A phononic crystal with adjustable band gap and a band gap adjustment method

Abstract

The present invention discloses a phononic crystal with adjustable band gap and a band gap adjustment method. The phononic crystal includes a plurality of flexible right-angled triangular prisms connected by thin ribbons, plug-in scatterers and a fluid matrix. The plug-in scatterers are fixed in the flexible right-angled triangular prisms and can rotate with the flexible right-angled triangular prisms. The fluid matrix is ​​filled around the lower part of the acoustic scatterers. The phononic crystal adjusts the band gap by transforming between configurations. The present invention realizes a real-time dynamically adjustable band gap by driving the movement of the flexible right-angled triangular prisms in the phononic crystal. The design of the plug-in scatterers improves the stiffness of the flexible paper-cut metamaterial, thereby improving the reliability of deformation. At the same time, the plug-in acoustic scatterers are flexible in design, easy to operate, and easy to control the band gap. Secondly, the phononic crystal has C4V symmetry and can be used to dynamically control the acoustic topological properties of the structure and the propagation of sound waves.

Description

Technical Field

[0001] The present invention relates to the field of phononic crystals, and in particular to a phononic crystal with adjustable band gap and a band gap adjustment method. Background Art

[0002] With the rapid development of modern industry, processing and production are becoming increasingly large-scale, integrated, complex, and intelligent. Consequently, noise and vibration issues in human living and working environments are becoming increasingly prominent. Noise reduction and suppression have been a hot research topic in recent years. In particular, the government's requirements for noise reduction and suppression are becoming increasingly comprehensive and systematic, particularly in response to noise pollution. Therefore, effectively suppressing vibration and reducing noise has become a critical issue in industrial production and civil engineering development.

[0003] Artificial bandgap materials, materials or structures characterized by a periodic arrangement of elastic constants and densities based on structural design, have been widely used in vibration damping and isolation. Specifically, when elastic waves propagate through an artificial bandgap material, they are blocked within a certain frequency range (the bandgap) by internal periodic scatterers, while continuing to propagate within other frequency ranges (the passband). Therefore, by rationally designing the bandgap frequency range of the artificial bandgap material, vibration damping and isolation can be achieved across diverse frequency ranges. However, once an artificial bandgap material structure is designed, its geometry is difficult to alter, limiting its ability to isolate vibration within a fixed frequency range. Furthermore, any deviation from the desired bandgap range requires re-fabrication. Existing tunable bandgap structures primarily incorporate piezoelectric materials (piezoelectric stacks), embedded magnets (magnetorheological fluids), shape memory alloys (temperature / stress), and auxetic metamaterials (mechanical motion) into metamaterial designs. These structures achieve real-time control of the metamaterial's bandgap by varying external physical stimuli without changing the metamaterial's structure. However, due to the non-reconfigurability of these tunable bandgap structures, they can only achieve multi-level vibration isolation within a limited number of configurations. It is difficult to meet the complex and changing engineering requirements.

[0004] In summary, existing structures for real-time adjustable vibration isolation and noise reduction suffer from poor control accuracy, cumbersome operation, a single functional structure, and non-reconfigurability. Therefore, a reconfigurable phononic crystal with real-time adjustable band gap is urgently needed in practical engineering construction. This can not only meet the functional requirements of real-time band gap adjustment but also allow the structure of artificial band gap materials to be reconfigured according to actual working conditions. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a phononic crystal with high control precision and real-time adjustable band gap; another purpose of the present invention is to provide a band gap adjustment method for the above-mentioned phononic crystal with adjustable band gap that is simple to operate.

[0006] Technical Solution: The present invention provides a phononic crystal with adjustable bandgap. This phononic crystal is a two-dimensional fluid-solid coupling phononic crystal with a square lattice arrangement, primarily used to construct a C4v lattice. The lattice is primarily, but not limited to, a square lattice. The phononic crystal comprises a plurality of flexible rectangular prisms connected by thin ribbons, plug-in scatterers, and a fluid matrix. The plug-in scatterers are fixed within the flexible rectangular prisms and can rotate with them. The fluid matrix is ​​filled around the lower portion of the acoustic scatterers. The phononic crystal comprises an initial configuration, a primary configuration, and a secondary configuration. The initial configuration consists of a unit cell composed of 16n flexible rectangular prisms, the primary configuration consists of 2n flexible rectangular prisms, and the secondary configuration consists of n flexible rectangular prisms. The phononic crystal adjusts its bandgap by switching between these configurations.

[0007] The thickness of the thin strip connection between the flexible right-angled triangular prisms is 0.2-1mm. After optimization, this thickness can not only provide a certain prestress for maintaining the structural shape, but also ensure that the deformation of the thin strip is localized at the connection corresponding to the top surface of the flexible right-angled triangular prism 101, thereby improving the accuracy of structural deformation and the accuracy of the band gap controlled by the scatterer.

[0008] Furthermore, the plug-in scatterer includes an acoustic scatterer, a connecting layer and a positioning column connected in sequence from top to bottom, wherein the acoustic scatterer is located above the connecting layer, the connecting layer is located between the acoustic scatterer and the top surface of the flexible right-angled triangular prism, the positioning column is placed in the flexible right-angled triangular prism, and a groove matching the shape of the positioning column is provided in the flexible right-angled triangular prism.

[0009] The plug-in scatterer is made by photocuring printing and is made of a hard resin, which is much harder than TPU. The fluid matrix is ​​preferably water or methanol.

[0010] Furthermore, the plug-in scatterer is a first plug-in scatterer or a second plug-in scatterer; in the first plug-in scatterer, the top surface of the connecting layer is a right triangle, and the acoustic scatterer is fixed on the perpendicular bisector of the top surface of the connecting layer; in the second plug-in scatterer, the top surface of the connecting layer is a right triangle, and the acoustic scatterer is fixed on the hypotenuse of the top surface of the connecting layer.

[0011] Furthermore, in the primary configuration, the unit cell is composed of eight flexible right-angled triangular prisms, and every two right-angled triangular prisms form a cuboid, which together form four cuboids. The adjacent faces of the four cuboids form a four-prism space with a rhombus bottom, and the two acoustic scatterers in each cuboid are arranged relatively parallel to each other.

[0012] Preferably, the flexible right-angled triangular prism is a flexible isosceles right-angled triangular prism, the top surface of which is an isosceles right triangle, and the unit cell of the primary configuration of the phononic crystal satisfies the following geometric relationship:

[0013] a1=2Lcos(θ / 2)

[0014]

[0015] a=2L[cos(θ / 2)+sin(θ / 2)]

[0016] The Poisson's ratio of the primary structure is

[0017] Among them, a is the length of the unit cell, that is, the distance between the left and right vertices of the unit cell in the horizontal direction; b is the width of the unit cell, that is, the distance between the two vertices of the unit cell in the vertical direction; a1 is the distance between the two top vertices of the two horizontal rectangular parallelepipeds in the unit cell; L is the length of the waist of the isosceles right triangle, θ is the angle between the two horizontal rectangular parallelepipeds, and β is the angle at which the hypotenuse of the corresponding isosceles right triangle deviates from the vertical straight line.

[0018] Furthermore, in the secondary configuration of the phononic crystal, the unit cell is composed of sixteen flexible right-angled triangular prisms, and every four right-angled triangular prisms form a cuboid, forming a total of four cuboids. The adjacent faces of the four cuboids are arranged to form a four-prism space with a rhombus bottom, where the acoustic scatterers are arranged on the four sides of the top surface of each cuboid.

[0019] Preferably, the flexible right-angled triangular prism is a flexible isosceles right-angled triangular prism, the top surface of which is an isosceles right triangle, and the unit cell of the secondary configuration of the phononic crystal satisfies the following geometric relationship:

[0020]

[0021]

[0022]

[0023]

[0024] The Poisson's ratio of the secondary structure is v2 = -1;

[0025] Among them, a is the length of the unit cell, that is, the distance between the left and right vertices of the unit cell in the horizontal direction; b is the width of the unit cell, that is, the distance between the two vertices of the unit cell in the vertical direction; a2 is half the length of the unit cell, b2 is the minimum distance between the two vertical vertices of the rectangular parallelepiped, and β is the angle at which the hypotenuse of the corresponding isosceles right triangle deviates from the vertical straight line.

[0026] Furthermore, the flexible right-angled triangular prism is a flexible and reconfigurable kirigami metamaterial, which is made by TPU printing. Preferably, the flexible and reconfigurable kirigami metamaterial is made by fused deposition modeling (FDM).

[0027] In another aspect, the present invention provides a method for adjusting the band gap of the phononic crystal, characterized in that the method comprises the following steps:

[0028] (1) In the initial configuration, the unit cell is composed of four flexible right-angled triangular prisms, and the adjacent faces of the four right-angled triangular prisms form a quadrangular prism space with a rhombus bottom surface;

[0029] (2) In the initial configuration, the A points corresponding to the upper and lower sides of the phononic crystal are fixed, and compressive forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, driving the rotation of the acoustic scatterer, so that the phononic crystal is transformed from the initial configuration to the primary configuration; in the primary configuration, the A points corresponding to the upper and lower sides of the phononic crystal are fixed, and tensile forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, so that the phononic crystal is transformed from the primary configuration to the initial configuration; wherein, the connection points of the outermost adjacent right triangular prisms in each unit cell on the upper and lower sides of the phononic crystal are selected as the A points; the distance between the A points is b;

[0030] (3) In the initial configuration, the B points corresponding to the upper and lower sides of the phononic crystal are fixed, and compression forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, driving the rotation of the acoustic scatterer, so that the phononic crystal is transformed from the initial configuration to the secondary configuration; in the secondary configuration, the B points corresponding to the upper and lower sides of the phononic crystal are fixed, and tensile forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, so that the phononic crystal is transformed from the secondary configuration to the initial configuration, and the outermost points of the two right-angled triangular prisms with the farthest outermost distance in each two unit cells on the upper and lower sides of the phononic crystal are selected as the B points; the distance between the B points is b;

[0031] (4) According to the band gap requirements, the phononic crystal is transformed from the primary configuration to the primary configuration or the secondary configuration, from the primary configuration or the secondary configuration to the primary configuration, and then from the primary configuration to the primary configuration or the secondary configuration to adapt to different working conditions; according to the band gap requirements, the band gap under each level of configuration is adjusted by adjusting the angle of the flexible right-angled triangular prism of each level of configuration.

[0032] Furthermore, a dual-axis variable pitch module loading device is used to apply tensile or compressive force to the phononic crystal to adjust the band gap; the dual-axis variable pitch module loading device includes a pair of symmetrically arranged guide rails of the variable pitch module, each of which is equipped with a variable pitch module guide rod driving unit, one end of the variable pitch module guide rod driving unit is equipped with a first stepper motor, and the other end is equipped with a first limit cap; a plurality of second guide rods are arranged perpendicular to the guide rails of the variable pitch modules and a second guide rod is installed at one end of the second guide rod. a stepper motor, and a second limit cap is installed at the other end; a plurality of first guide rods are arranged in the guide rail of the variable pitch module and parallel to the guide rail of the variable pitch module, a third stepper motor is installed at one end of the first guide rod, and a third limit cap is installed at the other end; a profile is provided under the first guide rod; two rectangular steels are symmetrically provided on the profile, and the rectangular steels are connected to the profile through a slider, and the two rectangular steels can approach or separate from each other under the drive of the slider; a loading fixture is fixed on the top of the guide rail of the variable pitch module, and the loading fixture is used to fix point A or point B of the phononic crystal.

[0033] Furthermore, the dual-axis variable pitch module loading device is provided with a water tank on the periphery for filling the fluid matrix around the lower part of the scatterer, a fixing device for fixing the water tank on a plane is provided under the water tank, a spirit level is provided on the water tank, and the fixing device is respectively equipped with water tank fixing sliders on the four corners of the water tank, the water tank fixing sliders are connected to the water tank, and a linear stepping motor is installed on the top surface of the water tank fixing slider for driving the water tank fixing slider to move up and down.

[0034] The dual-axis variable pitch module loading device of the present invention is used to control the geometric configuration of the flexible paper-cut metamaterial; the linear stepper motor lifting platform and the spirit level are used for leveling the water tank; the water tank is used to fill the fluid around the flexible right-angled triangular prism; the present invention changes the position and number of the dual-axis variable pitch module loading fixtures to achieve the switching of the motion path of the flexible right-angled triangular prism at the motion bifurcation point, thereby realizing the reconstruction of the phononic crystal. This phononic crystal with coexisting multi-level configurations has C4V symmetry and can be used to dynamically control the acoustic topological properties of the structure and the propagation of sound waves. The present invention realizes a real-time dynamically adjustable band gap by driving the movement of the flexible right-angled triangular prism, and the design of the plug-in scatterer improves the stiffness of the flexible paper-cut metamaterial, thereby improving the reliability of deformation; at the same time, the plug-in acoustic scatterer is flexible in design, easy to operate, and easy to control the band gap.

[0035] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0036] (1) Multifunctional integrated artificial bandgap materials, showing excellent functional integration characteristics, based on reconfigurable kirigami bandgap-adjustable phononic crystals with designable Poisson's ratio (positive Poisson's ratio / negative Poisson's ratio);

[0037] (2) The scatterers of the phononic crystal are pluggable, which makes it easy to disassemble the scatterers and thus reduces the maintenance cost in actual use; the topological characteristics can be modulated by changing the shape and combination of the scatterers;

[0038] (3) The band gap structure has high control precision and the band gap adjustment method is simple to operate. The phononic crystal structure of the present invention not only realizes accurate real-time adjustment of the band gap, but also provides a good experimental design platform for the study of acoustic topological properties and the design of functional mechanical metamaterials. The present invention has both good economic and social benefits and broad scientific research value and application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A top view of the phononic crystal of the present invention;

[0040] Figure 2 is a schematic diagram of a phononic crystal structure with a first pluggable scatterer;

[0041] Figure 3 Schematic diagram of the structure of the first pluggable scatterer; (a) is a schematic diagram of the three-dimensional structure, (b) is a front view; (c) is a top view; (d) is a left view;

[0042] Figure 4 Schematic diagram of a phononic crystal structure with a second pluggable scatterer;

[0043] Figure 5 Schematic diagram of the structure of the second pluggable scatterer; (a) is a schematic diagram of the three-dimensional structure, (b) is a front view; (c) is a top view; (d) is a left view;

[0044] Figure 6 Schematic diagram of the unit cell of the primary configuration;

[0045] Figure 7 Schematic diagram of the unit cell of the secondary configuration;

[0046] Figure 8 An overall stereogram of a device for adjusting the band gap of a phononic crystal provided by an embodiment of the present invention;

[0047] Figure 9 This is a partial top view of the dual-axis variable pitch module loading device;

[0048] Figure 10 A partial stereoscopic view of the pitch-variable module and some of its components in the dual-axis pitch-variable module loading device;

[0049] Figure 11 This is a partial stereoscopic view of the rectangular steel and some parts on it in the dual-axis variable pitch module loading device;

[0050] Figure 12This is the overall top view of the dual-axis variable pitch module loading device and the water tank;

[0051] Figure 13 A partial perspective view of the water tank and its leveling lifting device;

[0052] Figure 14 This is a partial stereoscopic view of the four linear stepper motor lifting platform;

[0053] Figure 15 It is a partial three-dimensional diagram of the sink and its parts;

[0054] Figure 16 Schematic diagram of the scatterer layout of several typical states in the primary, secondary and transition states of the phononic crystal with adjustable band gap based on reconfigurable kirigami in Example 1;

[0055] Figure 17 The band structure of the phononic crystal with adjustable band gap based on reconfigurable kirigami in Example 1 at the primary structure (θ=45°);

[0056] Figure 18 The band structure of the phononic crystal with adjustable band gap based on reconfigurable kirigami in Example 1 at the primary structure (θ=90°);

[0057] Figure 19 The band structure of the phononic crystal with adjustable band gap based on reconfigurable kirigami in Example 1 in the secondary structure (θ=0°);

[0058] Figure 20 The band structure of the phononic crystal with adjustable band gap based on reconfigurable kirigami in the secondary structure (θ=45°) in Example 1;

[0059] Figure numerals: 1. Phononic crystal; 101. Flexible right-angle triangular prism; 102. Plug-in scatterer; 1021. Acoustic scatterer; 1022. Connecting layer; 1023. Positioning column; 2. Loading fixture; 3. Guide rail of variable pitch module; 4. Guide rod driving unit of variable pitch module; 5. First stepper motor; 6. First limiting cap; 7. Rectangular steel; 8. Slider; 9. Profile; 10. First guide rod; 11. Second stepper motor; 12. Second limiting cap; 13. Third stepper motor; 14. Third limiting cap; 15. Water tank; 16. Level; 17. Linear stepper motor; 18. Water tank fixing slider; 19. Fixing device; 20. Second guide rod. DETAILED DESCRIPTION

[0060] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0061] like Figure 1As shown, in one embodiment, a phononic crystal 1 with adjustable band gap is provided. The phononic crystal is a two-dimensional fluid / solid coupling type phononic crystal. Its lattice arrangement is a square lattice, which can be mainly used to construct a C4v point group that considers slip symmetry, spatial inversion symmetry, and C4 rotational symmetry. The lattice is mainly a square lattice but is not limited to a square lattice.

[0062] The phononic crystal 1 comprises several flexible rectangular prisms 101 connected by thin ribbons, a pluggable scatterer 102, and a fluid matrix. The flexible rectangular prisms 101 are a flexible, reconfigurable kirigami metamaterial, manufactured by printing TPU. The thickness of the thin ribbon connections between the flexible rectangular prisms 101 is optimized to provide a certain amount of prestress to maintain the structural shape while ensuring that the deformation of the thin ribbon is localized at the corresponding connection on the top surface of the flexible rectangular prisms 101, thereby improving the accuracy of structural deformation and the precision of the band gap controlled by the scatterers.

[0063] The pluggable scatterer 102 is fixed within the flexible rectangular prism 101 and can rotate with the flexible rectangular prism 101. A fluid matrix is ​​filled around the lower portion of the acoustic scatterer 1021. The pluggable scatterer is manufactured using a photocurable printing method. The scatterer is made of a hard resin with a hardness significantly higher than that of TPU. The fluid matrix is ​​preferably water or methanol.

[0064] like Figure 2-3 As shown, in one embodiment, the pluggable scatterer 102 includes an acoustic scatterer 1021, a connecting layer 1022, and a positioning post 1023, which are sequentially connected from top to bottom. The acoustic scatterer 1021 is located on the top surface of the connecting layer 1022, which is located between the acoustic scatterer 1021 and the top surface of the flexible right-angled triangular prism 101. The positioning post 1023 is positioned within the flexible right-angled triangular prism 101, which has a groove that matches the shape of the positioning post 1023. Pluggable scatterer 102 is a first pluggable scatterer, and the top surface of its connecting layer 1022 is a right triangle. The acoustic scatterer 1021 is fixed to the perpendicular midline of the right triangle on the top surface of the connecting layer 1022.

[0065] like Figure 4-5As shown, in one embodiment, pluggable scatterer 102 includes an acoustic scatterer 1021, a connecting layer 1022, and a positioning post 1023, which are sequentially connected from top to bottom. Acoustic scatterer 1021 is located on the top surface of connecting layer 1022, which is located between acoustic scatterer 1021 and the top surface of flexible right-angled triangular prism 101. Positioning post 1023 is positioned within flexible right-angled triangular prism 101, which has a groove that matches the shape of positioning post 1023. Pluggable scatterer 102 is a second pluggable scatterer, and the top surface of its connecting layer 1022 is a right triangle. Acoustic scatterer 1021 is fixed to the hypotenuse of the right triangle on the top surface of connecting layer 1022.

[0066] In one embodiment, the acoustic scatterer 1021 on the upper part of the plug-in scatterer 102 is a flat rectangular parallelepiped, and the intermediate connecting layer 1022 is a right triangular prism, which is exactly the same size as the flexible right triangular prism 101, and is used to improve the stiffness of the flexible TPU and the connection strength between the various parts of the scatterer; the central positioning column 1023 at the lower part of the plug-in scatterer 102 is a rectangular parallelepiped. The length, width, and height of the acoustic scatterer are It, Wt, and H, respectively; the size (It, Wt, and H) and layout of the acoustic scatterer are determined by the required band gap and topological characteristics. Each flexible right triangular prism has a rectangular positioning groove that matches the central positioning column 1023, and the size of the central positioning column 1023 is slightly smaller than the rectangular positioning groove in the flexible right triangular prism 101.

[0067] The central positioning column 1023 may also be other straight prisms to improve the positioning accuracy of the scatterer, and is used to fix the plug-in scatterer and drive the scatterer to rotate.

[0068] In one embodiment, in addition to the initial configuration, the phononic crystal includes two configurations: a primary configuration and a secondary configuration. Each configuration's supercell contains at least eight periods to ensure that the band gap and acoustic topological properties can be easily detected. The initial configuration's unit cell consists of 16n flexible right-angled triangular prisms, the primary configuration's unit cell consists of 2n flexible right-angled triangular prisms, and the secondary configuration's unit cell consists of n flexible right-angled triangular prisms. The phononic crystal adjusts its band gap by switching between these configurations.

[0069] In one embodiment, the unit cell of the initial configuration is composed of four flexible right triangular prisms, and the adjacent faces of the four right triangular prisms form a rhombus-shaped column space; in the primary configuration, the unit cell is composed of eight flexible right triangular prisms, and every two right triangular prisms form a cuboid, which together form four cuboids, and the adjacent faces of the four cuboids form a quadrangular prism space with a rhombus-shaped bottom, wherein the two acoustic scatterers in each cuboid are arranged relatively parallel to each other; in the secondary configuration, the unit cell is composed of sixteen flexible right triangular prisms, and every four right triangular prisms form a cuboid, which together form four cuboids, and the adjacent faces of the four cuboids form a quadrangular prism space with a rhombus-shaped bottom, wherein the acoustic scatterers are arranged on the four edges of the top surface of each cuboid.

[0070] In one embodiment, as shown in the figure, the flexible right triangular prism is a flexible isosceles right triangular prism. The top surface of the flexible isosceles right triangular prism is an isosceles right triangle with a side length of L. The thickness t at the connection is approximately 1% of the side length. Each right triangular prism has a rectangular positioning groove for fixing the plug-in scatterer and driving the scatterer to rotate. The depth of the rectangular groove is approximately 1 / 3 of the side length, and the length and width of the groove are approximately 1 / 2 and 1 / 5 of the side length, respectively.

[0071] In one embodiment, considering that the number of cells used in acoustic bandgap control and topological property research is large and the cell size is also in the centimeter level, the thickness H of the flexible and reconfigurable kirigami metamaterial is the same as the side length of the isosceles triangle in the cell. In addition, the action points of the two configurations corresponding to the flexible and reconfigurable kirigami metamaterial are as follows: Figure 1 As shown in the figure, when the variable-pitch module loading fixture acts on point A corresponding to the flexible kirigami metamaterial, the phononic crystal is defined as a primary configuration. When the variable-pitch module loading fixture acts on point B corresponding to the flexible kirigami metamaterial, the phononic crystal is defined as a secondary configuration.

[0072] Specifically, the band gap adjustment method of the phononic crystal includes the following steps:

[0073] (1) In the initial configuration, the unit cell is composed of four flexible right-angled triangular prisms, and the adjacent faces of the four right-angled triangular prisms form a quadrangular prism space with a rhombus bottom surface;

[0074] (2) In the initial configuration, the A points corresponding to the upper and lower sides of the phononic crystal are fixed, and compressive forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, driving the rotation of the acoustic scatterer, so that the phononic crystal is transformed from the initial configuration to the primary configuration; in the primary configuration, the A points corresponding to the upper and lower sides of the phononic crystal are fixed, and tensile forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, so that the phononic crystal is transformed from the primary configuration to the initial configuration; wherein, the connection point of the outermost adjacent right triangular prisms in each unit cell on the upper and lower sides of the phononic crystal is selected as the A point;

[0075] (3) In the initial configuration, the B points corresponding to the upper and lower sides of the phononic crystal are fixed, and compressive forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, driving the rotation of the acoustic scatterer, so that the phononic crystal is transformed from the initial configuration to the secondary configuration; in the secondary configuration, the B points corresponding to the upper and lower sides of the phononic crystal are fixed, and tensile forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, so that the phononic crystal is transformed from the secondary configuration to the initial configuration, and the outermost points of the two right-angled triangular prisms with the farthest outermost distance in each two unit cells on the upper and lower sides of the phononic crystal are selected as the B points;

[0076] (4) According to the actual working conditions, the phononic crystal is transformed from the primary configuration to the primary configuration or the secondary configuration, from the primary configuration or the secondary configuration to the primary configuration, and then from the primary configuration to the primary configuration or the secondary configuration to adapt to different working conditions. According to the band gap requirements, the band gap of each level of configuration is adjusted by adjusting the angle of the flexible right-angled triangular prism.

[0077] like Figure 6 As shown, the first-order phononic crystal satisfies the following geometric relationship

[0078] a1=2Lcos(θ / 2)

[0079]

[0080] a=2L[cos(θ / 2)+sin(θ / 2)]

[0081] The Poisson's ratio of the primary structure is

[0082] like Figure 7 As shown, the secondary configuration of the kirigami metamaterial satisfies the following geometric relationship

[0083]

[0084]

[0085]

[0086]

[0087] Therefore, the Poisson's ratio of the secondary structure is v2 = -1.

[0088] like Figure 8 As shown, in one embodiment, a device for adjusting the band gap of a phononic crystal is provided, wherein the device includes a dual-axis variable pitch module loading device, and the dual-axis variable pitch module loading device is used to apply a tensile force or a compressive force to the phononic crystal to adjust the band gap.

[0089] like Figure 9-11As shown, the dual-axis variable pitch module loading device includes a circuit synchronization trigger device, a loading fixture 2, a variable pitch module guide rail 3, a variable pitch module guide rod drive unit 4, a first stepper motor 5, a first limit cap 6, a rectangular steel material 7, a slider 8, a profile 9, a first guide rod 10, a second stepper motor 11, a second limit cap 12, a third stepper motor 13, a third limit cap 14, and a second guide rod 20. The circuit synchronization trigger device is used to achieve dual-axis loading of the variable pitch module and the rectangular steel material 7 by controlling the circuit.

[0090] One end of the pitch module guide rod drive unit 4 is installed with a first stepper motor 5, and the other end is installed with a first limit cap 6, wherein the guide rail 3 of the pitch module is installed in the pitch module guide rod drive unit 4, and the two constitute a multi-station pitch module. A pair of multi-station pitch modules are arranged symmetrically in the transverse direction, and the multi-station pitch module is provided with a plurality of second guide rods 20 in the vertical direction. The stations of the multi-station pitch module are installed with a plurality of second guide rods 20, and the second guide rods 20 pass through the two multi-station pitch modules. A second stepper motor 11 is installed at one end of the second guide rod 20, and a second limit cap 12 is installed at the other end; a plurality of first guide rods 10 are provided in parallel with the multi-station pitch module, and the first guide rods 10 are provided in parallel with the multi-station pitch module. A third stepper motor 13 is mounted on one end, and a third limiting cap 14 is mounted on the other. A profile 9 is positioned beneath the first guide rod 10. Two rectangular steel bars 7 are symmetrically mounted on the profile 9, connected to the profile 9 by a slider 8. These bars 7 can be moved toward or away from each other under the influence of the slider 8. A loading fixture 2 is affixed to the top of the variable-pitch module's guide rail 3, securing the corresponding point A or B of the phononic crystal. Under the control of a circuit synchronization trigger, the guide rails and guide rods of each stepper motor drive the loading mechanism of the dual-axis variable-pitch module to adjust the band gap and topological characteristics of each configuration.

[0091] Specifically, a removable loading fixture 2 is installed on the sliding assembly of the multi-station variable pitch module, facilitating replacement of the appropriate loading fixture according to actual loading requirements. To ensure the rigidity of the loading fixture 2, the thickness of the loading fixture 2 is at least greater than 3 mm. To prevent damage to the specimen by the loading fixture 2, the loading end of the loading fixture 2 is chamfered. Therefore, the equidistant loading method adopted by the present invention effectively solves the problem of loading fixture interference during traditional biaxial compression. In addition, the flexible, reconfigurable paper-cut metamaterial is subjected to biaxial loading in both the transverse and longitudinal directions, with the loading fixture action point located at the connection between the thin strips of the flexible paper-cut. During deformation, the flexible paper-cut structure is under tensile stress. Due to the large difference in rigidity (introduced hard resin scatterers), deformation is mainly concentrated in the middle thin strip, resulting in uniform force and coordinated deformation throughout the flexible paper-cut structure. To prevent friction from disturbing the deformation during compression loading, an appropriate lubricant is applied to the loading end of the loading fixture. Therefore, the present invention can precisely control the band gap of the flexible, reconfigurable paper-cut through a mechanical loading structure.

[0092] The loading fixture 2 of the variable pitch module is adjusted to an appropriate position by the variable pitch module guide rod drive unit 4, serving as the point of action for driving the movement of the flexible right-angled triangular prism 101, thereby driving the rotation of the acoustic scatterer. Simultaneously, four profiles are placed beneath the phononic crystal 1 to ensure the stability of the drive mechanism and prevent significant bending deformation of the phononic crystal 1. In the transverse (longitudinal) direction, the multi-station variable pitch module and rectangular steel 7 are driven by stepper motor guide rods to compress or stretch the flexible, reconfigurable phononic crystal 1. Then, under the control of a circuit synchronization trigger device, the loading fixture's position is continuously adjusted according to the actual motion path of the flexible, reconfigurable phononic crystal 1. Simultaneously, the guide rods continuously adjust the spacing between the multi-station variable pitch module and rectangular steel 7 to achieve biaxial loading. Here, each profile 9 is independently controlled by a stepper motor, adjusting the relative distance between the profiles according to the deformation of the phononic crystal 1. The profile 9 adjacent to the multi-station variable pitch module is welded to the module. In addition, the rectangular steel 7 is connected to the profile 9 via a slider 8. The rectangular steel 7 is driven along the guide rail of the profile 9 by a guide rod passing through the slider 8. The outermost phononic crystal 1 corresponding to the loading fixture 2 on the multi-station variable pitch module is not equipped with a plug-in scatterer and is mainly used to guide the deformation of the flexible paper-cut structure.

[0093] like Figure 12-15 As shown, in one embodiment, a water tank 15 is provided outside the dual-axis variable pitch module loading device. This tank 15 is filled with a fluid matrix that covers the flexible rectangular triangular prism 101 and does not extend beyond the acoustic scatterer 1021. The fluid matrix is ​​water or methanol. Additionally, a water outlet is provided on one side of the tank's edge and is plugged with a rubber stopper.

[0094] In one embodiment, the lifting device is a linear stepper motor lifting platform, which includes a linear stepper motor 17 and a fixture 19. The linear stepper motor 17 is mounted on the fixture 19. A water tank fixing slider 18 is installed between the linear stepper motor 17 and the fixture 19. The linear stepper motor lifting platform is connected to the water tank 15 via the water tank fixing slider 18. Specifically, the fixture 19 is fixed to the laboratory work surface, and the water tank fixing slider 18 is connected to the four corners of the water tank 15. A level 16 is embedded in the middle of two adjacent sides of the water tank 15 to determine whether the water tank 15 is horizontal. The linear stepper motor 17 then adjusts the height of the water tank to ensure its levelness.

[0095] Example 1

[0096] The proposed phononic crystal with adjustable bandgap based on reconfigurable kirigami has a primary structure with 21 and 17 cells in the horizontal and vertical directions, respectively, for a total of 357 cells. 40×32 scatterers are inserted in the horizontal and vertical directions, for a total of 1,280 scatterers. Its main dimensional parameters include:

[0097] The flexible right-angled triangular prism is an isosceles right-angled flexible triangular prism with a length of 20mm and a height of 20mm. The thickness of the flexible thin strip at the connection of the flexible triangular prism is approximately 0.2mm. The rectangular positioning groove of the positioning column is 7.5mm deep, with a length and width of 10mm and 3.5mm respectively. The flexible triangular prism and thin strip are made of PolyFlex TPU95, with an elastic modulus E = 9.4MPa, a Poisson's ratio v = 0.45, and a density ρ = 1240kg / m 3 The initial printing state of the flexible and reconfigurable kirigami metamaterial is a transitional state (primary configuration) between two configurations. The cell angle θ = 30°, and the entire model is 935.1 mm long, 754.3 mm wide, and 20 mm thick.

[0098] The length and width of the positioning column are 9.9mm and 3.4mm respectively, and its height is 7.4mm. The connecting layer is an isosceles right triangular prism with a side length of 20mm and a height of 3mm. The length and width of the acoustic scatterer are 19.2mm and 3mm respectively, and its height is 20mm. The layout is as follows Figure 3 The material used is light-curing resin, with elastic modulus E = 2510 MPa, Poisson's ratio v = 0.41, and density ρ = 1160 kg / m 3 .

[0099] The dual-axis variable pitch module consists of 21 stations in total. Each station is equipped with a 3mm thick rigid loading fixture made of 45 steel with elastic modulus E = 210GPa, Poisson's ratio v = 0.3, and density ρ = 7870kg / m 3 The length of the dual-axis variable pitch module is 1200mm, the width is 50mm, and the height is 100mm. The guide rod of the slider that runs through the water tank and the rectangular steel is 1650mm long and 15mm in diameter. Four profiles with a length of 1200mm, a width of 100mm, and a height of 100mm are placed under the flexible paper-cut meta-structure. It is made of aluminum with an elastic modulus E = 70GPa, a Poisson's ratio v = 0.35, and a density ρ = 2700kg / m 3 The guide rod that runs through the water tank and the four profiles is 1450mm long and 20mm in diameter. The rectangular steel bar is 760mm long, 50mm wide, and 20mm high. It is made of 45 steel with an elastic modulus of E = 210GPa, a Poisson's ratio v = 0.3, and a density of ρ = 7870kg / m 3 .The length of the guide rod along the guide rail is 1650mm and the diameter is 15mm.

[0100] The tank is 1500mm long, 1300mm wide, and 150mm high, with a 30mm thickness around the sides and a 10mm thickness at the bottom. It is made of 45 steel with an elastic modulus of E = 210 GPa, a Poisson's ratio v = 0.3, and a density of ρ = 7870 kg / m³.

[0101] Four guide rods with a length of 500 mm and a diameter of 20 mm are fixed on the workbench through a limiting structure.

[0102] According to the difference in the positions of the action points of the loading fixtures corresponding to the two flexible paper-kirigami structure configurations, the following positional relationship of the action positions is given;

[0103] 1. First-level configuration structure, the loading fixture action point is located at point A, and the initial spacing is 54.3mm

[0104] The distance between the two loading fixtures satisfies the following relationship:

[0105]

[0106] Where b is the distance between the two loading fixtures, L is the length of the base of the isosceles right triangular prism, and β is Figure 6 Angle shown.

[0107] The corresponding Poisson's ratio satisfies

[0108] Based on the first-order configuration, we give the Figure 16 The band gaps of θ = 45° and θ = 90° are shown. Figure 17 、 18 It can be seen that when the angle changes from θ=90° to θ=45°, the first band gap changes from the passband shown in the figure to 14.40-17.72 kHz, and the band gap is 3.32 kHz.

[0109] 2. Secondary configuration structure, the loading fixture action point is located at point B, and the initial spacing is 108.6mm

[0110]

[0111] Where b is the distance between the two loading fixtures, L is the length of the base of the isosceles right triangular prism, and β is Figure 7 Angle shown.

[0112] The corresponding Poisson's ratio satisfies v2=-1.

[0113] Based on the secondary configuration, we give its Figure 16 The band gaps for θ = 45° and θ = 0° are shown. Figure 19 、 20As can be seen, when the angle changes from θ = 45° to θ = 0°, the first band gap changes from 18.02-25.01 kHz to 16.23-24.7 kHz. Not only does the bandwidth widen, but the lower cutoff frequency of the 1.32 kHz band gap also decreases by 1.79 kHz.

[0114] Therefore, the tunable bandgap phononic crystal based on reconfigurable kirigami described in this invention not only reconfigures the bandgap frequency range, but also the structural Poisson's ratio range. The pluggable acoustic scatterer design and biaxial loading mechanism provide an excellent experimental platform for studying tunable acoustic properties.

Claims

1. A phononic crystal with adjustable band gap, characterized in that: The phononic crystal includes several flexible right-angled triangular prisms connected by thin ribbons, plug-in scatterers and a fluid matrix. The plug-in scatterers are fixed in the flexible right-angled triangular prisms and can rotate with the flexible right-angled triangular prisms. The fluid matrix is ​​filled around the lower part of the acoustic scatterers. The phononic crystal includes an initial configuration, a primary configuration and a secondary configuration. The initial configuration is composed of 16n flexible right-angled triangular prisms, the primary configuration is composed of 2n unit cells composed of flexible right-angled triangular prisms, and the secondary configuration is composed of n unit cells composed of flexible right-angled triangular prisms. The phononic crystal adjusts the band gap by transforming between configurations.

2. The phononic crystal with adjustable band gap according to claim 1, characterized in that: The plug-in scatterer includes an acoustic scatterer, a connecting layer and a positioning column connected in sequence from top to bottom, wherein the acoustic scatterer is located above the connecting layer, the connecting layer is located between the acoustic scatterer and the top surface of the flexible right-angled triangular prism, the positioning column is placed in the flexible right-angled triangular prism, and a groove matching the shape of the positioning column is provided in the flexible right-angled triangular prism.

3. The bandgap-adjustable phononic crystal according to claim 2, characterized in that: The plug-in scatterer is a first plug-in scatterer or a second plug-in scatterer; in the first plug-in scatterer, the top surface of the connecting layer is a right triangle, and the acoustic scatterer is fixed on the perpendicular bisector of the top surface of the connecting layer; in the second plug-in scatterer, the top surface of the connecting layer is a right triangle, and the acoustic scatterer is fixed on the hypotenuse of the top surface of the connecting layer.

4. The phononic crystal with adjustable band gap according to claim 2, characterized in that: In the primary configuration, the unit cell is composed of eight flexible right-angled triangular prisms, and every two right-angled triangular prisms form a cuboid, which together form four cuboids. The adjacent faces of the four cuboids form a diamond column space, in which the two acoustic scatterers in each cuboid are arranged relatively parallel to each other.

5. The phononic crystal with adjustable band gap according to claim 2, characterized in that: In the secondary configuration, the unit cell is composed of sixteen flexible right-angled triangular prisms, and every four right-angled triangular prisms form a cuboid, which together form four cuboids. The adjacent faces of the four cuboids form a diamond-shaped column space, in which the acoustic scatterers are arranged on the four edges of the top surface of each cuboid.

6. The phononic crystal with adjustable band gap according to claim 1, characterized in that: The flexible right-angled triangular prism is a flexible and reconfigurable paper-cut metamaterial made by TPU printing.

7. A band gap adjustment method for a phononic crystal with adjustable band gap according to any one of claims 1 to 6, characterized in that: The method comprises the following steps: (1) In the initial configuration, the unit cell is composed of four flexible right-angled triangular prisms, and the adjacent faces of the four right-angled triangular prisms form a quadrangular prism space with a rhombus bottom surface; (2) In the initial configuration, the A points corresponding to the upper and lower sides of the phononic crystal are fixed, and compressive forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, driving the rotation of the acoustic scatterer, so that the phononic crystal is transformed from the initial configuration to the primary configuration; in the primary configuration, the A points corresponding to the upper and lower sides of the phononic crystal are fixed, and tensile forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, so that the phononic crystal is transformed from the primary configuration to the initial configuration; wherein, the connection point of the outermost adjacent right triangular prisms in each unit cell on the upper and lower sides of the phononic crystal is selected as the A point; (3) In the initial configuration, the B points corresponding to the upper and lower sides of the phononic crystal are fixed, and compressive forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, driving the rotation of the acoustic scatterer, so that the phononic crystal is transformed from the initial configuration to the secondary configuration; in the secondary configuration, the B points corresponding to the upper and lower sides of the phononic crystal are fixed, and tensile forces are applied to the phononic crystal in the longitudinal and transverse directions synchronously, so that the phononic crystal is transformed from the secondary configuration to the initial configuration, and the outermost points of the two right-angled triangular prisms with the farthest outermost distance in each two unit cells on the upper and lower sides of the phononic crystal are selected as the B points; (4) According to the working conditions, the phononic crystal is first transformed from the primary configuration to the primary configuration or the secondary configuration, then from the primary configuration or the secondary structure to the primary configuration, and then from the primary structure to the primary configuration or the secondary structure to adapt to different working conditions; according to the band gap requirements, the band gap under each level of configuration is adjusted by adjusting the angle of the flexible right-angled triangular prism of each level of configuration.

8. The band gap adjustment method of a phononic crystal with adjustable band gap according to claim 7, characterized in that: A dual-axis variable pitch module loading device is used to apply a tensile force or a compressive force to the phononic crystal to adjust the band gap; the dual-axis variable pitch module loading device comprises a pair of symmetrically arranged variable pitch module guide rails (3), each of which is equipped with a variable pitch module guide rod driving unit (4), one end of which is equipped with a first stepper motor (5), and the other end of which is equipped with a first limit cap (6); a plurality of second guide rods (20) are arranged perpendicularly to the guide rails (3) of the variable pitch modules and through the guide rails (3) of the variable pitch modules, one end of which is equipped with a second stepper motor (11), and the other end of which is equipped with a second limit cap (12); a plurality of first guide rods (10) are provided in parallel with the guide rail (3) of the variable pitch module in the guide rail (3) of the variable pitch module, a third stepping motor (13) is installed at one end of the first guide rod (10), and a third limit cap (14) is installed at the other end; a profile (9) is provided on the first guide rod (10); two rectangular steels (7) are symmetrically provided on the profile (9), the rectangular steels (7) are connected to the profile (9) through a slider (8), and the two rectangular steels (7) can be moved closer to or separated from each other under the drive of the slider (8); a loading fixture (2) is fixed on the top of the guide rail (3) of the variable pitch module, and the loading fixture (2) is used to fix point A or point B corresponding to the phononic crystal.

9. The band gap adjustment method of a phononic crystal with adjustable band gap according to claim 7, characterized in that: A water tank (15) for filling a fluid matrix around the lower portion of the acoustic scatterer is provided on the periphery of the dual-axis variable pitch module loading device, a fixing device (19) for fixing the water tank (15) on a plane is provided below the water tank (15), and a level (16) is provided on the water tank (15).

10. The band gap adjustment method of a phononic crystal with adjustable band gap according to claim 9, characterized in that: The four corners of the fixing device (19) are respectively provided with water tank fixing sliders (18), the water tank fixing sliders (18) are connected to the water tank (15), and a linear stepping motor (17) is installed on the top surface of the water tank fixing slider (18) for driving the water tank fixing slider (18) to move up and down.

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