CN118959490A - Three-dimensional compression-torsion coupled negative Poisson's ratio honeycomb lattice structure - Google Patents
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Abstract
本发明涉及一种三维压扭耦合负泊松比蜂窝点阵结构，包括多个压扭耦合负泊松比蜂窝单胞结构，每一所述压扭耦合负泊松比蜂窝单胞结构具有竖杆、与所述竖杆连接且向外倾斜的第一类斜杆、以及与不同的所述第一类斜杆交错连接的第二类斜杆，所述三维压扭耦合负泊松比蜂窝点阵结构经由所述压扭耦合负泊松比蜂窝单胞结构周期阵列形成。本发明的结构具有优异的承载能力和稳定的扭转变形，对带隙频率范围内的弹性波传播起到明显的抑制效果，具有较高的工程应用潜力。
The present invention relates to a three-dimensional compression-torsion coupled negative Poisson's ratio honeycomb lattice structure, comprising a plurality of compression-torsion coupled negative Poisson's ratio honeycomb unit cell structures, each of the compression-torsion coupled negative Poisson's ratio honeycomb unit cell structures having a vertical rod, a first type of oblique rod connected to the vertical rod and inclined outward, and a second type of oblique rod staggeredly connected to different first type oblique rods, and the three-dimensional compression-torsion coupled negative Poisson's ratio honeycomb lattice structure is formed by a periodic array of the compression-torsion coupled negative Poisson's ratio honeycomb unit cell structures. The structure of the present invention has excellent bearing capacity and stable torsional deformation, has a significant inhibitory effect on the propagation of elastic waves within the band gap frequency range, and has high engineering application potential.
Description
Technical Field
The invention relates to the technical field of engineering structures, in particular to a three-dimensional compression-torsion coupling negative poisson ratio honeycomb lattice structure.
Background
Metamaterials are a well-designed class of artificial structural materials whose mechanical properties are determined primarily by the design of the structure, rather than the inherent properties of the matrix material. Compared with natural materials, metamaterial has excellent performance such as excellent vibration isolation effect, high-efficiency energy absorption capability and extraordinary physical properties such as negative poisson ratio, negative rigidity, negative compressibility, compression-torsion coupling and the like, and has received extensive attention in academia.
In 2017, frenzel et al originally integrated four-reverse chiral structures on six faces of a cubic unit cell and arranged the four-reverse chiral structures in an array manner, and firstly proposed a compression-torsion coupling effect and a three-dimensional mechanical compression-torsion metamaterial and realized that the torsion angle exceeds 2 degrees/percent under the axial unit strain. The metamaterial shows unique torsional deformation along a compression axis in the uniaxial compression process, can effectively convert translational motion into rotational motion, attracts the interest of students and motivates the students to explore an array or cylindrical shell type design method. Zheng et al uses inclined rods to connect adjacent chiral honeycomb layers and arrange the adjacent chiral honeycomb layers in an array manner, so that a novel three-dimensional compression-torsion metamaterial is obtained. They then replaced the chiral cellular loops with a square lattice structure and analyzed the factors affecting the torsion angle. In pursuit of larger torsion angles, farrell et al devised a cylindrical shell-like compression-torsion structure with pre-deformed ligaments. Notably, both types of designs suffer from deficiencies: the torsion angle of the array design is smaller, and the torsion effect gradually disappears as the number of the in-plane unit cells increases; the cylinder design has poor load carrying capacity.
CN112820362a proposes a zigzag compression-torsion coupled metamaterial, whose unit cell is composed of four identical positive beams and 45 ° oblique beams, and the structure in this scheme can see obvious torsion effect, but its bearing capacity is poor.
CN117703977a proposes a negative poisson ratio press-twist coupled honeycomb structure, which consists of multiple layers of torsion unit cells and connecting rods, but the constraint between adjacent unit cells on the same layer in the structure in this scheme is too strong, so as the number of unit cells on the same layer increases, the torsion effect will gradually disappear.
Therefore, it is needed to propose a new three-dimensional press-torsion coupled negative poisson ratio honeycomb lattice structure to overcome the problem of low bearing capacity or weak torsion effect of the structure.
Disclosure of Invention
The invention aims to solve the problems of low bearing capacity or weak torsion effect of the existing compression-torsion coupling structure.
In order to solve the technical problems, the invention provides a three-dimensional press-torsion coupling negative poisson ratio honeycomb lattice structure, which comprises a plurality of press-torsion coupling negative poisson ratio honeycomb lattice structures, wherein each press-torsion coupling negative poisson ratio honeycomb lattice structure is provided with a vertical rod, a first type inclined rod connected with the vertical rod and inclined outwards, and a second type inclined rod connected with different first type inclined rods in a staggered manner, and the three-dimensional press-torsion coupling negative poisson ratio honeycomb lattice structure is formed by a press-torsion coupling negative poisson ratio honeycomb lattice structure periodic array.
Further, the vertical rods comprise a first vertical rod and a second vertical rod which are sequentially distributed along the positive direction of a z-axis of a three-dimensional space coordinate system, wherein one end which is the same as the positive direction of the z-axis is used as the first end of the first vertical rod and the first end of the second vertical rod, one end which is the same as the negative direction of the z-axis is used as the second end of the first vertical rod and the second end of the second vertical rod, the distance between the second end of the first vertical rod and the first end of the second vertical rod is defined as H, the distance between the first end of the first vertical rod and the second end of the second vertical rod is H 1, and the lengths of the first vertical rod and the second vertical rod are (H-H 1)/2;
The first type diagonal rod comprises 4 first type diagonal rods and 4 first type second diagonal rods which are respectively connected with the first vertical rod and the second vertical rod, wherein:
The first ends of all the first inclined rods of the first type are connected with the first ends of the first vertical rods, and the second ends of the first inclined rods of the different 4 types extend towards the negative direction of the z-axis along the positive direction of the x-axis, the positive direction of the y-axis, the negative direction of the x-axis and the negative direction of the y-axis respectively;
the first ends of all the first type second inclined rods are connected with the second ends of the second vertical rods, and the second ends of the different 4 first type second inclined rods extend towards the positive direction of the z-axis along the positive direction of the x-axis, the positive direction of the y-axis, the negative direction of the x-axis and the negative direction of the y-axis respectively;
The second type diagonal rods comprise 4, the first end of each second type diagonal rod is respectively connected with the second ends of different first type diagonal rods, and the second end of each second type diagonal rod is respectively connected with the second ends of the first type diagonal rods on the x-z plane or the y-z plane where the connected first type diagonal rods are located on other planes different from each other.
Further, an inclination angle of θ 1 is formed between the straight line where each first-type first diagonal rod is located and the x-y plane, and between the straight line where each second-type second diagonal rod is located and the x-y plane.
Further, an included angle between a straight line where each inclined rod of the second type is located and an x-y plane is theta 2.
Further, defining a length L 1 of each first-type diagonal rod, a projection length L of the first-type diagonal rod on an x-y plane, a length L 2 of each second-type diagonal rod, and a distance h 2 between a second end of the first-type diagonal rod and a second end of the first-type second diagonal rod in the same extension direction of the positive direction, the negative direction and the negative direction of the x-axis, with the z-axis as an origin, the effective young's modulus E t of the press-torsion coupled negative poisson ratio honeycomb unit cell structure is as follows:
poisson ratio v satisfies:
Corner stiffness The method meets the following conditions:
where E is the young's modulus of the base material, and i=pi r 4/64 is the circular cross-sectional moment of inertia.
Still further, a plurality of the press-torque coupled negative poisson ratio cell structures are interconnected by sharing the end points of the rods of the press-torque coupled negative poisson ratio cell structures.
Furthermore, the plurality of the press-torsion coupled negative poisson ratio honeycomb unit cell structures form an N x×Ny×Nz lattice structure in a three-dimensional space coordinate system along the directions of an x axis, a y axis and a z axis.
The honeycomb lattice structure with the compression-torsion coupling negative poisson ratio has the beneficial effects that the structure can regulate the mechanical properties of the structure in a large range by regulating and controlling independent parameters and the number of arrays, and has excellent bearing capacity and stable torsional deformation under uniaxial compression compared with the existing structure; in addition, the lattice structure has three band gaps, has obvious inhibiting effect on elastic wave propagation in band gap frequency, and has higher engineering application potential.
Drawings
FIG. 1 is a schematic diagram of a pressure-torsion coupled negative Poisson's ratio honeycomb unit cell structure provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of parameters of a pressure-torsion coupled negative Poisson's ratio honeycomb unit cell structure provided by an embodiment of the invention;
FIG. 3 is a schematic diagram of a voltage-torsion coupled negative Poisson's ratio honeycomb lattice structure according to an embodiment of the present invention;
FIG. 4 is a graph of the unit cell potency performance profile provided by an embodiment of the present invention;
FIG. 5 is a schematic diagram of simulation results of a3×3×4 lattice structure provided in an embodiment of the present invention under different compression amounts;
FIG. 6 is an embodiment of the present invention provided 4X 4 and 5 simulation compression result schematic diagram of the x 5 x 4 lattice structure;
FIG. 7 is a schematic diagram of stress-strain curves of three lattice structures according to an embodiment of the present invention;
FIG. 8 is a graph showing torsion angle-strain trends of three lattice structures according to an embodiment of the present invention;
FIG. 9 is a schematic diagram of a chromatic dispersion relationship of a pressure-torsion coupled negative Poisson ratio honeycomb unit cell structure provided by an embodiment of the invention;
FIG. 10 is a schematic diagram of a frequency response function of a voltage-torsion coupled negative Poisson's ratio cellular lattice structure provided by an embodiment of the present invention;
Fig. 11 is a schematic diagram of stress distribution of a compression-torsion coupled negative poisson ratio honeycomb lattice structure according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The embodiment of the invention provides a three-dimensional press-twist coupling negative poisson ratio honeycomb lattice structure, which comprises a plurality of press-twist coupling negative poisson ratio honeycomb single cell structures, please refer to fig. 1 to 3, fig. 1 is a three-dimensional schematic diagram of the press-twist coupling negative poisson ratio honeycomb single cell structure provided by the embodiment of the invention, fig. 2 is a parameter schematic diagram of the press-twist coupling negative poisson ratio honeycomb single cell structure provided by the embodiment of the invention, and fig. 3 is a schematic diagram of the press-twist coupling negative poisson ratio honeycomb lattice structure provided by the embodiment of the invention, wherein each press-twist coupling negative poisson ratio honeycomb single cell structure is provided with a vertical rod, a first type inclined rod connected with the vertical rod and inclined outwards, and a second type inclined rod connected with different inclined rods in a staggered manner, and the three-dimensional press-twist coupling negative poisson ratio honeycomb lattice structure is formed by the press-twist coupling negative poisson ratio honeycomb single cell structure periodic array.
The vertical rods comprise a first vertical rod and a second vertical rod which are sequentially distributed along the positive direction of a z-axis of a three-dimensional space coordinate system, wherein one end which is the same as the positive direction of the z-axis is used as the first vertical rod and the first end of the second vertical rod, one end which is the same as the negative direction of the z-axis is used as the second end of the first vertical rod and the second end of the second vertical rod, the distance between the second end of the first vertical rod and the first end of the second vertical rod is defined as H, the distance between the first end of the first vertical rod and the second end of the second vertical rod is H 1, and the lengths of the first vertical rod and the second vertical rod are (H-H 1)/2;
The first type diagonal rod comprises 4 first type diagonal rods and 4 first type second diagonal rods which are respectively connected with the first vertical rod and the second vertical rod, wherein:
The first ends of all the first inclined rods of the first type are connected with the first ends of the first vertical rods, and the second ends of the first inclined rods of the different 4 types extend towards the negative direction of the z-axis along the positive direction of the x-axis, the positive direction of the y-axis, the negative direction of the x-axis and the negative direction of the y-axis respectively;
the first ends of all the first type second inclined rods are connected with the second ends of the second vertical rods, and the second ends of the different 4 first type second inclined rods extend towards the positive direction of the z-axis along the positive direction of the x-axis, the positive direction of the y-axis, the negative direction of the x-axis and the negative direction of the y-axis respectively;
The second type diagonal rods comprise 4, the first end of each second type diagonal rod is respectively connected with the second ends of different first type diagonal rods, and the second end of each second type diagonal rod is respectively connected with the second ends of the first type diagonal rods on the x-z plane or the y-z plane where the connected first type diagonal rods are located on other planes different from each other.
And the angle of inclination between the straight line of each first inclined rod and the x-y plane and between the straight line of each second inclined rod and the x-y plane is theta 1.
And the included angle between the straight line where each second class inclined rod is positioned and the x-y plane is theta 2.
Defining the length of each first inclined rod as L 1, the projection length of the first inclined rods on an x-y plane as L 2, and the distance between the second end of each first inclined rod and the second end of each second inclined rod in the same extending direction of the first inclined rod in the positive direction of the x axis, the positive direction of the y axis, the negative direction of the x axis and the negative direction of the y axis, which are the same with the z axis as the origin, as h 2, wherein the cross-section circle radius of each vertical rod, each first inclined rod and each second inclined rod is r, and the effective Young modulus E t of the press-torsion coupled negative Poisson ratio honeycomb unit cell structure is as follows:
poisson ratio v satisfies:
Corner stiffness The method meets the following conditions:
where E is the young's modulus of the base material, and i=pi r 4/64 is the circular cross-sectional moment of inertia.
And a plurality of the press-torque coupling negative poisson ratio honeycomb unit cell structures are connected with each other by sharing the end points of the rods of the press-torque coupling negative poisson ratio honeycomb unit cell structures.
And the plurality of pressure-torsion coupled negative poisson ratio honeycomb unit cell structures form an N x×Ny×Nz lattice structure in a three-dimensional space coordinate system along the directions of an x axis, a y axis and a z axis in a periodical array mode.
The embodiment of the invention performs performance analysis on the compression-torsion coupling negative poisson ratio honeycomb lattice structure, and according to the effective Young modulus E t, poisson ratio v and corner rigidityNormalizing h 1,h2 to give a single cell efficacy performance profile as shown in fig. 4, it can be seen from (a) in fig. 4 that E t/E and h 2 are closely related, increasing with h 2, e t/E decreases; h 1 affects E t/E slightly, and as h 1 increases, E t/E increases. As can be seen from fig. 4 (b), the structure exhibits a negative poisson's ratio characteristic regardless of the parameter change, and h 1 and h 2 have an important effect on poisson's ratio, and decreasing h 1 or increasing h 2 can reduce the poisson's ratio value. as can be seen from fig. 4 (c), as h 2 increases, K φ increases significantly and h 1 has little effect on K φ. In general, fig. 4 shows that adjusting the heights h 1 and h 2 can significantly affect the mechanical properties of the press-torsion coupled negative poisson ratio cellular unit cell structure, thereby adjusting the bearing capacity and the torsion characteristics of the press-torsion coupled negative poisson ratio cellular lattice structure.
Furthermore, the embodiment of the invention carries out uniaxial compression test and finite element simulation on lattice structures with different array numbers.
Fig. 5 shows simulation results of a 3×3×4 lattice structure at different compression amounts. The obvious torsion effect can be seen from fig. 5, and the experimental result is very consistent with the simulation result, which accurately captures the torsion deformation in the compression process;
FIG. 6 shows 4X 4 and 5X 4 simulation compression results of lattice structure. It can be seen that the torsion angle of 5×5×4 is relatively reduced from the previous two;
FIG. 7 shows 3X 4, 4X 4 and 5X stress-strain curves for the three lattice structures. It can be seen that the strain region of 0-0.13 can be seen as an approximate line elasticity phase, with 3 x 4 stresses and stiffness slightly less than the other two. Along with the continuation of compression, the structure enters a platform stage, and the stress of the three structures all presents a slightly increased oscillation trend, so that the excellent bearing capacity of the pressure-torsion coupling negative poisson ratio honeycomb lattice structure provided by the embodiment of the invention is shown;
FIG. 8 shows three of 3X 4, 4X 4 and 5X 4 the torsion angle of the lattice structure changes with the strain. In the elastic strain area of 0-0.13, the torsion angles of the three structures are approximately equal in size and change trend; the 3 x 4 twist angle is then more pronounced, eventually stabilizing at about 33, the 4 multiplied by 4 and the 5 multiplied by 4 are gradually upward trend, and finally are respectively stabilized at 29.5 degrees and 28 degrees, thus showing obvious torsion effect.
The embodiment of the invention also explores the dispersion relation of the pressure-torsion coupling negative poisson ratio honeycomb unit cell structure and the vibration transmission characteristic of the 1 multiplied by 5 lattice structure so as to realize the vibration isolation and vibration reduction application in the aspect of vibration.
The unit cell shown in fig. 1 is discretized into 19,681 four-node triangular units and swept along the boundary of the first brillouin zone to obtain a dispersion relation as shown in fig. 9, in which the hatched portion represents the band gap. Three distinct bandgaps can be seen in FIG. 9, with the frequency ranges 488-517Hz,748-832Hz and 980-991Hz, respectively. Next, five unit cells are arranged in a 1×1×5 lattice structure and subjected to harmonic excitation at the input end in the frequency range from 0 to 1200Hz, and the corresponding output response is monitored at the other end, wherein the frequency response function (Frequency response function, FRF) is defined as FRF (ω) =20log 10(uout(ω)/uin (ω)), where u out is the displacement output response and u in is the displacement input response;
Fig. 10 shows a frequency response function FRF as a function of frequency. As can be seen from fig. 10, the harmonic excitation is significantly attenuated in the three band gap regions, the attenuation amplitude exceeds 40dB, and the harmonic excitation has an obvious suppression effect on elastic waves;
The stress distribution diagrams of the 1×1×5 lattice structure with harmonic input frequencies of 501hz,799hz and 985hz are shown in (a), (b) and (c) in fig. 11, respectively, and as can be seen from (a), (b) and (c) in fig. 11, the harmonic cannot pass through the 1×1×5 lattice structure, and the vibration isolation and vibration reduction application of the pressure-torsion coupling negative poisson ratio honeycomb lattice structure provided by the embodiment of the invention is verified again.
The honeycomb lattice structure with the compression-torsion coupling negative poisson ratio has the beneficial effects that the structure can regulate the mechanical properties of the structure in a large range by regulating and controlling independent parameters and the number of arrays, and has excellent bearing capacity and stable torsional deformation under uniaxial compression compared with the existing structure; in addition, the lattice structure has three band gaps, has obvious inhibition effect on elastic wave propagation in the band gap range, and has higher engineering application potential.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
While the embodiments of the present invention have been illustrated and described in connection with the drawings, what is presently considered to be the most practical and preferred embodiments of the invention, it is to be understood that the invention is not limited to the disclosed embodiments, but on the contrary, is intended to cover various equivalent modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (7)
1. The three-dimensional press-twist coupling negative poisson ratio honeycomb lattice structure is characterized by comprising a plurality of press-twist coupling negative poisson ratio honeycomb unit cell structures, wherein each press-twist coupling negative poisson ratio honeycomb unit cell structure is provided with a vertical rod, a first type of inclined rod connected with the vertical rod and inclined outwards, and a second type of inclined rod connected with the different first type of inclined rod in a staggered manner, and the three-dimensional press-twist coupling negative poisson ratio honeycomb lattice structure is formed by the press-twist coupling negative poisson ratio honeycomb unit cell structure periodic array.
2. The three-dimensional press-twist coupling negative poisson ratio honeycomb lattice structure according to claim 1, wherein the vertical rods comprise a first vertical rod and a second vertical rod which are sequentially distributed along a positive direction of a z-axis of a three-dimensional space coordinate system, wherein one end which is the same as the positive direction of the z-axis is taken as a first end of the first vertical rod and one end which is the same as the negative direction of the z-axis is taken as a second end of the first vertical rod and one end which is the negative direction of the z-axis is taken as a second end of the second vertical rod, a distance between the second end of the first vertical rod and the first end of the second vertical rod is defined as H, a distance between the first end of the first vertical rod and the second end of the second vertical rod is H 1, and the lengths of the first vertical rod and the second vertical rod are respectively (H-H 1)/2;
The first type diagonal rod comprises 4 first type diagonal rods and 4 first type second diagonal rods which are respectively connected with the first vertical rod and the second vertical rod, wherein:
The first ends of all the first inclined rods of the first type are connected with the first ends of the first vertical rods, and the second ends of the first inclined rods of the different 4 types extend towards the negative direction of the z-axis along the positive direction of the x-axis, the positive direction of the y-axis, the negative direction of the x-axis and the negative direction of the y-axis respectively;
the first ends of all the first type second inclined rods are connected with the second ends of the second vertical rods, and the second ends of the different 4 first type second inclined rods extend towards the positive direction of the z-axis along the positive direction of the x-axis, the positive direction of the y-axis, the negative direction of the x-axis and the negative direction of the y-axis respectively;
The second type diagonal rods comprise 4, the first end of each second type diagonal rod is respectively connected with the second ends of different first type diagonal rods, and the second end of each second type diagonal rod is respectively connected with the second ends of the first type diagonal rods on the x-z plane or the y-z plane where the connected first type diagonal rods are located on other planes different from each other.
3. The three-dimensional crush-twist coupled negative poisson's ratio cellular lattice structure of claim 2, wherein each of the first diagonal rods of the first type is disposed at an angle θ 1 between a line of the first type and the x-y plane and between a line of the second diagonal rods of the first type and the x-y plane.
4. The three-dimensional crush-twist coupled negative poisson's ratio cellular lattice structure of claim 3, wherein each of the second type diagonal rods is positioned at an angle θ 2 between a line and an x-y plane.
5. The three-dimensional crush-torsion coupled negative poisson ratio honeycomb lattice structure according to claim 4, wherein a length L 1 of each first-type diagonal is defined, a projection length L of the first-type diagonal on an x-y plane is defined, a length L 2 of each second-type diagonal is defined, a distance h 2 between a second end of the first-type diagonal and a second end of the first-type second diagonal in the same extension direction of the first-type first diagonal, the negative x-axis and the negative y-axis is defined with a z-axis as an origin, a positive x-axis direction, a positive y-axis direction, and a positive z-axis direction, and a cross-sectional circle radius r of each of the vertical rod, the first-type diagonal, and the second-type diagonal is defined as r, and an effective young modulus E t of the crush-torsion coupled negative poisson ratio honeycomb structure is defined as follows:
poisson ratio v satisfies:
Corner stiffness The method meets the following conditions:
where E is the young's modulus of the base material, and i=pi r 4/64 is the circular cross-sectional moment of inertia.
6. The three-dimensional, press-and-twist coupled negative poisson ratio cell lattice structure of claim 1, wherein a plurality of the press-and-twist coupled negative poisson ratio cell structures are interconnected by sharing endpoints of rods of the press-and-twist coupled negative poisson ratio cell structures.
7. The three-dimensional press-twist coupled negative poisson ratio cellular lattice structure of claim 1, wherein a plurality of the press-twist coupled negative poisson ratio cellular lattice structures form an N x×Ny×Nz lattice structure in a three-dimensional space coordinate system in a periodic array along the x-axis, y-axis and z-axis directions.
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