Bistable vibration absorbing unit, bistable mechanical metamaterial structure and preparation method thereof

Abstract

The present invention discloses a bistable vibration-absorbing unit, a bistable mechanical metamaterial structure, and a method for preparing the same. The bistable vibration-absorbing unit is characterized by comprising a track frame, a vibrator, and an elastic mechanism; the track frame is provided with opposing tracks on both sides, and the track profile is a parabola; the vibrator is located between the tracks on both sides of the track frame; the first end of the elastic mechanism is connected to the side of the vibrator, and the second end of the elastic mechanism is slidably connected to the track on the corresponding side; the elastic mechanism has the freedom to compress or extend, and the elastic mechanism has a travel along the track. The present invention is applicable to the fields of vibration and noise control and nonlinear metamaterial structures, and can be applied to impact energy-absorbing structures. It has higher strength and stability, and achieves low-frequency, broadband, and efficient vibration suppression and impact attenuation effects with low additional mass.

Description

Technical Field

[0001] The present invention relates to the fields of mechanical engineering, mechanics, vibration and noise control, and nonlinear metamaterial structure technology, and specifically to a bistable vibration absorbing unit, a bistable mechanical metamaterial structure, and a preparation method thereof. Background Art

[0002] Structural vibration and shock are widespread in the aerospace, shipbuilding, marine, and nuclear industries. Structural vibration and shock suppression are crucial for equipment safety and acoustic stealth performance. Lightweight design and vibration and shock control are especially important for equipment in demanding environments, such as aerospace. The vibration and shock generated by structures subjected to flow shock and various vibration sources not only degrades the safety and stability of equipment and the performance of precision instruments, but can also, in severe cases, directly lead to accidents such as loss of control, structural vibration fatigue, and fracture. Vibration also radiates noise, impacting the stealth and survivability of equipment. In manned equipment, it can damage hearing and vision, posing a health risk. Designing materials and structures with shock suppression and vibration control is crucial for improving equipment safety, stability, and other performance characteristics. For equipment in aerospace and other applications, which have stringent engineering requirements regarding size, weight, and environmental adaptability, traditional vibration reduction and damping technologies are ineffective in effectively addressing low-frequency vibration and shock. Therefore, the development of new vibration and noise reduction technologies is urgently needed.

[0003] Mechanical metamaterials are still-unusual structures that achieve extraordinary mechanical properties through elastic wave manipulation. Compared to traditional material structures, metamaterials exhibit many novel phenomena in statics and dynamics. Through the rational design of periodic microstructures, special properties such as elastic wave band gaps, extraordinary mechanical properties, negative Poisson's ratio, and lightweight yet high-strength properties can be achieved. These properties hold broad application prospects in vibration and noise reduction, as well as impact protection.

[0004] Research has shown that specially designed mechanical metamaterials based on localized resonant excitation can generate localized resonant band gaps, effectively suppressing elastic wave propagation and enabling manipulation of elastic waves. This provides new insights into vibration and noise control in beam-slab structures. Currently, much of the research on mechanical metamaterials is still focused on linear metamaterials.

[0005] However, the localized resonant bandgap of linear mechanical metamaterials is narrow, failing to reconcile the conflict between lightweight, low-frequency, and broadband elastic wave suppression. Furthermore, the spectral passband of a finite-sized linear metamaterial is composed of densely packed resonance peaks. The greater the number of cells, the greater the number of resonance peaks within the passband. In other words, while the narrow elastic wave bandgap of a linear metamaterial attenuates structural vibrations, the response within its wider passband is amplified by resonance.

[0006] Nonlinear mechanical metamaterials are mechanical metamaterials that exhibit nonlinear dynamic properties. Research has shown that the introduction of nonlinear factors has the potential to overcome the bandwidth limitations of traditional linear metamaterials in vibration suppression, achieving ultra-low-frequency, ultra-wideband, and highly efficient vibration suppression. Bistable mechanical metamaterials, as a key component of nonlinear mechanical metamaterials, can achieve dynamic properties such as sudden springback, negative stiffness, and tunability, offering broad application prospects in elastic wave control and impact protection.

[0007] The properties of bistable mechanical metamaterials depend largely on the design of the cellular units. The design of lightweight and small-sized bistable structures is rarely involved at present, and the design technology of bistable nonlinear cells needs to be innovated. The design of lightweight and adjustable bistable units can promote the vibration reduction and impact resistance applications of bistable mechanical metamaterials. Summary of the Invention

[0008] In response to the above-mentioned deficiencies in the prior art, the present invention provides a bistable vibration absorption unit, a bistable mechanical metamaterial structure and a preparation method thereof, which can be applied to impact energy absorption structures, have higher strength and stability, and achieve low-frequency, broadband, and efficient vibration suppression and efficient impact attenuation effects under conditions of small additional mass.

[0009] To achieve the above-mentioned object, the present invention provides a bistable vibration absorbing unit, comprising a track frame, a vibrator and an elastic mechanism;

[0010] Opposite tracks are provided on both sides of the track frame, and the track has a parabolic profile;

[0011] The vibrator is located between the tracks on both sides of the track frame, the first end of the elastic mechanism is connected to the side of the vibrator, and the second end of the elastic mechanism is slidably connected to the track on the corresponding side;

[0012] The elastic mechanism has a degree of freedom of compression or extension, and the elastic mechanism has a stroke of displacement along the track.

[0013] In one embodiment, the elastic mechanism includes a spring and a sleeve, a countersunk hole is provided on the side of the vibrator, and the sleeve is a cylindrical structure with one end open;

[0014] The first end of the spring is connected to the bottom of the countersunk hole, the second end of the spring is embedded in the open end of the sleeve and connected to the bottom of the sleeve, and the closed end of the sleeve is in contact with the track.

[0015] In one embodiment, the open end of the sleeve is coaxially embedded in the counterbore, and the outer wall of the sleeve is clearance-matched with the hole wall of the counterbore.

[0016] In one embodiment, the number of the rails and the number of the elastic mechanisms are both four, and the elastic mechanisms correspond one to one with the rails;

[0017] The four tracks are distributed in a rectangular array on the track frame. The first end of the elastic mechanism is connected to the side of the vibrator, and the second end of the elastic mechanism is slidably connected to the corresponding track.

[0018] In one embodiment, the springs in the four elastic mechanisms have the same stiffness, and the springs have prestress.

[0019] To achieve the above object, the present invention further provides a bistable mechanical metamaterial structure, comprising a plurality of the above-mentioned bistable vibration absorbing units;

[0020] The bistable vibration absorbing units are distributed in an array in one direction; or

[0021] The bistable vibration absorbing units are distributed in an array in two orthogonal directions; or

[0022] The bistable vibration absorbing units are distributed in an array in three orthogonal directions; or

[0023] The bistable vibration absorbing units are distributed in a circular array; or

[0024] The bistable vibration absorbing units are distributed in a cylindrical array.

[0025] To achieve the above object, the present invention further provides a method for preparing the above-mentioned bistable mechanical metamaterial structure, comprising the following steps:

[0026] Step 1: determining the resonant frequency of the bistable vibration absorbing unit based on the target vibration frequency band;

[0027] Step 2: determining the equivalent negative stiffness and nonlinear stiffness coefficient of the bistable vibration absorbing unit based on the resonant frequency and the additional mass limit of the bistable vibration absorbing unit;

[0028] Step 3, determining the track coefficient, protrusion height, and spring stiffness coefficient of the track according to the equivalent negative stiffness and the nonlinear stiffness coefficient;

[0029] Step 4: designing a bistable vibration absorbing unit according to the parameters determined in steps 1 to 3, and combining it with a matrix designed for vibration reduction and impact resistance to form a cell of the bistable mechanical metamaterial;

[0030] Step 5: Arrange multiple cells of the bistable mechanical metamaterial according to a preset array to form a bistable mechanical metamaterial structure.

[0031] Compared with the prior art, the present invention has the following beneficial technical effects:

[0032] The bistable vibration absorbing unit in the present invention slides on a parabolic track through an elastic mechanism to produce steady-state jump and sliding damping effects, thereby realizing a bistable effect. The nonlinear stiffness coefficient and the position of the local resonance band gap of the bistable vibration absorbing unit can be controlled by controlling the stiffness coefficient of the elastic mechanism, the track height and the track length. At the same time, the damping coefficient can be adjusted by controlling the roughness of the track and the elastic mechanism, thereby controlling the impact energy absorption efficiency. The cells constituting the bistable vibration absorbing unit are periodically arranged on the base beam structure to construct a bistable mechanical metamaterial structure, which can achieve low-frequency, broadband, and efficient vibration suppression and efficient impact attenuation effects under the condition of additional mass. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0034] Figure 1 This is an axonometric diagram of the bistable vibration absorbing unit in Example 1 of the present invention;

[0035] Figure 2 4 is a cross-sectional view of the bistable vibration absorbing unit in Example 1 of the present invention;

[0036] Figure 3 This is a partial schematic diagram of the track frame and elastic mechanism in Example 1 of the present invention;

[0037] Figure 4 is a partial schematic diagram of the vibrator in Example 1 of the present invention;

[0038] Figure 5 Schematic diagram of force analysis at the contact position between the sleeve and the track in the bistable vibration absorbing unit in Example 2 of the present invention;

[0039] Figure 6 Schematic diagram of reaction force-displacement curve in Example 2 of the present invention;

[0040] Figure 7 This is a schematic diagram of the arrangement, installation, and testing of the bistable mechanical metamaterial cantilever beam in Example 2 of the present invention, wherein: Figure 7 (a) is a schematic diagram of the test scheme for the impact transient vibration characteristics of the bistable metamaterial cantilever beam. Figure 7 (b) Schematic diagram of the impact excitation application scheme;

[0041] Figure 8 Schematic diagram of the one-dimensional cantilever beam impact transient vibration test results in Example 2 of the present invention, wherein: Figure 8(a) is a speed-time diagram, Figure 8 (b) is the amplitude-frequency diagram;

[0042] Reference numerals: track frame 1 , track 101 , vibrator 2 , countersunk hole 201 , elastic mechanism 3 , spring 301 , sleeve 302 , base 4 .

[0043] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0045] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative position relationship, movement status, etc. between the various components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0046] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in this field can implement it. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0047] Example 1

[0048] like Figure 1 The bistable vibration-absorbing unit disclosed in this embodiment is shown, which primarily comprises a track frame 1 made of structural steel, a vibrator 2, and an elastic mechanism 3. The track frame 1 is fixedly connected to a base 4 requiring vibration reduction and impact resistance via bolts. Opposite rails 101 are provided on either side of the track frame 1. The length of the rails 101 is perpendicular to the plane of the base 4, and the profile of the rails 101 is parabolic. The vibrator 2 is located between the rails 101 on either side of the track frame 1 and slidably engages with the rails 101 via the elastic mechanism 3. The first end of the elastic mechanism 3 is connected to the side of the vibrator 2, and the second end of the elastic mechanism 3 is slidably connected to the rail 101 on the corresponding side. The elastic mechanism 3 has the freedom to compress or extend, and has a travel range along the rail 101. That is, the elastic mechanism 3 can drive the vibrator 2 to slide along the rail 101 under the action of an external force.

[0049] In this embodiment, the elastic mechanism 3 includes a spring 301 and a sleeve 302. A circular countersunk hole 201 is provided on the side of the vibrator 2 at the connection position of the elastic mechanism 3. The sleeve 302 is a cylindrical structure with one end open. The first end of the spring 301 is fixedly connected to the bottom of the countersunk hole 201 by gluing, fixing with a connecting piece, etc. The second end of the spring 301 is embedded in the open end of the sleeve 302 and fixedly connected to the bottom of the sleeve 302 by gluing, fixing with a connecting piece, etc. The closed end of the sleeve 302 is in contact with the track 101 and is spherical or curved to prevent interference when the sleeve 302 slides on the track 101. In specific applications, the friction coefficient between the sleeve 302 and the track 101 can be controlled by controlling the surface roughness of the contact surface between the sleeve 302 and the track 101.

[0050] During the specific implementation process, the open end of the sleeve 302 is coaxially embedded in the countersunk hole 201, and the outer wall of the sleeve 302 is gap-matched with the hole wall of the countersunk hole 201. In specific applications, even if the sleeve 302 slides to the most recessed position of the track 101, the open end of the sleeve 302 is still located in the countersunk hole 201, so as to avoid the spring 301 being exposed and causing the spring 301 to bend during the sliding process.

[0051] In the specific implementation, there are four rails 101 and four elastic mechanisms 3, each corresponding to one rail 101. The four rails 101 are arranged in a rectangular array on the rail frame 1. The first ends of the elastic mechanisms 3 are connected to the sides of the vibrator 2, and the second ends of the elastic mechanisms 3 are slidably connected to the corresponding rail 101. The springs 301 in the four elastic mechanisms 3 have the same stiffness and are prestressed, which can be controlled by designing the wire diameter, number of coils, and length of the springs 301.

[0052] The bistable vibration absorbing unit in this embodiment slides on the parabolic track 101 through the elastic mechanism 3 to produce steady-state jump and sliding damping effects, thereby achieving a bistable effect. The nonlinear stiffness coefficient and local resonance band gap position of the bistable vibration absorbing unit can be controlled by the stiffness coefficient of the spring 301, the height of the track 101, and the length of the track 101. At the same time, the damping coefficient can be adjusted by controlling the roughness of the track 101 and the elastic mechanism 3, thereby controlling the impact energy absorption efficiency. The cells constituting the bistable vibration absorbing unit are periodically arranged on the beam-plate structure of the substrate 4 to construct a bistable mechanical metamaterial structure, which can achieve low-frequency, broadband, and efficient vibration suppression and efficient impact attenuation effects under additional mass conditions.

[0053] Example 2

[0054] This embodiment discloses a bistable mechanical metamaterial structure, which includes several bistable vibration absorbing units according to Embodiment 1. Specifically, the bistable vibration absorbing units are arranged in an array in one direction on a substrate requiring vibration reduction and impact resistance, or in an array in two orthogonal directions on the substrate requiring vibration reduction and impact resistance. Alternatively, the bistable vibration absorbing units may be arranged in an array in three orthogonal directions on the substrate requiring vibration reduction and impact resistance, or in a circular array or cylindrical array on the substrate requiring vibration reduction and impact resistance.

[0055] This embodiment also discloses a method for preparing the aforementioned bistable mechanical metamaterial structure, which primarily involves determining the resonant frequency, equivalent negative stiffness coefficient, nonlinear stiffness coefficient, track coefficient, track protrusion height, and spring stiffness coefficient of the bistable vibration absorbing unit in Example 1. Specifically, the method for preparing the bistable mechanical metamaterial structure in this embodiment primarily includes the following steps:

[0056] Step 1: determining the resonant frequency of the bistable vibration absorbing unit based on the target vibration frequency band;

[0057] Step 2: determining the equivalent negative stiffness and nonlinear stiffness coefficient of the bistable vibration absorbing unit based on the resonant frequency and the additional mass limit of the bistable vibration absorbing unit;

[0058] Step 3, determining the track coefficient, protrusion height and spring stiffness coefficient of the track according to the equivalent negative stiffness and nonlinear stiffness coefficient;

[0059] Step 4: designing a bistable vibration absorbing unit according to the parameters determined in steps 1 to 3, and combining it with a matrix that needs vibration reduction and impact resistance to form a cell of the bistable mechanical metamaterial;

[0060] Step 5: Arrange multiple cells of the bistable mechanical metamaterial according to a preset array to form a bistable mechanical metamaterial structure.

[0061] According to the principle of local resonance type mechanical metamaterial, the local resonance band gap of the mechanical metamaterial composed of the bistable vibration absorbing unit in this embodiment will be determined by the resonance frequency of the bistable vibration absorbing unit. In order to achieve the low-frequency and broadband vibration suppression and shock attenuation effect of the bistable mechanical metamaterial, this embodiment sets the resonant frequency The design is near the first-order natural frequency of the matrix (generally 80%~100% of the first-order natural frequency of the matrix is ​​considered).

[0062] In the specific application process of the bistable mechanical metamaterial in this embodiment, when the vibration amplitude or impact excitation is small, the vibrator mainly vibrates near the steady-state position, mainly showing the linear metamaterial characteristics, and suppressing vibration and impact to a limited extent near the band gap frequency; when the vibration amplitude is large or the impact excitation is severe, the vibrator will undergo a steady-state jump, thereby generating negative stiffness and nonlinear dynamic effects, efficiently dissipating the transfer matrix energy, and achieving low-frequency broadband vibration suppression and impact attenuation. The resonant frequency of the bistable vibration absorption unit is The equivalent linear stiffness of the bistable vibration-absorbing unit near the steady-state position and the mass of the oscillator are jointly determined. Analysis shows that the mass of the oscillator has no significant effect on the vibration suppression and impact attenuation effects of the bistable mechanical metamaterial. Therefore, a smaller oscillator mass can be selected to achieve low-frequency vibration suppression and impact attenuation effects while having a lower added mass ratio. In the specific implementation process, when the specific vibration reduction frequency range of the bistable mechanical metamaterial is determined, the linear resonant frequency of the bistable vibration-absorbing unit can be determined within 80% to 100% of the first-order natural frequency of the substrate according to actual needs. , at the linear resonant frequency Under the premise that the structural dimensions, additional mass ratio and other limiting requirements of the bistable vibration absorption unit are known, a lower vibrator mass can also be determined while meeting the vibration shock suppression effect. m .

[0063] According to the dynamic characteristics of the bistable vibration absorbing unit, when the response amplitude is small, the oscillator only moves near one of the equilibrium positions, which is close to the linear mechanical metamaterial characteristics, and the resonant frequency is:

[0064]

[0065] in, is the linear stiffness of the bistable vibration absorbing unit at the equilibrium position;

[0066] According to the linear resonance frequency determined in step 1 and the vibrator mass m , the linear stiffness of the bistable vibration absorbing unit at the equilibrium position can be calculated , and the linear stiffness of the bistable vibration absorbing unit at the equilibrium position is Also satisfied ,in, k is the equivalent negative stiffness of the bistable vibration absorbing unit, k n is the nonlinear stiffness coefficient of the bistable vibration absorbing unit. Under the premise that the size of the bistable vibration absorbing unit is known and the working load is limited, its stable distance It can be determined according to the actual size of the bistable vibration absorbing unit, and further according to the linear stiffness , the equivalent negative stiffness can be calculatedk and nonlinear stiffness coefficient k n .

[0067] According to the dynamic characteristics of a single bistable vibration absorbing unit, the system motion differential equation can be expressed as:

[0068]

[0069] in, m is the oscillator mass, c is the damping coefficient, u is the excitation displacement, then the absolute displacement of the system motion is x + u ;

[0070] refer to Figure 5 According to the force analysis of the bistable unit, the bistable effect is achieved by the horizontal spring compression through the track to generate a vertical force. The force on the oscillator during the movement process is F ( x ) with displacement x The changing rules are:

[0071]

[0072] in, y To design the track trajectory, k y is the spring stiffness coefficient, θ is the orbital inclination;

[0073] In order to realize the bistable unit force displacement relationship is The expression of the orbital trajectory should be In order to ensure the realization of negative stiffness, the track profile equation of this embodiment is designed as .in, a is the parabolic trajectory coefficient, r 1 is the height of the track protrusion, then the stable distance of the bistable unit is .consider y Minimum x =0, bring the relevant design parameters into F ( x ) with displacement x The change law of can obtain the bistable unit force-displacement relationship as follows:

[0074]

[0075] It can be seen from this that the equivalent negative stiffness of the bistable vibration absorbing unit is , nonlinear stiffness coefficient The parabola trajectory coefficient a , Track protrusion height r 1 and horizontal spring rate k y related.

[0076] Due to the limited roughness of the metal structure processing surface, there is a friction coefficient between the contact between one end of the sleeve and the track. f y , when the track protrusion height r 1 is larger, steady-state distance When the orbital inclination is small, θ If it is too small, self-locking will occur due to sliding friction. a Determined by the steady-state distance and the protrusion height (i.e. ), the specific value is set according to the bending vibration amplitude and force of the vibrator in actual use. Theoretically, the larger the steady-state distance, the smaller the protrusion height, and the smaller the trajectory coefficient, the vibrator can produce a steady-state jump under the action of a very weak force, and efficiently dissipate the matrix energy. However, since the equivalent negative stiffness coefficient and nonlinear stiffness coefficient mainly depend on the parabolic trajectory coefficient of the track a , Track protrusion height r 1. Both should not be too small, otherwise the negative stiffness coefficient and nonlinear stiffness coefficient of the bistable vibration absorbing unit will be too small, which is not conducive to vibration control and impact suppression. Therefore, the steady-state distance designed in step 2 of this embodiment is and the calculated equivalent negative stiffness k and nonlinear stiffness coefficient k n Under the premise of 、 as well as , the track protrusion height can be calculated r 1. Orbital parabola trajectory coefficient a and spring rate k y .

[0077] Spring rate k y The calculation formula is:

[0078]

[0079] in, d is the spring wire diameter, D is the outer diameter of the spring, n is the effective working turns of the spring, G is the shear modulus of the material, E is the Young's modulus of the material, is the Poisson's ratio of the material;

[0080] The spring material in this embodiment is spring steel, and its material parameters are determined. k y After the determination, the appropriate spring wire diameter, outer diameter and number of working turns can be selected according to the structural size, additional mass and other limitations of the bistable vibration absorbing unit. For example, in this embodiment, considering the design size limitation of the bistable vibration absorbing unit, the designed stable distance =2.5mm, track protrusion height r 1=1.5mm, calculate the track coefficient a =240; horizontal spring length is 11.5mm, wire diameter d =0.4mm, outer diameter D =4mm, number of circles n =14, oscillator mass m = 25g. The force-displacement curve of the bistable nonlinear unit is finally calculated as follows Figure 6 As shown in the figure, within the working stroke (-2.5~2.5mm), the curve shows a good bistability effect.

[0081] During the specific implementation of step 5, the entire bistable mechanical metamaterial is composed of a periodic array of bistable vibration-absorbing units. A one-dimensional nonlinear mechanical metamaterial beam is composed of an array of cells in a single direction; a two-dimensional nonlinear mechanical metamaterial plate is composed of an array of cells in two orthogonal directions; and a three-dimensional nonlinear mechanical metamaterial structure is composed of a periodic array of cells in a circumferential direction or in three orthogonal directions. Cells are arranged circumferentially at a periodic angle or in an axial array.

[0082] According to Steps 1 to 5 above, various specific structures of bistable vibration absorbing units and bistable mechanical metamaterials can be obtained. To verify the vibration suppression effect of the bistable mechanical metamaterial obtained by the preparation method of this embodiment, the following is a further explanation based on the specific example of a one-dimensional cantilever beam bistable mechanical metamaterial.

[0083] According to the linear natural frequency of the bistable vibration absorbing unit near the stable position, the bistable nonlinear local resonance frequency is determined f 0. The natural frequency vibration of the bistable vibration absorbing unit is caused by the exciter, and the velocity signal of the vibrator is measured by the laser vibrometer to analyze its natural frequency. f 0=40Hz.

[0084] The bistable mechanical metamaterial structure is constructed by periodically arranging the above-mentioned bistable vibration absorbing units on a finite beam-plate structure. Taking a one-dimensional cantilever beam as an example, 4×1 bistable vibration absorbing units are attached to the cantilever beam base to form a bistable mechanical metamaterial cantilever beam structure, as shown in FIG. Figure 7 As shown in (a), the average mass of the attached oscillator ism r =25g. Thickness of the cantilever beam of the mechanical metamaterial h =16mm, length L =500mm, lattice constant a =100mm.

[0085] Next, impact vibration test experiments will be carried out to test the dynamic response characteristics of the bistable mechanical metamaterial cantilever beam under impact excitation, and verify the effectiveness of the design method of the lightweight, low-frequency, broadband, and high-efficiency impact-resistant bistable vibration absorption unit.

[0086] For the one-dimensional cantilever beam structure, in the experimental test, one end of the metamaterial cantilever beam is fixedly suspended on the bracket to simulate the fixed constraint boundary, such as Figure 7 As shown in (a). Impact excitation is applied to the side of the bistable metamaterial cantilever beam near the free end. The specific excitation method is the swinging and falling impact of a steel ball. Different excitation amplitudes can be achieved by adjusting the mass of the steel ball and the drop height, as shown in Figure 7 (b) The vibration response near the center of the cantilever beam is measured using a laser vibrometer.

[0087] The vibration response of the cantilever beam without the bistable vibration absorbing unit was tested as a reference value. The bistable mechanical metamaterial one-dimensional cantilever beam is composed of four bistable vibration absorbing units arranged periodically on the cantilever beam. At this time, the added mass ratio of the structure is 11.57%. The transient vibration response and spectrum of the metamaterial cantilever beam under the same impact excitation are shown in Figure 2. Figure 8 Compared to a cantilever without a bistable vibration-absorbing unit, the bistable metamaterial cantilever exhibits an average attenuation of 9.3 dB across the dense resonant peaks in the 30-500 Hz range, demonstrating significant vibration reduction. Comparing the impact time-domain peaks, the cantilever effectively reduces the time-domain peaks, with the first impact peak reduced by up to 35%. Furthermore, the addition of the bistable vibration-absorbing unit accelerates impact peak attenuation, providing effective shock resistance. This demonstrates that strong bistable transitions and nonlinear effects can be achieved under impact excitation, enabling low-frequency, broadband vibration reduction and efficient shock resistance.

[0088] The above experimental results show that the bistable mechanical metamaterial cantilever beam constructed according to the bistable vibration absorbing unit designed in this embodiment can achieve low-frequency, broadband, high-efficiency vibration reduction and high-efficiency impact attenuation effects with light additional mass.

[0089] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made by using the contents of the present invention description and drawings under the inventive concept of the present invention, or direct / indirect application in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A bistable vibration absorbing unit, characterized in that: It includes a track frame, a vibrator and an elastic mechanism; Opposite tracks are provided on both sides of the track frame, and the profile of the tracks is a parabola; The vibrator is located between the tracks on both sides of the track frame, the first end of the elastic mechanism is connected to the side of the vibrator, and the second end of the elastic mechanism is slidably connected to the track on the corresponding side; The elastic mechanism has a degree of freedom of compression or extension, and the elastic mechanism has a stroke of displacement along the track.

2. The bistable vibration absorbing unit according to claim 1, characterized in that: The elastic mechanism includes a spring and a sleeve. A countersunk hole is provided on the side of the vibrator. The sleeve is a cylindrical structure with one end open. The first end of the spring is connected to the bottom of the countersunk hole, the second end of the spring is embedded in the open end of the sleeve and connected to the bottom of the sleeve, and the closed end of the sleeve is in contact with the track.

3. The bistable vibration absorbing unit according to claim 2, characterized in that: The open end of the sleeve is coaxially embedded in the countersunk hole, and the outer wall of the sleeve is clearance-matched with the hole wall of the countersunk hole.

4. The bistable vibration absorbing unit according to claim 2 or 3, characterized in that: There are four rails and four elastic mechanisms, and the elastic mechanisms correspond one to one with the rails; The four tracks are distributed in a rectangular array on the track frame. The first end of the elastic mechanism is connected to the side of the vibrator, and the second end of the elastic mechanism is slidably connected to the corresponding track.

5. The bistable vibration absorbing unit according to claim 4, characterized in that: The springs in the four elastic mechanisms have the same stiffness, and the springs have prestress.

6. A bistable mechanical metamaterial structure, characterized in that: comprising the bistable vibration absorbing unit according to any one of claims 1 to 5; The bistable vibration absorbing units are distributed in an array in one direction; or The bistable vibration absorbing units are distributed in an array in two orthogonal directions; or The bistable vibration absorbing units are distributed in an array in three orthogonal directions; or The bistable vibration absorbing units are distributed in a circular array; or The bistable vibration absorbing units are distributed in a cylindrical array.

7. A method for preparing a bistable mechanical metamaterial structure according to claim 6, characterized in that: The steps include: Step 1: determining the resonant frequency of the bistable vibration absorbing unit based on the target vibration frequency band; Step 2: determining the equivalent negative stiffness and nonlinear stiffness coefficient of the bistable vibration absorbing unit based on the resonant frequency and the additional mass limit of the bistable vibration absorbing unit; Step 3, determining the track coefficient, protrusion height, and spring stiffness coefficient of the track according to the equivalent negative stiffness and the nonlinear stiffness coefficient; Step 4: designing a bistable vibration absorbing unit according to the parameters determined in steps 1 to 3, and combining it with a matrix designed for vibration reduction and impact resistance to form a cell of the bistable mechanical metamaterial; Step 5: Arrange multiple cells of the bistable mechanical metamaterial according to a preset array to form a bistable mechanical metamaterial structure.

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