressive stress generated in the cross section, is the displacement of the section, For time.

[0056] After simplifying formula (24), we can get: (25) Formula (25) can be written as follows: (26) And because: (27) From formula (26) (27), we can know that: (28) So the propagation speed of the compression wave in the rod is: (29) The equivalent propagation velocity of reusable honeycomb material is calculated as The propagation speed of elastic waves in this material is very small compared to that in metals, and the loading speed can easily reach the equivalent wave propagation speed. The strain rate of numerical analysis is 、 、 When the loading speed is 、 、 When , the force and displacement response curve of the material and the stress distribution under different strains, such as Figures 13-18 Comparison of stress-strain response curves under different strain rates and static compression Figure 19 and Figure 20 shown.

[0057] The reasons for the significant differences in force-displacement curves at different strain rates are analyzed from the perspectives of stress wave propagation and deformation during loading, as well as the energy conversion within the material. It is shown that the reproducible energy absorption effect of the honeycomb material can be achieved through the recoverable elastic deformation of the flexible rubber rod and the mass motion of the oscillator.

[0058] When the strain rate When the compression rate is much smaller than the wave propagation speed, the material is almost uniformly deformed. At this time, the dynamic mechanical response of the material is close to the quasi-static compression. When the compression rate is no longer much smaller than the propagation speed of the elastic wave, its influence on the dynamic mechanical behavior of the material cannot be ignored. The deformation and stress distribution of the material between the plates show a state of large edges and small middle. When the compression speed is close to the wave propagation speed in the flexible honeycomb material, the structural uneven deformation is more obvious.

[0059] The strain rate is When the strain rate is , the trend and amplitude of the stress-strain curve of the structure are closest to those of quasi-static compression, at which time the internal kinetic energy of the material has little effect on the structural response; when the strain rate is The inertial force and deformation generated by the internal kinetic energy of the structure simultaneously resist the external load, showing high dynamic stiffness and high dynamic limit load; the strain rate is The strain rate dependence is more pronounced on the external load and dynamic stiffness when the material is subjected to the strain rate dependence. The material exhibits a dynamic stiffness 1800 times greater than the static stiffness and a dynamic load limit nearly 60 times greater than the static load limit.

[0060] From the energy conversion diagram inside the structure under different loading speeds, we can see that ( Figure 13 b, 15b, and 17b). When the reusable honeycomb structure is loaded, the work done by the external force is converted into the material's recoverable deformation energy and the kinetic energy of the concentrated mass within the structure. This energy absorption method of recoverable elastic deformation and kinetic energy absorption breaks the energy absorption behavior of the metal lattice structure's irreversible plastic deformation, making the material capable of repeated energy absorption.

[0061] The present invention discloses a reusable honeycomb material having the dual functions of vibrator string vibration isolation and energy absorption through micro-configuration design. The micro-configuration of the material is as follows: multiple concentrated masses are distributed on the six corners of a regular hexagon, and the concentrated masses are connected by rods made of flexible superelastic rubber material.

[0062] In terms of vibration isolation, a multi-lumped-mass equivalent dynamics theoretical model of a periodic unit cell was established. By using different mass points as different types of elastic wave oscillators, the corresponding band gap initial frequencies and corresponding vibration modes were obtained. Based on the corresponding vibration modes, the negative effective mass interval was solved, and the vibration isolation characteristics of the metamaterial oscillator were obtained. The low-frequency band gap vibration isolation performance was verified by numerically analyzing the unit cell's band structure and the metamaterial's transmission characteristic curve.

[0063] In terms of energy absorption, the presence of concentrated masses within the material and the design of flexible, hyperelastic rubber connecting rods between these concentrated masses result in significant differences in the material's dynamic and quasi-static behavior at different loading speeds, depending on the presence or absence of internal kinetic energy. Furthermore, the absorption of impact energy by converting it into the recoverable elastic strain energy of the flexible rubber connecting rods and the kinetic energy of the concentrated masses disrupts the energy absorption behavior inherent in the irreversible plastic deformation of the metal lattice structure, resulting in a repeatable energy absorption effect.

[0064] In summary, this flexible honeycomb metamaterial design with multiple oscillators achieves reusable performance for both oscillator-based vibration isolation and energy absorption. Compared to single-oscillator acoustic metamaterials, this multi-oscillator design enriches the types and widths of band gaps. It also achieves repeatable energy absorption through the recoverable elastic deformation of the flexible rods and the mass motion of the oscillators. This invention holds significant implications for the design of impact-resistant, vibration-reducing, and noise-reducing materials for aerospace equipment structures.

[0065] 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 it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A reusable honeycomb material, characterized in that: The reusable honeycomb material is constructed by the following method: The concentrated mass of low-carbon steel is distributed on the six corners of a regular hexagon and connected with rubber rods. Half a rubber rod is also connected to the outside of the two corners located in the middle horizontal position to form a rectangular unit cell; the rectangular unit cells are periodically arranged to form a flexible honeycomb structure.

2. The reusable honeycomb material according to claim 1, characterized in that: The flexible honeycomb metamaterial has a shear wave band gap between 37-148 Hz and a compression wave band gap between 273-310 Hz.

3. The method for predicting vibration isolation characteristics of a reusable honeycomb material according to claim 1 or 2, characterized in that: The following steps are involved: S1. Equivalently transform the rectangular unit cell into a mass-spring system; S2. Set the degrees of freedom of motion of the concentrated mass within the unit cell according to the motion mode of the mass point when different waves pass through the unit cell. Determine the initial frequency of the band gap and its corresponding theoretical vibration mode when shear waves and compression waves pass through. Calculate the negative effective mass interval based on the theoretical vibration mode to obtain the solution to the vibration isolation performance of the oscillator string variable.

4. The method for predicting vibration isolation characteristics of reusable honeycomb materials according to claim 3, characterized in that: S1 is specifically: The six corners of the regular hexagon represent six mass points, and the rubber rod is equivalent to a spring; There are two mass points connected with half a rubber rod on the outside, and the mass of a low carbon steel concentrated mass and three half rubber rods is equivalent to For the remaining 4 mass points, the mass of a low-carbon steel concentrated mass and two half rubber rods are equivalent to , .

5. The method for predicting vibration isolation characteristics of reusable honeycomb materials according to claim 3, characterized in that: In S2, when the shear wave passes through the unit cell, the particle moves Movement in the same direction The particle motion mode at the same location is the same; the boundary conditions of the vibration mode corresponding to the initial frequency of the band gap are: the output boundary displacement is equal to the source boundary displacement; Assume that the degree of freedom of motion of the mass point is , an equivalent dynamic model of the unit cell is established for the motion degrees of freedom of mass points at different positions: The degrees of freedom of the M1 point on one side are Y1 and Y5, and the degrees of freedom of the M1 point on the other side are Y4 and Y5, located at the same position The degree of freedom of the two M2 points at the same position is Y2. The degree of freedom of the two M2 points at is Y3; The two horizontal rubber rods are marked as , the four inclined rubber rods are all recorded as , the two half inclined rubber rods are recorded as ; set up Same direction, when When tilting the rubber rod The equivalent stiffness is ;when When tilting the rubber rod The equivalent stiffness is ;Horizontal rubber rod , half an inclined rubber rod The equivalent stiffnesses are ; The initial frequency of the band gap when the shear wave passes through is 41.7 Hz; the corresponding theoretical vibration mode is: 。 6. The method for predicting vibration isolation characteristics of reusable honeycomb materials according to claim 5, characterized in that: Based on the theoretical vibration mode, the effective mass of the unit cell system is obtained as follows: ； in, represents the angular frequency of the propagation wave in the reusable honeycomb material, and the frequency The relationship is ; The effective mass curve is obtained based on the angular frequency and the effective mass of the unit cell system, where the frequency range corresponding to the negative effective mass is the vibration isolation range.

7. The method for predicting vibration isolation characteristics of reusable honeycomb materials according to claim 3, characterized in that: In S2, when the compression wave passes through the unit cell, the particle moves Movement in the same direction The particle motion mode at the same location is the same; the boundary condition of the vibration mode corresponding to the initial frequency of the band gap is that the output boundary displacement is equal to the source boundary displacement; Assume that the degree of freedom of motion of the mass point in the system is , an equivalent dynamic model of the unit cell is established for the motion degrees of freedom of mass points at different positions: The degrees of freedom of the M1 point on one side are X1 and X5, and the degrees of freedom of the M1 point on the other side are X4 and X5, located at the same position The degrees of freedom of the two M2 points at the same position are X2. The degrees of freedom of the two M2 points at is X3; The two horizontal rubber rods are marked as , the four inclined rubber rods are all recorded as , the two half inclined rubber rods are recorded as , rubber rod The equivalent stiffnesses are ; The initial frequency of the band gap when the compression wave passes through is 272.13 Hz; the corresponding theoretical vibration mode is: 。 8. The method for predicting vibration isolation characteristics of reusable honeycomb materials according to claim 7, characterized in that: Based on the theoretical vibration mode, the effective mass of the unit cell system is obtained as follows: The effective mass of the unit cell system is: in, , represents the angular frequency of the propagation wave in the reusable honeycomb material, and the frequency The relationship is ; The effective mass curve is obtained based on the angular frequency and the effective mass of the unit cell system, where the frequency range corresponding to the negative effective mass is the vibration isolation range.

9. The method for analyzing the energy absorption characteristics of a reusable honeycomb material according to claim 1 or 2, characterized in that: The following steps are involved: S1. deriving an equivalent propagation velocity of elastic waves in the reusable honeycomb material; S2. As the loading speed increases, the energy absorption characteristics of the reusable honeycomb material gradually improve; When the loading velocity is close to the equivalent propagation velocity, the energy absorption characteristics of the reusable honeycomb material reach the optimum.

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