Hybrid origami metamaterials, unit cells, vibration isolation methods based on kresling and hydroelastic kirigami

Abstract

The present disclosure provides a hybrid origami metamaterial based on Kresling and water bomb-based origami, a unit cell and a vibration isolation method, and relates to the technical field of vibration isolation. The unit cell comprises a panel and a core; the panel comprises a first panel and a second panel arranged in parallel, and the first panel and the second panel are both hexagonal prism structures formed based on Kresling origami; the core comprises a plurality of sub-units, the plurality of sub-units are uniformly distributed around the axis of the panel and are arranged between the first panel and the second panel; each sub-unit comprises four beam structures formed based on water bomb-based origami, and one end of the four beam structures is respectively connected to two adjacent vertices of the first panel and two vertices of the second panel corresponding to the vertices of the first panel. The unit cell of the hybrid origami metamaterial based on Kresling origami and water bomb-based origami can increase the band gap range of the metamaterial and improve the vibration isolation performance of the structure.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of vibration isolation, in particular, to a hybrid origami metamaterial based on Kresling and hydroelastic origami, a unit cell, and a vibration isolation method. BACKGROUND

[0002] Vibration is widespread in engineering projects, and in actual engineering applications, vibration can cause equipment damage or failure, therefore, suppressing vibration in equipment becomes an important means to protect engineering equipment. Passive isolators are concerned due to their simple structure and are applied to equipment to isolate vibration and protect equipment.

[0003] Metamaterials are some artificial composite structures or composite materials with super-normal physical properties that natural materials do not have, and due to their excellent mechanical properties, they provide a new strategy for the design of passive vibration isolators. However, the vibration isolation effect of the metamaterials currently applied in vibration isolators is not good, especially the isolation effect of low-frequency vibration is poor, and the band gap range is small, which cannot achieve the ideal vibration isolation effect.

[0004] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present disclosure, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] Therefore, a hybrid origami metamaterial based on Kresling and hydroelastic origami, a unit cell, and a vibration isolation method are provided, which can increase the band gap range of the metamaterial and improve the vibration isolation effect.

[0006] Other characteristics and advantages of the present disclosure will become apparent from the following detailed description, or will be learned by practice of the present disclosure.

[0007] According to one aspect of the present disclosure, a unit cell of a hybrid origami metamaterial based on Kresling and hydroelastic origami is provided, the unit cell comprising:

[0008] a panel, the panel comprising a first panel and a second panel, the first panel and the second panel are arranged in parallel, and the first panel and the second panel are both hexagonal prism structures formed based on Kresling origami, each vertex of the first panel corresponds to each vertex of the second panel one by one and is located on the same straight line;

[0009] a core, the core comprising a plurality of subunits, the plurality of subunits are uniformly distributed around an axis of the panel and are arranged between the first panel and the second panel;

[0010] Each of the sub-units comprises four beam structures, each of the beam structures being formed based on a water bomb-based base paper of a peak line, one end of the four beam structures being connected to form a vertex of the sub-unit, the other end of two of the beam structures being connected to adjacent two vertices of the first panel respectively, and the other end of the other two of the beam structures being connected to vertices of the second panel corresponding to the adjacent two vertices of the first panel respectively.

[0011] In some embodiments of the present disclosure, based on the foregoing scheme, a height of the unit cell is a maximum vertical distance between a surface of the first panel and a surface of the second panel, and a length of the beam structure and the height of the unit cell satisfy a first relationship;

[0012] The first relationship is H < 2L, where H is the height of the unit cell, and L is the length of the beam structure.

[0013] In some embodiments of the present disclosure, based on the foregoing scheme, a side length of the panel and the length of the beam structure satisfy a second relationship;

[0014] The second relationship is C < 2L, where C is the side length of the panel, and L is the length of the beam structure.

[0015] In some embodiments of the present disclosure, based on the foregoing scheme, the side length of the panel, the length of the beam structure, and the height of the unit cell satisfy a third relationship;

[0016] The third relationship is H 2 + C 2 < 4L 2 , where H is the height of the unit cell, L is the length of the beam structure, and C is the side length of the panel.

[0017] According to another aspect of the present disclosure, a vibration isolation method of a unit cell of a hybrid paper metamaterial based on Kresling and water bomb-based paper is provided, applied to the unit cell of the paper metamaterial, the method comprising:

[0018] establishing a structural dynamics model of the unit cell of the paper metamaterial;

[0019] calculating and obtaining a bandgap characteristic of the unit cell of the paper metamaterial according to the model;

[0020] adjusting geometric parameters of the unit cell of the paper metamaterial according to a target bandgap, so that the bandgap of the unit cell of the paper metamaterial covers the target bandgap.

[0021] In some embodiments of the present disclosure, based on the foregoing scheme, adjusting the geometric parameters of the unit cell of the paper metamaterial according to the target bandgap, so that the bandgap of the unit cell of the paper metamaterial covers the target bandgap, comprises:

[0022] adjusting thickness of the panel in the unit cell to change mass of the origami metamaterial;

[0023] and / or, adjusting height of the unit cell, side length of the panel, diameter of the beam structure, length of the beam structure to change stiffness of the origami metamaterial.

[0024] According to another aspect of the present disclosure, a hybrid origami metamaterial based on Kresling and hydroelastic origami is provided, the origami metamaterial comprising:

[0025] a plurality of the unit cells, the plurality of the unit cells being connected in series along the axis direction of the first panel, and adjacent unit cells being connected by the connection of the panel.

[0026] In some embodiments of the present disclosure, based on the foregoing scheme, the heights of the plurality of unit cells are equal.

[0027] In some embodiments of the present disclosure, based on the foregoing scheme, the metamaterial comprises a plurality of unit cell groups, each of the unit cell groups comprising at least five unit cells, and the heights of the plurality of unit cells in each of the unit cell groups being equal, and the heights of the unit cells in the plurality of unit cell groups being arranged in a gradient along the axis direction of the panel.

[0028] According to another aspect of the present disclosure, a vibration isolation method of a hybrid origami metamaterial based on Kresling and hydroelastic origami is provided, applied to the origami metamaterial, the method comprising:

[0029] establishing a structural dynamics model of the origami metamaterial;

[0030] calculating bandgap characteristics of the origami metamaterial according to the model;

[0031] adjusting geometric parameters of the origami metamaterial according to a target bandgap, so that the bandgap of the origami metamaterial covers the target bandgap.

[0032] According to a first aspect of the present disclosure, a unit cell of an origami metamaterial is provided, comprising a panel and a core connected together, the panel being a hexagonal prism structure formed based on Kresling origami, and the core comprising a plurality of subunits, each of the subunits being formed based on hydroelastic origami, and the plurality of subunits being uniformly distributed around the axis of the panel. By hybridizing the unit cell based on two different origami structures, the bandgap range of the metamaterial can be increased, mechanical vibration can be effectively isolated, wideband low-frequency bandgap can be achieved, the structure mass can be reduced, and the adverse effects of vibration can be avoided.

[0033] In a second aspect of the present disclosure, a vibration isolation method of a unit cell of a paper metamaterial is provided, and the geometric parameters of the unit cell can be adjusted according to a target band gap so that the band gap of the unit cell covers the target band gap, thereby achieving the purpose of effectively isolating vibration.

[0034] In a third aspect of the present disclosure, a paper metamaterial is provided, and the vibration isolation of a larger frequency and band gap can be achieved by superimposing the band gaps of the unit cells, thereby avoiding damage to the equipment.

[0035] In a fourth aspect of the present disclosure, a vibration isolation method of a paper metamaterial is provided, and the geometric parameters of the paper metamaterial are adjusted according to a target band gap so that the band gap of the paper metamaterial covers the target band gap, thereby achieving the purpose of effectively isolating vibration.

[0036] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0037] The accompanying drawings, which are incorporated into and form part of the specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure. Obviously, the drawings in the following description are only some embodiments of the present disclosure, and other drawings can be obtained from these drawings without creative labor for those skilled in the art.

[0038] Figure 1 FIG. 1 is a schematic diagram of a three-dimensional structure of a unit cell of a paper metamaterial in an exemplary embodiment of the present disclosure.

[0039] Figure 2 FIG. 2 is a side view of a unit cell of a paper metamaterial in an exemplary embodiment of the present disclosure.

[0040] Figure 3 FIG. 3 is a top view of a unit cell of a paper metamaterial in an exemplary embodiment of the present disclosure.

[0041] Figure 4 FIG. 4 is a flowchart of a vibration isolation method of a unit cell of a paper metamaterial in an exemplary embodiment of the present disclosure.

[0042] Figure 5 FIG. 5 is a schematic diagram of a simplified model of a structural dynamics model of a unit cell of a paper metamaterial in an exemplary embodiment of the present disclosure.

[0043] FIG. 6(a) is a schematic diagram of the relationship between the normalized height of a unit cell of a paper metamaterial and the structural band gap in an exemplary embodiment of the present disclosure.

[0044] FIG. 6(b) is a schematic diagram of the relationship between the edge length of a normalized panel of a unit cell of a paper metamaterial and the structural band gap in an exemplary embodiment of the present disclosure.

[0045] Figure 6(c) is a diagram showing the relationship between the diameter of the normalized beam structure and the structural band gap of a unit cell of a paper metamaterial according to an example embodiment of the present disclosure.

[0046] Figure 6(d) is a diagram showing the relationship between the thickness of the normalized panel and the structural band gap of a unit cell of a paper metamaterial according to an example embodiment of the present disclosure.

[0047] Figure 7 Figure 7 is a diagram showing a three-dimensional structure of a paper metamaterial according to an example embodiment of the present disclosure.

[0048] Figure 8 Figure 8 is a diagram showing a three-dimensional structure of another paper metamaterial according to an example embodiment of the present disclosure.

[0049] Figure 9 Figure 9 is a front view of a paper metamaterial according to an example embodiment of the present disclosure. Figure 8

[0050] Figure 10 Figure 10 is a diagram showing the band gap of a folded paper metamaterial with unit cells of two heights in series according to an example embodiment of the present disclosure.

[0051] Figure 11 Figure 11 is a diagram showing the band gap of a folded paper metamaterial with unit cells of three heights in series according to an example embodiment of the present disclosure.

[0052] Figure 12 Figure 12 is a flowchart of a method of vibration isolation of a paper metamaterial according to an example embodiment of the present disclosure.

[0053] In the drawings, the same reference numerals are used to represent the same elements throughout the several views.

[0054] 10, unit cell; 101, group of unit cells; 100, panel; 110, first panel; 120, second panel; 200, core; 210, subunit; 211, first beam structure; 212, second beam structure; 213, third beam structure; 214, fourth beam structure. DETAILED DESCRIPTION

[0055] Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments, however, can be implemented in many different forms and should not be construed as limited to the implementations set forth herein; rather, these implementations are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. Like reference numerals refer to like elements throughout the several views of the drawings, and description of these will be omitted. Further, the drawings are diagrammatic and schematic and are not necessarily to scale.

[0056] ​Although relative terms are used in this specification, such as "upper", "lower", to describe one component's relative position to another component of the icon, these terms are used herein for convenience only and are not intended to limit the scope of the application, for example, according to the orientation of the examples shown in the drawings. It is to be understood that if the device of the icon is turned upside down, the component described as "upper" will become the component described as "lower". When a structure is "on" another structure, it can mean that the structure is formed integrally on the other structure, or that the structure is "directly" disposed on the other structure, or that the structure is "indirectly" disposed on the other structure through another structure.

[0057] The terms "one", "a", "an", "the", and "at least one" are used to indicate the existence of one or more elements / components / etc.; the terms "including" and "having" are used to indicate the inclusion of one or more elements / components / etc. in the described steps, elements and / or components, and that not all steps / elements / components are necessarily present; the terms "first", "second", and "third", etc. are merely used to identify the names of the elements, and are not a limitation on the number of elements.

[0058] Vibration is one of the important factors leading to damage and even failure of equipment, and in order to suppress or isolate vibration, a vibration isolator is arranged on the equipment. At present, the vibration isolator is divided into an active isolator and a passive vibration isolator. The active isolator is seriously limited in practical engineering application due to problems such as complex structure, high cost and signal lag, especially in the equipment with limited space. Therefore, compared with the active isolator, the passive vibration isolator has more engineering application value due to the advantages such as simple structure. However, due to the limitation of material structure, the vibration isolation effect of the passive vibration isolator on some frequency vibrations is not ideal.

[0059] Metamaterial refers to some artificial composite structures or composite materials with super-normal physical properties that natural materials do not have. Due to the excellent mechanical properties of metamaterials, the application of metamaterials in passive vibration isolators can change the vibration isolation performance of passive vibration isolators, so as to achieve the purpose of attenuating or isolating vibration.

[0060] Origami is an ancient art that has attracted widespread attention due to its large storage ratio and excellent mechanical properties. Based on the deformation mechanism of the fold at the fold line of the origami structure, the origami structure can be applied to metamaterials to change the performance of the metamaterials. However, the vibration isolation performance of the current origami metamaterial is not ideal.

[0061] Based on this, the disclosure embodiment provides a unit cell of a hybrid origami metamaterial based on Kresling and water bomb-based origami, as shown in the figure, the unit cell 10 comprises a panel 100 and a core 200. Figure 1

[0062] ​The panel 100 includes a first panel 110 and a second panel 120, the first panel 110 and the second panel 120 are arranged in parallel, and the first panel 110 and the second panel 120 are both hexagonal prism structures formed based on Kresling origami, the vertices of the first panel 110 correspond to the vertices of the second panel 120 one by one and are located on the same straight line.

[0063] The core 200 includes a plurality of sub-units 210, the plurality of sub-units 210 are uniformly distributed around the axis of the panel 100 and are arranged between the first panel 110 and the second panel 120; each sub-unit 210 includes four beam structures, each beam structure is formed based on a peak line of water bomb-based origami, one end of the four beam structures connects to form a vertex of the sub-unit 210, the other end of two beam structures is connected to two adjacent vertices of the first panel 110 respectively, and the other end of the other two beam structures is connected to the vertices of the second panel 120 corresponding to the two adjacent vertices of the first panel 110 respectively.

[0064] The unit cell 10 of the origami metamaterial provided by the present disclosure is connected by the panel 100 formed based on Kresling origami and the sub-unit 210 with the beam structure formed based on water bomb-based origami to form the unit cell 10 of the metamaterial, which can increase the band gap range of the origami metamaterial, improve the isolation effect of the origami metamaterial on vibrations of various frequencies, and avoid the adverse effects of vibrations.

[0065] The various parts of the unit cell of the origami metamaterial provided by the embodiments of the present disclosure will be described in detail below in combination with the drawings:

[0066] In the embodiments provided by the present disclosure, the unit cell 10 of the origami metamaterial includes a panel 100, as shown in Figure 1 , Figure 2 and Figure 3 The panel 100 includes a first panel 110 and a second panel 120, the first panel 110 and the second panel 120 are arranged in parallel, and the first panel 110 and the second panel 120 are both hexagonal prism structures formed based on Kresling origami, the vertices of the first panel 110 correspond to the vertices of the second panel 120 one by one and are located on the same straight line. The vertical distance between the outer surface of the first panel 110 and the outer surface of the second panel 120 is the height H of the unit cell 10.

[0067] The first panel 110 and the second panel 120 can be made of metal materials or non-metal materials, for example, can be formed of polyurethane, polyethylene, polystyrene, polylactic acid or steel, alloy and the like, and can be prepared by casting, laser cutting, 3D printing and the like. The specific material and forming process of the first panel 110 and the second panel 120 are not limited in the present disclosure, which can be adjusted adaptively according to actual application requirements.

[0068] In some embodiments, the first panel 110 and the second panel 120 are arranged in parallel, for example, the first panel 110 and the second panel 120 are parallel to the horizontal plane, the orthographic projection of the first panel 110 and the second panel 120 on the horizontal plane coincide, and the projection of the first panel 110 and the second panel 120 is a regular hexagon, and the axis of the first panel 110 and the second panel 120 coincide. The side length of the first panel 110 and the second panel 120 is C, and the side length of the first panel 110 and the second panel 120 is equal. In the axial direction of the first panel 110 and the second panel 120, the thickness of the first panel 110 is Th1, and the thickness of the second panel 120 is Th2, wherein the thickness of the first panel 110 and the thickness of the second panel 120 can be the same or different, preferably Th1 = Th2.

[0069] In the embodiments provided in the present disclosure, the unit cell 10 of the origami metamaterial includes a core 200, as shown in Figure X The core 200 includes a plurality of sub-units 210, which are distributed between the first panel 110 and the second panel 120 in the circumferential direction with the axis of the panel 100 as the center of symmetry.

[0070] Each sub-unit 210 includes four beam structures, as shown in Figure 2 Specifically, the four beam structures can be a first beam structure 211, a second beam structure 212, a third beam structure 213, and a fourth beam structure 214. The four beam structures correspond to the four peak lines in the water bomb-based origami, respectively. The first end of the first beam structure 211, the first end of the second beam structure 212, the first end of the third beam structure 213, and the first end of the fourth beam structure 214 converge into a vertex, which can be used as the vertex of the sub-unit 210, and the vertex of the sub-unit 210 is arranged towards the inside of the structure. The second end of the first beam structure 211 and the second end of the second beam structure 212 are connected to two vertices of the first panel 110, respectively, and the second end of the third beam structure 213 and the second end of the fourth beam structure 214 are connected to two vertices of the second panel 120, respectively. The two vertices of the first panel 110 and the two vertices of the second panel 120 correspond one-to-one. The vertical distance between each beam structure end point and the axis of the panel 100 can be equal to the side length of the panel 100, for example, the vertical distance between the end point of the second end of the first beam structure 211 and the axis of the first panel 110 can be C, and the vertical distance between the end point of the other beam structure and the axis of the panel 100 is the same, which will not be described here.

[0071] According to the structure of the single sub-unit 210, the single sub-unit 210 is rotated around the axis of symmetry of the axis of the first panel 110 and the second panel 120 in the circumferential direction to form a plurality of sub-units 210 connected with the panel 100. Specifically, six sub-units 210 are connected between the first panel 110 and the second panel 120. The four beam structures of each sub-unit 210 can be cylindrical structures, which can have equal lengths and equal diameters. The length of the beam structure is L, and the diameter of the beam structure is D.

[0072] The core 200 can be made of metal materials or non-metal materials, for example, can be thermoplastic polyurethane, polylactic acid, polystyrene or alloy materials, etc., which can be prepared by casting, laser cutting, 3D printing and other processes. For example, 3D printing process technology can be used to make, respectively form each beam structure, and then connect to form the sub-unit 210 of the core 200; or simultaneously form a plurality of sub-units 210 to form the core 200. The specific material and forming process of the core 200 are not limited in the disclosure, which can be adjusted according to the actual application requirements.

[0073] After the panel 100 and the core 200 are formed, the panel 100 and the core 200 can be connected to form the unit cell 10. The panel 100 and the core 200 can be connected by a fixed connection, of course, other connection methods can also be used, which are not limited in the disclosure.

[0074] In the embodiments provided in the disclosure, in order to effectively isolate mechanical vibration, realize wideband low-frequency bandgap, and at the same time make the origami metamaterial capable of isolating mechanical vibration in a larger frequency range, the structure parameters in the panel 100 and the core 200 in the unit cell 10 of the origami metamaterial need to satisfy the following relationships: the length of the beam structure and the height of the unit cell 10 satisfy the first relationship H < 2L, where H is the height of the unit cell 10, and L is the length of the beam structure; the side length of the panel 100 (the first panel 110 or the second panel 120) and the length of the beam structure satisfy the second relationship C < 2L, where C is the side length of the panel 100, and L is the length of the beam structure; the side length of the panel 100, the length of the beam structure and the height of the unit cell 10 satisfy the third relationship H < 2C, where H is the height of the unit cell 10, C is the side length of the panel 100, and L is the length of the beam structure; the side length of the panel 100, the length of the beam structure and the height of the unit cell 10 satisfy the fourth relationship C < 4L, where H is the height of the unit cell 10, L is the length of the beam structure, and C is the side length of the panel 100. 2 2 2 where H is the height of the unit cell 10, L is the length of the beam structure, and C is the side length of the panel 100.

[0075] ​​In some specific embodiments, as shown in Table 1, specific values of the geometric parameters in the origami metamaterial unit cell 10 are given in Table 1, the thickness Th1 of the first panel 110 (the thickness Th2 of the second panel 120) is 6 mm, the length L of the beam structure, the side length C of the panel 100, R are all 60 mm, the diameter D of the beam structure is 4 mm, the number N of the sides of the panel 100 is 6, and the height H of the unit cell 10 is 50 mm. According to the relationship between the geometric parameters in the above embodiment, the specific values of the geometric parameters provided in Table 1 all satisfy the above relationship, so that the origami metamaterial has good vibration isolation performance.

[0076]

[0077] Table 1

[0078] The origami metamaterial unit cell 10 provided by the present disclosure is connected by the panel 100 formed based on the Kresling origami and the sub-unit 210 having the beam structure formed based on the water bomb-based origami, to form the unit cell 10 of the metamaterial, which can increase the band gap range of the origami metamaterial, improve the vibration isolation effect of the origami metamaterial on various frequencies, and avoid the adverse effects of vibration.

[0079] The present disclosure provides a vibration isolation method for an origami metamaterial unit cell, as shown in Figure 4 The vibration isolation method is applied to the above-mentioned origami metamaterial unit cell, and includes steps S110-S130.

[0080] Step S110: establishing a structural dynamics model of the origami metamaterial unit cell;

[0081] Step S120: calculating and obtaining the band gap characteristics of the origami metamaterial unit cell according to the model;

[0082] Step S130: adjusting the geometric parameters of the origami metamaterial unit cell according to the target band gap, so that the band gap of the origami metamaterial unit cell covers the target band gap.

[0083] The vibration isolation method for the origami metamaterial unit cell provided by the present disclosure adjusts the geometric parameters of the unit cell so that the band gap of the origami metamaterial unit cell covers the target band gap, which can increase the band gap range of the origami metamaterial and improve the vibration isolation performance of the origami metamaterial.

[0084] The steps of the vibration isolation method for the origami metamaterial unit cell provided by the present disclosure will be described in detail below in combination with the accompanying drawings:

[0085] In step S110, a structural dynamics model of the unit cell 10 of the origami metamaterial is established. Based on the unit cell 10 provided in the above embodiment, a dynamics model of the unit cell 10 is established. Specifically, it can be assumed that the material of the structure is linear elastic, homogeneous and isotropic, for example, the material parameters can be as shown in Table 2. The unit cell 10 is placed in a three-dimensional coordinate system, and in order to facilitate the analysis of the mechanical properties of the structure, the structure in the three-dimensional coordinate system is simplified, as shown in Figure 5 the unit cell 10 can be simplified as a mass-spring-mass model structure, so as to simplify the complexity of subsequent dynamics calculation of the structure.

[0086]

[0087] Table 2

[0088] In step S120, the bandgap characteristics of the unit cell 10 of the origami metamaterial are obtained according to the model calculation. By using model simulation technology, the bandgap characteristics of the elastic wave in the unit cell 10 are obtained by performing dynamics calculation on the simplified model of the structure formed in step S110.

[0089] By performing dynamics calculation and analysis on the simplified model of the structure shown in Figure 5 In the above model, mass and support stiffness are the main factors affecting the bandgap characteristics of the structure. In the unit cell 10 of the origami metamaterial, the mass is determined by the mass of the panel 100 in the unit cell 10, and the mass of the panel 100 is determined by the thickness of the first panel 110 and the second panel 120, that is, changing the thickness of the panel 100 can change the mass of the structure; the support stiffness can be determined by the stiffness of the unit cell 10, the side length of the panel 100 and the diameter of the beam structure, that is, changing one or more of the above three geometric parameters can change the support stiffness of the structure, and then the bandgap characteristics of the structure can be changed.

[0090] In some embodiments, since the bandgap characteristics of the structure are determined by mass and support stiffness, when it is necessary to change the bandgap characteristics of the structure, the mass or the support stiffness of the structure can be changed alone, or the mass and the support stiffness can be changed simultaneously, and the geometric parameters affecting the mass and the support stiffness can be selected according to the actual required bandgap characteristics.

[0091] In step S130, the geometric parameters of the unit cell 10 of the origami metamaterial are adjusted according to the target band gap, so that the band gap of the unit cell 10 of the origami metamaterial covers the target band gap. Since the unit cell 10 has multiple geometric parameters that affect the structural mass and support stiffness, in actual engineering applications, the geometric parameters of the structure can be adjusted according to the target band gap to change the band gap characteristics of the structure, so that the band gap of the structure covers the target band gap. The thickness of the panel 100 in the unit cell 10 can be adjusted to change the mass of the origami metamaterial; and / or, the height of the unit cell 10, the side length of the panel 100, the diameter of the beam structure, and the length of the beam structure can be adjusted to change the stiffness of the origami metamaterial.

[0092] Of course, when adjusting the band gap characteristics of the structure, the band gap of the structure can be the same as the target band gap, or the band gap of the structure can have multiple different band gap ranges, and part of the band gap of the structure is the same as the target band gap. The target band gap can be a band gap range including mechanical vibrations that need to be isolated in actual engineering applications, so as to effectively isolate the vibrations.

[0093] The vibration isolation method of the unit cell 10 of the origami metamaterial provided by the present disclosure can increase the band gap range of the origami metamaterial and improve the vibration isolation performance of the origami metamaterial by adjusting the geometric parameters of the unit cell 10 so that the band gap of the unit cell 10 of the origami metamaterial covers the target band gap.

[0094] In specific embodiments provided by the present disclosure, the geometric parameters of the unit cell 10 can include the height H of the unit cell 10, the side length C of the panel 100, the diameter D of the beam structure, the length L of the beam structure, and the thickness Th of the panel 100 (the thickness of the first panel 110 or the thickness of the second panel 120).

[0095] In the model simulation calculation, in order to simplify the calculation process, the above geometric parameters can be normalized first, for example, the height of the unit cell 10 can be normalized as h = H / L, the side length of the panel can be normalized as c = C / L, the diameter of the beam structure (i.e. the slenderness ratio) can be normalized as d = D / L, and the thickness of the panel can be normalized as t = Th / L; the frequency of the material can be normalized as f = (ω x L) / f t , ω is the excitation frequency, G = E / (2 x (1 + v)), f t is the velocity of the shear wave, G is the shear modulus, E is the Young's modulus, v is the Poisson's ratio, and p is the density.

[0096] After normalizing the parameters of the model, the structural dynamics of the model is calculated to obtain the influence of each normalized parameter on the band gap of the unit cell 10, for example, Figure 6(a) to Figure 6(d)As shown in the drawings, in Fig. 6(a), it can be seen that the different heights of the unit cells 10 have different band gap ranges and frequencies; in Fig. 6(b), it can be seen that the different side lengths of the panels 100 have different band gap ranges and frequencies; in Fig. 6(c), it can be seen that the different diameters of the beam structures have different band gap ranges and frequencies; in Fig. 6(d), it can be seen that the different thicknesses of the panels 100 have different band gap ranges and frequencies.

[0097] Through the analysis of the structural geometric parameters, the influence of different geometric parameters on the band gap characteristics of the structure can be obtained, so as to provide a basis for subsequent adjustment of the structural geometric parameters to adapt to the target band gap.

[0098] The disclosure embodiment also provides a hybrid origami metamaterial based on Kresling and water bomb-based origami, as shown in the drawings. Figure 7 As shown in the drawings, the origami metamaterial includes the unit cells 10 of the above origami metamaterial. Wherein, a plurality of unit cells 10 are connected in series along the axis direction of the first panel 110, and adjacent unit cells 10 are connected through the connection of the panels 100.

[0099] The origami metamaterial provided by the disclosure increases the band gap range of the origami metamaterial by connecting a plurality of unit cells 10 in series, so as to further improve the vibration isolation performance.

[0100] The various parts of the origami metamaterial provided by the disclosure embodiment will be described in detail below in combination with the drawings:

[0101] Wherein, the origami metamaterial adopts a plurality of unit cells 10 connected in series, and the band gap ranges of each unit cell 10 can be the same or different, but at least two unit cells 10 have different band gap ranges. By connecting a plurality of unit cells 10 in series, the band gap ranges of different unit cells 10 are superimposed to increase the band gap range of the origami metamaterial.

[0102] Adjacent unit cells 10 can be connected through the connection of the panels 100, for example, the panels 100 of adjacent unit cells 10 can be laminated, and the two are connected by welding or other methods, and the vertices and side lengths of the panels 100 of the adjacent two unit cells 10 can be connected one by one, so that the two connected panels 100 completely coincide to form the series-connected unit cells 10.

[0103] In an embodiment provided by the disclosure, the heights of the plurality of unit cells 10 are equal. In the disclosure, the number of series-connected unit cells 10 is at least 5 to ensure the vibration isolation performance of the metamaterial. For example, as shown in the drawings, Figure 7 20 unit cells 10 with the same height can be connected in series to form an origami metamaterial. In actual application, the number of series-connected unit cells 10 can be selected according to the requirements, which is not limited in the disclosure.

[0104] In another embodiment provided in the present disclosure, as shown in Figure 8 and Figure 9 , the metamaterial includes a plurality of cell groups 101, each cell group 101 includes at least five cells 10, and the heights of the plurality of cells 10 in each cell group 101 are equal, and the heights of the cells 10 in the plurality of cell groups 101 are arranged in a gradient along the axis direction of the panel 100. Among them, the heights of the cells 10 in the plurality of cell groups 101 can be arranged in an increasing or decreasing gradient along the axis direction of the panel 100. Taking three cell groups 101 as an example, the height of the cells 10 in the first cell group 101 is H, the height of the cells 10 in the second cell group 101 can be H+a, and the height of the cells 10 in the third cell group 101 can be H+2a; or the height of the cells 10 in the first cell group 101 is H, the height of the cells 10 in the second cell group 101 can be H-a, and the height of the cells 10 in the third cell group 101 can be H-2a. Of course, the relationship between the heights of the cells 10 in the plurality of cell groups 101 can also be in the form of a geometric progression or other regular forms, which can be selected according to actual engineering structures and design requirements.

[0105] As shown in Figure 8 and Figure 9 , taking an example of five cells included in each cell group 101, in an embodiment, as shown in Figure 8 and Figure 9 , the origami metamaterial includes two series of cell groups 101, wherein the height H1 of the cells 10 in the first cell group 101 is 50mm, the height H2 of the cells 10 in the second cell group 101 is 55mm, and the rest of the geometric parameters are the same: the length L of the beam structure is 50mm, the side length C of the panel 100 is 60mm, the diameter D of the beam structure is 4mm, and the thickness Th of the panel 100 is 6mm.

[0106] The band gap of the first cell group 101 is shown in part (a) of Figure 10 , the band gap of the second cell group 101 is shown in part (b) of Figure 10 , and the band gap of the series of metamaterials is shown in part (c) of Figure 10 . It can be seen that the band gap range of the series of metamaterials includes the band gap of the first cell group 101 and the band gap of the second cell group 101, and the band gap range of the series of metamaterials can be larger than the superposition of the band gap range of the first cell group 101 and the band gap range of the second cell group 101. The series of cell groups 101 can isolate vibrations with a larger band gap range, and the vibration isolation performance is better.

[0107] In another embodiment, the origami metamaterial can further include three sets of the cell groups 101 connected in series, wherein the height H1 of the cell 10 in the first set of the cell groups 101 is 50 mm, the height H2 of the cell 10 in the second set of the cell groups 101 is 55 mm, and the height H3 of the cell 10 in the third set of the cell groups 101 is 60 mm, and the rest of the geometric parameters are the same: the length L of the beam structure is 50 mm, the side length C of the panel 100 is 60 mm, the diameter D of the beam structure is 4 mm, and the thickness Th of the panel 100 is 6 mm.

[0108] The band gap of the first set of the cell groups 101 is as shown in part (d) of FIG. 6, the band gap of the second set of the cell groups 101 is as shown in part (e) of FIG. 6, the band gap of the third set of the cell groups 101 is as shown in part (f) of FIG. 6, and the band gap of the metamaterial connected in series is as shown in part (g) of FIG. 6. Figure 11 Figure 11 Figure 11 Figure 11 As can be seen from FIG. 6, the band gap range of the metamaterial connected in series includes the band gap of the first set of the cell groups 101, the band gap of the second set of the cell groups 101, and the band gap of the third set of the cell groups 101, and the band gap range of the metamaterial connected in series can be larger than the sum of the band gap range of the first set of the cell groups 101, the band gap range of the second set of the cell groups 101, and the band gap range of the third set of the cell groups 101. The cell groups 101 connected in series can isolate vibrations of a larger band gap range, and the vibration isolation performance is better.

[0109] It should be noted that the number of the cell groups 101 connected in series in the origami metamaterial and the height of the cell 10 in each cell group 101 can be selected according to actual engineering requirements, and the disclosure does not make specific limitations.

[0110] The origami metamaterial provided by the disclosure increases the band gap range of the origami metamaterial by connecting a plurality of cells 10 in series, so as to further improve the vibration isolation performance.

[0111] The disclosure also provides a vibration isolation method based on a hybrid origami metamaterial of Kresling and water bomb-based origami, as shown in FIG. 7, the vibration isolation method is applied to the origami metamaterial described above, and includes steps S210-S230. Figure 12

[0112] In step S210, a structural dynamics model of the origami metamaterial is established.

[0113] In step S220, the band gap characteristics of the origami metamaterial are calculated and obtained according to the model.

[0114] In step S230, the geometric parameters of the origami metamaterial are adjusted according to a target band gap, so that the band gap of the origami metamaterial covers the target band gap.

[0115] ​​​​The vibration isolation method for origami metamaterials disclosed herein achieves effective vibration isolation by adjusting the geometric parameters of the metamaterial so that the band gap of the origami metamaterial covers the target band gap, and can also increase the band gap range of the metamaterial, thereby improving the vibration isolation performance of the metamaterial.

[0116] The following will describe in detail each step of the vibration isolation method using origami metamaterials provided in the embodiments of this disclosure, with reference to the accompanying drawings:

[0117] In step S210, a structural dynamics model of the origami metamaterial is established. The modeling process for each unit cell 10 of the origami metamaterial is the same or similar to that provided in the previous embodiment, and will not be repeated here. Connecting multiple unit cells 10 in series yields the dynamics model of the origami metamaterial in this embodiment.

[0118] In step S220, the band gap characteristics of the origami metamaterial are calculated based on the model. For example, such as... Figure 8 As shown, taking two unit cell groups 101 as an example, the first group contains 5 unit cells 10 with a height of H1, and the second group contains 5 unit cells 10 with a height of H2. All other geometric parameters are the same. The two unit cell groups 101 are connected in series to form a paper-like metamaterial. Using simulation methods, a frequency-domain sinusoidal displacement excitation is applied to one end of the metamaterial, and the frequency-domain displacement response is acquired at the other end. Then, the formula T = 20lg(U...) is used... output / U input After calculating the transmission rate, the vibration isolation characteristics of the origami metamaterial are obtained by plotting characteristic curves. Among them, U... output For frequency domain displacement response output, U input The input is a sinusoidal displacement excitation in the frequency domain, and T is the transmission rate.

[0119] In step S230, the geometric parameters of the origami metamaterial are adjusted according to the target bandgap so that the bandgap of the origami metamaterial covers the target bandgap. The adjustment of the geometric parameters of the origami metamaterial is based on the same principle as in step S130, and will not be repeated here. Of course, in addition to adjusting the geometric parameters of each unit cell 10, the number of unit cell groups 101 of the metamaterial and the number of unit cells 10 within each unit cell group 101 can also be adjusted to modify the bandgap characteristics of the metamaterial.

[0120] The vibration isolation method for origami metamaterials disclosed herein achieves effective vibration isolation by adjusting the geometric parameters of the metamaterial so that the band gap of the origami metamaterial covers the target band gap, and can also increase the band gap range of the metamaterial, thereby improving the vibration isolation performance of the metamaterial.

[0121] The origami metamaterials provided by the present disclosure can be applied to mechanical equipment, such as vibration isolation mechanical equipment or structures in the fields of aerospace, automobile, civil engineering, etc., especially for structures with space limitations, such as the limited effective space of a spacecraft, the limited carrying capacity of a rocket, etc. In addition to high vibration isolation performance, the equipment or structure formed by the origami metamaterials provided by the present disclosure also has the characteristics of lightweight and small space occupation, and has great application value for practical engineering applications.

[0122] It should be noted that although the vibration isolation method of the unit cell of the origami metamaterial and the steps of the vibration isolation method of the origami metamaterial in the present disclosure are described in a specific order in the drawings, this does not require or imply that the steps must be performed in this specific order, or that all the steps shown must be performed to achieve the desired results. In addition or alternatively, some steps can be omitted, a plurality of steps can be combined into one step, and / or one step can be divided into a plurality of steps, etc.

[0123] Other embodiments of the present disclosure will be apparent to those skilled in the art upon consideration of the specification and practice of the subject disclosure. The present application is intended to cover any variations, uses or adaptive changes of the present disclosure following the general principles of the present disclosure and including common general knowledge or conventional technical means in the art not disclosed by the present disclosure. The specification and examples are only considered as exemplary, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A unit cell of a hybrid origami metamaterial based on Kresling and waterbomb-based origami, characterized in that, The application relates to a unit cell of a paper-based metamaterial, comprising: a panel, the panel comprising a first panel and a second panel, the first panel and the second panel being arranged in parallel, and each of the first panel and the second panel being a hexagonal prism structure formed based on Kresling origami, each vertex of the first panel corresponding to each vertex of the second panel and being located on a same straight line, the first panel and the second panel having a same orthographic projection on a plane parallel to the first panel and the second panel, and the orthographic projection being a regular hexagon; a core, the core comprising a plurality of subunits, the plurality of subunits being uniformly distributed around an axis of the panel and being arranged between the first panel and the second panel; each of the subunits comprising four beam structures, the four beam structures having a same length, each of the beam structures being formed based on a peak line of water bomb-based origami, one end of the four beam structures being connected to a vertex of the subunit, the vertex being arranged towards an inside of the structure, the other end of two of the beam structures being connected to two adjacent vertices of the first panel, and the other end of the other two of the beam structures being connected to two vertices of the second panel corresponding to the two adjacent vertices of the first panel.

2. The unit cell according to claim 1, wherein: a height of the unit cell is a maximum vertical distance between a surface of the first panel and a surface of the second panel, and a first relationship is satisfied between the length of the beam structure and the height of the unit cell; the first relationship is H < 2L, wherein H is the height of the unit cell, and L is the length of the beam structure.

3. The unit cell according to claim 2, wherein: a side length of the panel and the length of the beam structure satisfy a second relationship; the second relationship is C < 2L, wherein C is the side length of the panel, and L is the length of the beam structure.

4. The unit cell according to claim 3, wherein: the side length of the panel, the length of the beam structure and the height of the unit cell satisfy a third relationship. The third relationship is H 2 +C 2 <4L 2 where H is the height of the unit cell, L is the length of the beam structure, and C is the side length of the panel.

5. A method of vibration isolation based on the unit cell of a hybrid origami metamaterial based on Kresling and waterbomb-based origami, applied to the unit cell according to any one of claims 1-4, characterized in that, The application further relates to a method for designing a paper-based metamaterial, comprising: establishing a structural dynamics model of a unit cell of the paper-based metamaterial; calculating a band gap characteristic of the unit cell of the paper-based metamaterial according to the model; adjusting a geometric parameter of the unit cell of the paper-based metamaterial according to a target band gap, so that the band gap of the unit cell of the paper-based metamaterial covers the target band gap.

6. The method of claim 5, wherein, Adjusting a geometric parameter of the unit cell of the paper-based metamaterial according to a target band gap, so that the band gap of the unit cell of the paper-based metamaterial covers the target band gap, comprises: adjusting a thickness of the panel in the unit cell to change a mass of the paper-based metamaterial; and / or adjusting a height of the unit cell, a side length of the panel, a diameter of the beam structure and a length of the beam structure to change a stiffness of the paper-based metamaterial. The application further relates to a paper-based metamaterial, comprising:

7. A hybrid origami metamaterial based on Kresling and waterbomb-based origami, characterized in that, a plurality of unit cells according to any one of claims 1-4, the plurality of unit cells being connected in series along an axis direction of the first panel, and adjacent unit cells being connected through the panel. The plurality of unit cells have a same height.

8. The paper-folding metamaterial of claim 7, wherein, ​ 9. The paper-folding metamaterial of claim 7, wherein, The metamaterial comprises a plurality of unit cell groups, each of the unit cell groups comprises at least five unit cells, and the heights of the unit cells in each of the unit cell groups are equal, and the heights of the unit cells in the plurality of unit cell groups are arranged in a gradient along the axial direction of the panel.

10. A method of vibration isolation based on a hybrid origami metamaterial based on Kresling and waterbomb-based origami, applied to the origami metamaterial according to any one of claims 7-9, characterized in that, Comprise: establishing a structural dynamics model of the origami metamaterial; According to the model, the band gap characteristics of the origami metamaterial are calculated and obtained; According to the target band gap, the geometric parameters of the origami metamaterial are adjusted so that the band gap of the origami metamaterial covers the target band gap.

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