Superstructures that can achieve negative stiffness, negative poisson's ratio, negative thermal expansion, and band gap properties

Abstract

The application discloses a superstructure capable of realizing negative stiffness, negative Poisson's ratio, negative thermal expansion and band gap characteristics, which is formed by arranging a plurality of unit cells in a two-dimensional array form; the unit cell is a central symmetric structure, and the complete configuration of the unit cell is obtained by symmetrically arranging two adjacent quarter unit cells along two orthogonal directions; the quarter unit cell comprises a first connecting beam, a second connecting beam, a first side beam, a second side beam, a support beam and a bottom beam; the support beam is located at the center position of the bottom beam, the first side beam and the second side beam are symmetrically arranged on the two sides of the support beam, one end of the first side beam and the second side beam is connected with the support beam, the other end of the first side beam and the second side beam is connected with the two ends of the bottom beam respectively, the first side beam, the second side beam, the support beam and the bottom beam jointly enclose an isosceles right triangle, and the middle part of the first side beam and the second side beam is in a curved shape; the first connecting beam and the second connecting beam are located at the center positions of the first side beam and the second side beam respectively. The superstructure realizes the integration of negative stiffness, negative Poisson's ratio, negative thermal expansion and band gap characteristics, and can better adapt to harsh and complex multi-field environments.

Description

Technical Field

[0001] This invention belongs to the field of mechanical superstructure technology, specifically relating to a superstructure that can achieve negative stiffness, negative Poisson's ratio, negative thermal expansion and bandgap characteristics. Background Technology

[0002] Mechanical superstructures refer to special structures that achieve unusual mechanical properties through reasonable structural design. They can achieve mechanical properties such as negative Poisson's ratio, negative thermal expansion rate, and negative stiffness, and have potential applications in areas such as impact resistance and energy absorption, vibration reduction and noise reduction, sound absorption and stealth, and elimination of thermal effects.

[0003] Negative stiffness superstructures refer to periodic structures that exhibit periodic negative stiffness characteristics in response to loading. As energy-absorbing structures, they have advantages such as reusability, tolerance for large deformation, and no rebound upon impact, as well as a new energy absorption mechanism superior to traditional materials. They have broad application prospects in buffering and energy absorption, vibration reduction and noise reduction, high-performance actuation, and deployable structures.

[0004] Negative Poisson's ratio superstructures are special structures that exhibit a tensile or longitudinal expansion effect when subjected to longitudinal or transverse stretching or compression, possessing excellent resistance to deformation and buffering energy absorption capabilities.

[0005] Negative thermal expansion superstructures refer to structures that utilize the changes in internal forces of structural units during heating to achieve expansion and contraction effects. They are typically composed of two or more materials with different coefficients of thermal expansion and can produce specific structural deformation modes when heated.

[0006] Acoustic metastructures have extremely high application value in vibration reduction and noise reduction, acoustic cloaks, and negative refraction. The band gap refers to the frequency range in which elastic waves encounter resistance when propagating in an acoustic metastructure. The band gap can be controlled through structural design or material distribution to achieve sound insulation and vibration reduction.

[0007] Most existing mechanical superstructures can only achieve one of the following: negative stiffness, negative thermal expansion, and negative Poisson's ratio, or both. This limits their performance under specific operating conditions, making it impossible to simultaneously meet the requirements of force, thermal, and acoustic fields. They struggle to cope with harsh and complex multi-field environments, necessitating trade-offs between different performance characteristics, resulting in suboptimal overall performance. Achieving multiple properties simultaneously can further complicate structural design, making theoretical calculations and actual fabrication more challenging.

[0008] Compared with traditional superstructures, multi-performance superstructures that can achieve negative stiffness, negative Poisson's ratio, negative thermal expansion and bandgap characteristics have a better ability to adapt to harsh and complex multi-field environments, and have broad application prospects in aerospace, transportation and other fields. Summary of the Invention

[0009] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a superstructure that can realize negative stiffness, negative Poisson's ratio, negative thermal expansion and bandgap characteristics.

[0010] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0011] A superstructure capable of achieving negative stiffness, negative Poisson's ratio, negative thermal expansion, and bandgap characteristics is characterized in that the superstructure is composed of several single-cell units arranged in a two-dimensional array; the single-cell units are centrosymmetric structures, and the complete configuration of the single-cell units is obtained by symmetrically aligning two adjacent quarter-cell units along two orthogonal directions.

[0012] The quarter-cell unit includes a first connecting beam, a second connecting beam, a first side beam, a second side beam, a support beam, and a bottom beam. The support beam is located at the center of the bottom beam. The first and second side beams are symmetrically distributed on both sides of the support beam. One end of the first and second side beams is connected to the support beam, and the other end of the first and second side beams is connected to both ends of the bottom beam, respectively. The first side beam, the second side beam, the support beam, and the bottom beam together form an isosceles right triangle. The middle part of the first and second side beams is curved. The first connecting beam and the second connecting beam are located at the center of the first and second side beams, respectively.

[0013] Furthermore, both the first and second side beams include a first cosine curve segment, a straight line segment, and a second cosine curve segment. The first and second cosine curve segments are symmetrically distributed at both ends of the straight line segment. The shapes of the first and second cosine curve segments in their natural state satisfy: w0(x)=h / 2·[1-cos(2πx / l)], where h is the height of the cosine curve segment, l is the initial length of the cosine curve segment, and x is any position in the length direction.

[0014] Furthermore, when the coefficient of thermal expansion of the material used for the bottom beam is greater than the coefficient of thermal expansion of the materials used for the first connecting beam, the second connecting beam, the first side beam, the second side beam, and the support beam, the superstructure achieves negative thermal expansion.

[0015] Furthermore, the bottom beam is made of aluminum, and the first connecting beam, the second connecting beam, the first side beam, the second side beam, and the support beam are made of Invar alloy.

[0016] Furthermore, the thickness of the first side beam and the second side beam is less than the thickness of the remaining beams.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] This invention integrates multiple properties such as negative stiffness, negative Poisson's ratio, negative thermal expansion, and bandgap characteristics. It can not only cope with environments with varying temperature and pressure, but also adapt to vibration and noise environments, making it suitable for service in complex environments and meeting the special mechanical performance requirements of structures in aerospace and other fields.

[0019] Both the first and second side beams contain two cosine curve segments and one straight line segment. The shape of the cosine curve segment in its natural state satisfies a specific functional relationship. Therefore, when the unit cell is subjected to displacement load, the unit cell not only has the negative Poisson's ratio characteristic of tensile expansion, but also the first and second side beams undergo buckling deformation, giving the unit cell a negative stiffness characteristic. Therefore, the energy absorption characteristics of the superstructure of the present invention are far superior to structural forms with single or double negative characteristics.

[0020] The thermal expansion coefficient of the material used for the bottom beam is greater than that of the materials used for the other beams. Through the non-uniform tensile / contraction deformation generated by the beams made of materials with different thermal expansion coefficients when the ambient temperature changes, the thermal contraction and expansion of the entire unit cell is automatically realized, that is, equivalent negative thermal expansion. Attached Figure Description

[0021] Figure 1 This is a three-dimensional schematic diagram of the present invention;

[0022] Figure 2 This is a two-dimensional schematic diagram and a schematic diagram of a single-cell unit of the present invention;

[0023] Figure 3 This is a schematic diagram of the structure of a quarter-monomer cell of the present invention;

[0024] Figure 4 This is a schematic diagram of the structure of the first and second side beams of the present invention;

[0025] Figure 5 This is a schematic diagram of the single cell of the present invention subjected to displacement load along the y-axis direction and its force-deformation cloud diagram;

[0026] Figure 6 This is a schematic diagram of the single cell of the present invention subjected to displacement load along the x-axis and its force-deformation cloud diagram;

[0027] Figure 7 This is a thermal deformation cloud diagram of the monomer cell of the present invention under temperature load;

[0028] Figure 8 This is the band structure corresponding to the monomer cell of the present invention;

[0029] Figure 9 The force-displacement curve of the single cell element of the present invention under displacement load;

[0030] In the diagram, 1-first connecting beam; 2-second connecting beam; 3-first side beam; 4-second side beam; 5-support beam; 6-bottom beam; 31-first cosine curve segment; 32-straight line segment; 33-second cosine curve segment. Detailed Implementation

[0031] Specific embodiments are given below with reference to the accompanying drawings. These specific embodiments are only used to describe the technical solution of the present invention in detail, and are not intended to limit the scope of protection of this application.

[0032] This invention provides a superstructure (hereinafter referred to as superstructure, see below) that can achieve negative stiffness, negative Poisson's ratio, negative thermal expansion, and bandgap characteristics. Figures 1-9 The superstructure is composed of several single-cell units arranged in a two-dimensional array. The number and thickness of the single-cell units are determined according to the specific situation. The single-cell units are centrally symmetric structures. The complete configuration of the single-cell units is obtained by symmetrically aligning two adjacent quarter-cell units along two orthogonal directions.

[0033] Figure 3 The diagram shows the structure of a quarter-monomer cell. A quarter-monomer cell includes a first connecting beam 1, a second connecting beam 2, a first side beam 3, a second side beam 4, a support beam 5, and a bottom beam 6. The support beam 5 is located at the center of the bottom beam 6. The first side beam 3 and the second side beam 4 are symmetrically distributed on both sides of the support beam 5. One end of the first side beam 3 and the second side beam 4 connects to the support beam 5, and the other end connects to both ends of the bottom beam 6. The first side beam 3, the second side beam 4, the support beam 5, and the bottom beam 6 are integrally formed, together forming an isosceles right triangle. The support beam 5 is the height of the isosceles right triangle, and the first side beam 3 and the second side beam 4 are the legs of the isosceles right triangle. The first connecting beam 1 is located at the center of the first side beam 3, and the second connecting beam 2 is located at the center of the second side beam 4. The first connecting beam 1 and the second connecting beam 2 are used to connect adjacent quarter-monomer cells, that is, the first connecting beam 1 of one quarter-monomer cell is connected to the second connecting beam 2 of another quarter-monomer cell.

[0034] The first side beam 3 and the second side beam 4 have the same structure, each including a first cosine curve segment 31, a straight line segment 32, and a second cosine curve segment 33. The straight line segment 32 is located at the center and connected to either the first connecting beam 1 or the second connecting beam 2. The first cosine curve segment 31 and the second cosine curve segment 33 are symmetrically distributed at both ends of the straight line segment 32. The shape function of the first cosine curve segment 31 and the second cosine curve segment 33 in their natural state is: w0(x)=h / 2·[1-cos(2πx / l)], where h is the height of the cosine curve segment, l is the initial length of the cosine curve segment, and x is any position along the length direction of the cosine curve segment. The arrangement of the first cosine curve segment 31 and the second cosine curve segment 33 ensures that the first side beam 3 and the second side beam 4 can undergo buckling deformation after being subjected to displacement load, giving the unit cell negative stiffness characteristics. At the same time, all beams are made of TPU material, making the negative stiffness characteristics of the unit cell more obvious.

[0035] When the coefficient of thermal expansion of the material used for the bottom beam 6 is greater than that of the materials used for the first connecting beam 1, the second connecting beam 2, the first side beam 3, the second side beam 4, and the support beam 5, the unit cell achieves negative thermal expansion. When the bottom beam 6 is made of a material with a high coefficient of thermal expansion, such as aluminum, its theoretical coefficient of thermal expansion is 24 ppm / ℃; and the first connecting beam 1, the second connecting beam 2, the first side beam 3, the second side beam 4, and the support beam 5 are made of a material with a low coefficient of thermal expansion, such as Invar alloy, its theoretical coefficient of thermal expansion is 1.2 ppm / ℃; the equivalent negative coefficient of thermal expansion of the unit cell is -55.2 ppm / ℃.

[0036] The thickness of the first side beam 3 and the second side beam 4 is less than the thickness of the other beams, making the first side beam 3 and the second side beam 4 more prone to buckling deformation.

[0037] To verify that the superstructure of this invention achieves various mechanical properties, simulation analysis was performed on the single-cell unit. Specifically, the finite element model of the single-cell unit was established using the commercial finite element software ABAQUS 6.14 based on the eight-node linear hexahedral element C3D8R. Periodic boundary conditions were applied to the single-cell unit to simulate the infinite array lattice to simplify calculations and improve efficiency.

[0038] Figure 5 The diagram shows a schematic of a single-cell element subjected to a displacement load along the y-axis and the corresponding force-deformation contour plot. Fixed displacement constraints along the x and y axes are applied to the left and bottom boundaries of the single-cell element, respectively. A coupled constraint along the y-axis is applied to the top boundary of the single-cell element. Simultaneously, a displacement load along the y-axis is applied to the top boundary of the single-cell element. The relative displacement of the nodes at the boundary of the single-cell element along the x-axis is measured, and the corresponding equivalent negative Poisson's ratio value v is obtained using the equivalent Poisson's ratio calculation formula. yx It is -0.75. Figure 6This diagram illustrates the displacement load applied to a single-cell element along the x-axis and the corresponding force-deformation contour plot. Similarly, a displacement load along the x-axis is applied to the right boundary of the single-cell element, and the relative displacement of the nodes at the boundary along the y-axis is measured. The corresponding equivalent negative Poisson's ratio value v is obtained using the equivalent Poisson's ratio calculation formula. xy The value is -0.75. This proves that the monomer cell has a negative Poisson's ratio in both the x-axis and y-axis directions.

[0039] Figure 7 The figure shows the thermal deformation contours of a single-cell unit under temperature load along the x and y axes. Fixed displacement constraints in the x and y directions were applied to the left and bottom boundaries of the single-cell unit, respectively, while coupled constraints in the x and y directions were applied to the right and top boundaries, respectively. A single-cell unit with Al-Invar material was selected for simulation. The temperature field was uniformly distributed across the single-cell unit, and the temperature increased from 20℃ to 100℃. By measuring the relative thermal displacement and total length of corresponding nodes on opposite sides of the single-cell unit and substituting them into the equivalent calculation formula, the equivalent thermal expansion coefficients in the x and y directions were found to be -55.2 ppm / ℃. This demonstrates that the single-cell unit exhibits negative thermal expansion characteristics in both the x and y axes.

[0040] Figure 8 To study the bandgap characteristics of this invention, the band structure corresponding to the single-cell unit was modeled using the commercial software SOLIDWORKS. The band structure was calculated using the solid mechanics module in COMSOL Multiphysics. In the finite element analysis, periodic boundary conditions were introduced to simplify the computational domain to a single-cell unit. As shown in the figure, the single-cell unit generates seven bandgapes, including one relatively wide low-frequency bandgap, one relatively wide mid-frequency bandgap, and one relatively wide mid-to-high-frequency bandgap. This indicates that the superstructure of this invention has excellent bandgap performance, resulting in better sound insulation and vibration reduction effects.

[0041] Figure 9 The figure shows the force-displacement curve of a single cell under displacement load; the force-displacement curve contains two segments with negative slopes, indicating that the single cell has negative stiffness characteristics.

[0042] The working principle and workflow of this invention are as follows:

[0043] Under displacement load, the first side beam 3 and the second side beam 4 undergo buckling deformation, giving the unit cell negative stiffness characteristics. Furthermore, under displacement load, the buckling deformation of the first side beam 3 and the second side beam 4 causes the unit cell to contract in the x or y axis direction when subjected to displacement load along the y or x axis, thus achieving negative Poisson's ratio characteristics. Since the coefficient of thermal expansion of the material used for the bottom beam 6 is greater than that of the materials used for the first connecting beam 1, the second connecting beam 2, the first side beam 3, the second side beam 4, and the supporting beam 5, when the unit cell expands due to heat, the superstructure with different material components undergoes coordinated thermal deformation, giving the unit cell negative thermal expansion characteristics. The bandgap characteristic is generated by the interaction between the periodic arrangement of the unit cell and the properties of the wave vector.

[0044] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A superstructure capable of achieving negative stiffness, negative Poisson's ratio, negative thermal expansion, and bandgap characteristics, characterized in that, The superstructure is composed of several single-cell units arranged in a two-dimensional array. The single-cell units are centrally symmetric structures. When two adjacent quarter-cell units are symmetrical along two orthogonal directions, the complete configuration of the single-cell unit is obtained. The quarter-cell unit comprises a first connecting beam, a second connecting beam, a first side beam, a second side beam, a support beam, and a bottom beam. The support beam is located at the center of the bottom beam. The first and second side beams are symmetrically distributed on both sides of the support beam. One end of the first and second side beams is connected to the support beam, and the other end of the first and second side beams is connected to both ends of the bottom beam, respectively. The first side beam, the second side beam, the support beam, and the bottom beam together form an isosceles right triangle. The middle part of the first and second side beams is curved. The first connecting beam and the second connecting beam are located at the center of the first and second side beams, respectively. The coefficient of thermal expansion of the material used for the bottom beam is greater than that of the materials used for the first connecting beam, the second connecting beam, the first side beam, the second side beam, and the support beam, thus achieving negative thermal expansion in this superstructure. Both the first and second side beams include a first cosine curve segment, a straight line segment, and a second cosine curve segment, which are symmetrically distributed at both ends of the straight line segment. The shapes of the first and second cosine curve segments in their natural state satisfy the following: ,in The height of the cosine curve segment. Let be the initial length of the cosine curve segment. It represents any position along the length of the cosine curve segment.

2. The superstructure capable of achieving negative stiffness, negative Poisson's ratio, negative thermal expansion, and bandgap characteristics according to claim 1, characterized in that, The bottom beam is made of aluminum, and the first connecting beam, the second connecting beam, the first side beam, the second side beam, and the support beam are made of Invar alloy.

3. The superstructure capable of achieving negative stiffness, negative Poisson's ratio, negative thermal expansion, and bandgap characteristics according to claim 1, characterized in that, The thickness of the first side beam and the second side beam is less than the thickness of the remaining beams.

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