Local resonance phononic crystal based on Kresling origami

Abstract

The invention relates to the technical field of acoustic function material structure design, in particular to a Kresling origami-based local resonance phononic crystal, which comprises a substrate and a vibration reduction array embedded on the substrate, the vibration reduction array comprises a plurality of unit cell structures arranged in an array. Each unit cell structure comprises at least two spiral Kresling paper folding structures, and lead injection holes penetrating through the Kresling paper folding structures are formed in the Kresling paper folding structures. The substrate is one of an Archimedes spiral parallel plate, a chessboard embedded paper-cut, a double-layer Miura origami or a bistable shell based on a shape memory polymer; the material of the Kresling origami structure is lead, the density is 11600 kg / m < 3 >, the elastic modulus is 20.80 GPa, and the Poisson ratio is 0.369. According to the local resonance photonic crystal provided by the invention, through the unique geometric characteristics, a remarkable vibration band gap is generated in a low-frequency band, and vibration propagation in a specific frequency band is effectively inhibited; according to the Kresling paper folding structure, diversified vibration band gap configuration can be achieved by adjusting the folding angle and the number of layers.

Description

Technical Field

[0001] This application relates to the technical field of the structural design of acoustic functional materials, and particularly to a locally resonant phononic crystal based on Kresling origami. Background Art

[0002] Vibration and noise problems widely exist in modern engineering and often become one of the main challenges in product design and performance improvement. With the progress of technology, people's demand for efficient, lightweight, and intelligent materials is increasing day by day, which also prompts researchers to continuously explore and develop new mechanical metamaterials to achieve more efficient vibration and noise control. Due to their unique structures and functionalities, mechanical metamaterials can effectively change the propagation characteristics of sound waves and vibrations and gradually become a key means to solve vibration and noise problems.

[0003] In recent years, the research on bandgap tuning and vibration and noise reduction has become an important topic in the field of materials science. A bandgap refers to the phenomenon that the propagation of vibrations or sound waves in a material is suppressed within certain frequency ranges. This property has important application values in vibration control, acoustic filtering, waveguide design, etc. The formation of a bandgap mainly depends on the periodic structure and resonance characteristics of the material.

[0004] Due to its significant advantages in mechanics and structural changes, the Kresling origami structure has received extensive attention in the aerospace field in recent years. However, the application research in the field of metamaterials is relatively scarce. Because of its unique geometric tunability and dynamic mechanical properties, this origami structure is particularly suitable for high - requirement application scenarios that need precise control of mechanical properties and structural variability. Summary of the Invention

[0005] The embodiment of this application provides a locally resonant phononic crystal based on Kresling origami, which generates a significant vibration bandgap in the low - frequency band through its unique geometric characteristics, effectively suppressing the vibration propagation in a specific frequency band and having good prospects in low - frequency vibration and noise reduction.

[0006] To solve the above technical problems, an embodiment of the present application provides a locally resonant phononic crystal based on Kresling origami, including: a substrate and a vibration damping array embedded on the substrate; the vibration damping array includes a plurality of unit cell structures arranged in an array; the unit cell structure includes at least two spiral Kresling origami structures, the middle part of the Kresling origami structure is embedded in the substrate, and its upper and lower parts are exposed outside the substrate; a lead injection hole penetrating the Kresling origami structure is opened inside the Kresling origami structure; the substrate is one of an Archimedean spiral parallel plate, a checkerboard mosaic paper-cut, a double-layer Miura origami, or a bistable shell based on a shape memory polymer; the material of the Kresling origami structure is lead, with a density of 11600 kg / m 3 , with an elastic modulus of 20.80 GPa and a Poisson's ratio of 0.369.

[0007] In some exemplary embodiments, the substrate is an Archimedean spiral parallel plate; the Archimedean spiral inside the Archimedean spiral parallel plate can form a complex vibration propagation path to guide and control the propagation and local resonance of waves, thereby affecting its bandgap properties; the unit cell structure includes two spiral Kresling origami structures, and the two spiral Kresling origami structures are respectively embedded in the upper and lower parts of the Archimedean spiral parallel plate.

[0008] In some exemplary embodiments, the material of the Archimedean spiral parallel plate is aluminum, with a density of 2730 kg / m 3 , with an elastic modulus of 77.60 GPa, a Poisson's ratio of 0.352, a parallel plate length of 30 mm, a width of 30 mm, a thickness of 2 mm, and a parallel plate spiral groove width of 2 mm.

[0009] In some exemplary embodiments, the substrate is a checkerboard mosaic paper-cut; the deformation process of the checkerboard mosaic paper-cut has infinite scalability, and the substrate area can be flexibly adjusted, which is suitable for different vibration frequency bands and environmental requirements; the substrate includes a number of identical paper-cut squares, and each paper-cut square is connected by a flexible material to form an adjustable structure with a telescopic function; the unit cell structure includes two spiral Kresling origami structures, and the two spiral Kresling origami structures are respectively embedded in the upper and lower parts of the checkerboard mosaic paper-cut as the substrate.

[0010] In some exemplary embodiments, the material of the paper-cut is aluminum, with a density of 2730 kg / m 3 , with an elastic modulus of 77.60 GPa and a Poisson's ratio of 0.352.

[0011] In some exemplary embodiments, the substrate is a double-layer Miura origami; the symmetric arrangement of the double-layer Miura origami can reduce the non-uniform stress distribution, enhance the overall stability of the structure, and enable it to exhibit better anti-deformation ability during vibration; the substrate includes a number of identical parallelogram Miura origamis, each Miura origami is connected through the vertices of the parallelogram, and each Miura origami is connected through a flexible material; the unit cell structure includes a number of spiral Kresling origami structures, and each spiral Kresling origami structure is embedded in the raised parts of every two adjacent parallelogram Miura origamis.

[0012] In some exemplary embodiments, the material of the double-layer Miura origami is aluminum, with a density of 2730 kg / m 3 , an elastic modulus of 77.60 GPa, and a Poisson's ratio of 0.352; the side lengths of the parallelogram are all 6.66 mm, and its two adjacent interior angles are 84° and 96° respectively.

[0013] In some exemplary embodiments, the substrate is a bistable shell based on a shape memory polymer; the bistable shell deforms when the ambient temperature exceeds its glass transition temperature, the elastic modulus decreases significantly, and it can be folded by applying an external force, and after the temperature and pressure are released, the structure remains in the folded state; the unit cell structure includes a number of spiral Kresling origami structures, and each spiral Kresling origami structure is embedded in the upper and lower parts of the bistable shell based on the shape memory polymer.

[0014] In some exemplary embodiments, the material of the Kresling origami structure is lead, with a density of 11600 kg / m 3 , an elastic modulus of 20.80 GPa, and a Poisson's ratio of 0.369.

[0015] In some exemplary embodiments, the bandgap of the locally resonant phononic crystal is concentrated in the range of 55 Hz to 155 Hz, and as the folding angle increases, the bandgap width gradually decreases; when the locally resonant phononic crystal maintains the same total height but is asymmetrically compressed, the bandgap is concentrated in the low-frequency band below 100 Hz; when the Kresling origami structure is compressed by 30°, the bandgap regulation effect of symmetric bending remains consistent at different bending angles, and the low-frequency bandgap is not affected by the bending angle.

[0016] The technical solutions provided by the embodiments of this application have at least the following advantages:

[0017] An embodiment of the present application provides a locally resonant phononic crystal based on Kresling origami, including: a substrate and a vibration damping array embedded in the substrate; the vibration damping array includes a plurality of unit cell structures arranged in an array; the unit cell structure includes at least two spiral Kresling origami structures, the middle part of the Kresling origami structure is embedded in the substrate, and its upper and lower parts are exposed outside the substrate; a lead injection hole penetrating the Kresling origami structure is provided inside the Kresling origami structure; the substrate is one of an Archimedean spiral parallel plate, a checkerboard inlaid paper cut, a double-layer Miura origami, or a bistable shell based on a shape memory polymer; the material of the Kresling origami structure is lead, with a density of 11600 kg / m 3 , an elastic modulus of 20.80 GPa, and a Poisson's ratio of 0.369.

[0018] The locally resonant phononic crystal based on Kresling origami provided by the present application generates a significant vibration band gap in the low-frequency band through its unique geometric characteristics, effectively suppressing the vibration propagation in a specific frequency band. By adjusting the folding angle and number of layers, the Kresling origami structure can achieve diverse vibration band gap configurations. The simple manufacturing and assembly process of the Kresling origami structure makes it highly applicable even under harsh working conditions. The dynamic regulation ability of the Kresling origami structure provides new possibilities for the development of future intelligent vibration damping systems. Description of the Drawings

[0019] One or more embodiments are exemplarily illustrated by the pictures in the corresponding drawings. These exemplary illustrations do not limit the embodiments. Unless otherwise stated, the figures in the drawings do not constitute a proportional limitation.

[0020] Figure 1 It is a schematic structural diagram of a locally resonant phononic crystal based on Kresling origami provided by an embodiment of the present application.

[0021] Figure 2 It is a schematic diagram of the unit cell structure of a locally resonant phononic crystal based on an Archimedean spiral parallel plate provided by an embodiment of the present application.

[0022] Figure 3 It is a schematic diagram of the process of symmetric compression and folding of the upper and lower parts of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application.

[0023] Figure 4 It is a schematic diagram of the folding process of asymmetric compression of the upper and lower parts of the unit cell of the locally resonant phononic crystal with a certain total height provided by an embodiment of the present application.

[0024] Figure 5Schematic diagram of the deformation process of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application when symmetrically bent during 30° compression of the Kresling origami.

[0025] Figure 6 Schematic diagram of the deformation process of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application in different up and down directions during 30° compression and 90° bending of the Kresling origami.

[0026] Figure 7 The theoretical results of the Kresling model in the locally resonant phononic crystal provided by an embodiment of the present application based on the finite particle method.

[0027] Figure 8 The band gap regulation effect of the symmetric up and down compression deformation process of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application.

[0028] Fig. 9 The vibration modes and characteristic frequencies of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application during symmetric 30° compression.

[0029] Fig.10 The band gap regulation effect of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application during asymmetric compression while keeping the total height the same;

[0030] Fig.11 The band gap regulation effect of the symmetric bending of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application during 30° compression of the Kresling origami.

[0031] Fig.12 Research on the band gap regulation effect and vibration loss in different up and down directions of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application during 30° compression and 90° bending of the Kresling origami.

[0032] Fig.13 The band gap regulation effect in different directions of the omnidirectional bending of four arrays of the unit cell of the locally resonant phononic crystal provided by an embodiment of the present application in the Kresling origami.

[0033] Fig.14 Schematic diagram of a checkerboard mosaic array form based on paper-cutting provided by an embodiment of the present application.

[0034] Fig.15 Top view of a checkerboard mosaic array form based on paper-cutting provided by an embodiment of the present application.

[0035] Fig.16 Change process of the topological rotation of the paper-cutting substrate provided by an embodiment of the present application.

[0036] Fig.17 An array form provided by an embodiment of the present application based on a Miura origami substrate.

[0037] Fig.18 The folding process of the substrate based on Miura origami provided by an embodiment of the present application and its changes relative to the Kresling origami column array.

[0038] Fig.19 An array form of a bistable shell substrate based on SMP provided by an embodiment of the present application.

[0039] Fig. 20 The symmetric change process of the substrate of the bistable shell based on SMP provided by an embodiment of the present application.

[0040] Fig.21 The asymmetric change process of the substrate of the bistable shell based on SMP provided by an embodiment of the present application.

[0041] Fig. 22 An expandable origami and paper-cutting array form provided by an embodiment of the present application. Detailed implementation manners

[0042] As can be seen from the background art, the application research of the Kresling origami structure in the field of metamaterials is relatively less. Due to its unique geometric tunability and dynamic mechanical properties, this origami structure is particularly suitable for high-demand application scenarios that require precise control of mechanical properties and structural variability.

[0043] The paper-cutting structure shows significant potential due to its ability to achieve specific geometric shapes and complex three-dimensional structures. Traditional paper-cutting forms structures with complex geometric patterns and mechanical properties through the cutting and folding of planar materials. Due to their inherent symmetry and geometric complexity, these structures exhibit diversity and tunability in mechanical properties. The Miura origami structure has been widely used in the fields of space structures and flexible materials due to its excellent folding performance and high scalability. The uniqueness of this structure lies in its ability to achieve a rapid conversion between two dimensions and three dimensions through simple folding actions, with excellent reversibility and repeatability.

[0044] Locally Resonant Phononic Crystals (LRPCs) have attracted much attention in recent years due to their unique advantages in vibration control. By embedding local resonance units with specific resonance frequencies inside the material, LRPCs can form bandgaps at lower frequencies, thereby effectively suppressing the vibration propagation within a specific frequency range. Shape Memory Polymer (SMP), as a stimulus-responsive intelligent polymer material, can undergo morphological changes in response to specific stimuli, and has advantages such as fast response speed, adjustable response temperature, and diverse excitation methods, making it one of the current popular functional materials.

[0045] The main advantages of the Kresling origami structure itself lie in the flexibility and adjustability of structural changes, and the local resonance mechanism has a stable vibration suppression effect in a specific frequency band. To solve the above technical problems, the present application provides a locally resonant phononic crystal based on Kresling origami, which combines the Kresling origami structure and the local resonance mechanism. The locally resonant phononic crystal includes: a substrate and a vibration damping array embedded on the substrate; the vibration damping array includes a plurality of unit cell structures arranged in an array; the unit cell structure includes at least two spiral Kresling origami structures, the middle part of the Kresling origami structure is embedded in the substrate, and its upper and lower parts are exposed outside the substrate; a lead injection hole penetrating the Kresling origami structure is provided inside the Kresling origami structure; the substrate is one of an Archimedean spiral parallel plate, a checkerboard inlaid paper-cut, a double-layer Miura origami, or a bistable shell based on a shape memory polymer; the material of the Kresling origami structure is lead, with a density of 11600 kg / m 3 , an elastic modulus of 20.80 GPa, and a Poisson's ratio of 0.369.

[0046] The present application provides a locally resonant phononic crystal based on Kresling origami, which generates a significant vibration bandgap in the low-frequency band through its unique geometric characteristics, effectively suppressing the vibration propagation in a specific frequency band, and having good prospects in low-frequency vibration reduction and noise reduction. The structure of the locally resonant phononic crystal effectively enhances the bandgap width by relying on the local resonance mechanism and realizes precise regulation of multiple frequency bands, thereby greatly improving its adaptability and flexibility in complex vibration environments.

[0047] The following will elaborate on each embodiment of the present application with reference to the accompanying drawings. However, those of ordinary skill in the art can understand that in each embodiment of the present application, many technical details are provided to help readers better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in the present application can still be implemented.

[0048] An embodiment of the present application provides a locally resonant phononic crystal based on Kresling origami, including: a substrate and a vibration damping array embedded in the substrate; the vibration damping array includes a plurality of unit cell structures arranged in an array; the unit cell structure includes at least two spiral Kresling origami structures, the middle part of the Kresling origami structure is embedded in the substrate, and its upper and lower parts are exposed outside the substrate; a lead injection hole penetrating through the Kresling origami structure is opened inside the Kresling origami structure; the substrate is one of an Archimedean spiral parallel plate, a checkerboard inlaid paper-cut, a double-layer Miura origami or a bistable shell based on a shape memory polymer; the material of the Kresling origami structure is lead, with a density of 11600 kg / m 3 , an elastic modulus of 20.80 GPa, and a Poisson's ratio of 0.369.

[0049] Specific implementation manner 1: As Figure 1 shown, the present application discloses a locally resonant phononic crystal based on Kresling origami. The first vibration damping array substrate uses an Archimedean spiral parallel plate as the substrate, and the vibration damping array is arranged in the xy direction. The vibration damping and noise reduction effects are improved by increasing the number of unit cells. The Archimedean spiral inside the Archimedean spiral parallel plate can form a complex vibration propagation path to guide and control the propagation and local resonance of waves, thereby affecting its bandgap properties; the unit cell structure includes two spiral Kresling origami structures, and the two spiral Kresling origami structures are respectively embedded in the upper and lower parts of the Archimedean spiral parallel plate. As Figure 2 shown, a unit cell structure of a locally resonant phononic crystal based on an Archimedean spiral parallel plate with the Archimedean spiral 1-3 as the substrate is adopted. The unit cell structure includes two spiral Kresling origami structures 1-1, and a lead injection hole 1-4 is provided at the center position of the Kresling origami structure. The two spiral Kresling origami structures 1-1 are embedded in the upper and lower parts of a parallel plate 1-2 based on the Archimedean spiral 1-3.

[0050] As shown in Table 1, the structural parameters of a locally resonant phononic crystal based on an Archimedean spiral parallel plate are given. The size of the parallel plate 1-2 based on the Archimedean spiral 1-3 is 30 mm in length, 30 mm in width, 2 mm in thickness, and the width of the parallel plate spiral groove is 2 mm.

[0051] Table 1 Structural parameters of a locally resonant phononic crystal based on an Archimedean spiral parallel plate

[0052]

[0053] Among them, the formula for the Archimedean spiral 1-3 is:

[0054] xt :(6.25 + 3*t)*cos(2*π*t)

[0055] y t :(6.25 + 3*t)*sin(2*π*t)

[0056] Archimedean spiral parameter t 1 -t 2 : 0 - 2.5

[0057] As shown in Table 2, the material of the Kresling origami structure 1 - 1 is lead, with a density of 11600 kg / m 3 , an elastic modulus of 20.80 GPa, and a Poisson's ratio of 0.369. The parallel plate 1 - 2 based on the Archimedean spiral is made of aluminum, with a density of 2730 kg / m 3 , an elastic modulus of 77.60 GPa, and a Poisson's ratio of 0.352.

[0058] Table 2 Material parameters of the spiral resonant unit

[0059]

[0060] Specific implementation method 2: As Figures 3 to 6 shown, this implementation method is a further explanation of Specific implementation method 1, and this implementation method shows the deformation process of the unit cell with various geometric configurations. As Figure 3 shown, it shows the folding process (0°, 30°, 45°, 60°) of the unit cell under symmetric compression from top and bottom. As the folding angle increases, the structure gradually becomes compact, and reaches the tightest state at 60°, with a height of 1 / 10 of the unfolded height. As Figure 4 shown, it shows the deformation process of the unit cell under asymmetric compression from top and bottom while keeping the total height the same. The deformation process with a total height of 22 mm includes: (a) 2 mm at the top and 20 mm at the bottom, (b) 6 mm at the top and 16 mm at the bottom, (c) 10 mm at the top and 12 mm at the bottom, (d) 14 mm at the top and 8 mm at the bottom, (e) 18 mm at the top and 4 mm at the bottom. As Figure 5 shown, it shows the symmetric bending deformation process (0°, 30°, 60°, 90°, 120°, 150°) of the Kresling origami structure 1 - 1 under 30° compression. The structure maintains geometric integrity from the vertical state to the extreme bending. As Figure 6 shown, it shows the deformation process in different directions from top and bottom of the Kresling origami structure 1 - 1 under 30° compression and 90° bending, covering different bending angles (0°, 45°, 90°, 135°, 180°). These schematic diagrams reflect the deformation characteristics under different geometric configurations.

[0061] Specific implementation method 3: As Figure 7As shown, this embodiment is a further explanation of the specific embodiment one, and this embodiment shows the theoretical results of the Kresling model of the local resonant phononic crystal based on the finite particle method. (a) is the size parameter and particle position of the model. (b) shows the displacement curve of particle 7 in the x, y, and z directions over time, reflecting the dynamic response of the structure. With the addition of external force, the displacement in the z direction increases sharply, indicating that the structure enters the instability stage. (c) shows the 3D motion trajectory of particles 7-12 during the folding process, and each trajectory presents a 3D spiral. (d) The projection of the motion trajectory is an arc, which verifies the accuracy of the finite particle method. (e) shows the support reaction force change curve of particles 1-6. The support reaction force drops sharply after instability, reflecting the bistable characteristics of the Kresling origami structure 1-1. The simulation results accurately capture the complex deformation process of the structure under the action of external loads.

[0062] Specific implementation method four: Figure 8 As shown, this embodiment is a further explanation of the specific embodiment 1. This embodiment explores the band gap regulation effect during the upper and lower symmetrical compression deformation process of the local resonant phononic crystal unit cell. (a) The changes of the spiral resonance unit Kresling origami structure 1-1 at different folding angles (0°, 30°, 45°, 60°) are shown. As the folding angle increases, the structure gradually becomes more compact, reaching the most compact state at 60°, and the height is 1 / 10 of the unfolded height. (b)-(e) The band gap is mainly concentrated in the range of 55Hz-155Hz. As the folding angle increases, the band gap width gradually decreases, especially in the low frequency band, the band gap becomes significantly narrower. (f) The yellow area shows the change of the band gap width with the rotation angle. Folding causes the band gap to be reduced from two regions to one, and the lower limit increases significantly. The rotation angle of the Kresling origami structure 1-1 significantly affects the vibration band gap. This regulation capability is suitable for vibration filters and noise suppression systems.

[0063] Specific implementation method five: Fig. 9As shown, this embodiment is a further illustration of Embodiment 1. This embodiment shows the vibration modes and characteristic frequencies of the local resonance phononic crystal unit cell under symmetric 30° compression. The unit cell exhibits various vibration modes from global to local in the frequency range of 60.146 Hz to 79.99 Hz. (a) The Kresling origami structure 1-1 with a 45° rotation angle forms a helical resonance unit. (b) At 60.146 Hz, the deformation mainly concentrates in the middle and lower parts of the helix, showing shear deformation and slight torsion, reflecting the global stiffness and stability of the structure. (c) At 74.318 Hz, obvious torsion and bending occur in the surrounding band in the middle region, revealing the possibility of instability under local stress concentration. (d) At 79.99 Hz, the deformation gradually changes from top to bottom, showing periodic fluctuations, which may affect the dynamic performance of the structure.

[0064] Embodiment 6: As Fig.10 shown, this embodiment is a further illustration of Embodiment 1. This embodiment shows the bandgap regulation effect of the local resonance phononic crystal unit cell under asymmetric compression while keeping the total height the same. (a) The upper-middle bandgap slightly decreases, and there is no bandgap between 110 - 140 Hz. (b) The bandgap mainly concentrates in the low-frequency band below 100 Hz, and the upper structure is longer, enhancing the transmission characteristics in the high-frequency band. (c) When the upper height is small, the low-frequency bandgap is small and expands with the increase of height, and the middle-frequency bandgap is the most obvious. When the height difference between the upper and lower parts is large, the bandgap at 150 Hz above becomes smaller until it disappears; when the heights are close, the bandgap is the widest.

[0065] Embodiment 7: As Fig.11 shown, this embodiment is a further illustration of Embodiment 1. This embodiment shows the bandgap regulation effect of the local resonance phononic crystal unit cell under symmetric bending when the Kresling origami structure 1-1 is compressed at 30°. (a)-(c) The energy band structures at different bending angles (90°, 120°, 150°) hardly change significantly, and there are obvious low-frequency bandgaps, indicating that the bending angle has little effect on the low-frequency bandgap, showing the design robustness and stability of the structure. (d) shows the geometric shapes of the Kresling origami structure 1-1 at different bending angles, indicating that the structure can adapt to different spatial and angular changes without affecting the acoustic performance. (e) The bandgap distributions are consistent at different bending angles, further proving the stability of the design in maintaining the acoustic performance at multiple angles. In practical applications, the bending angle of the structure can be freely adjusted according to requirements, and the bandgap is not affected much, and it can still maintain a strong low-frequency vibration and noise reduction function.

[0066] Embodiment 8: As Fig.12As shown, this embodiment is a further illustration of the first specific embodiment. This embodiment demonstrates the study of bandgap regulation and vibration loss in different up and down directions when the local resonance phononic crystal unit cell is compressed at 30° and bent at 90° in the Kresling origami structure 1-1. (a)-(c) show the band diagrams and transmission loss frequency response curves of the up and down Kresling origami structures 1-1 at different relative angles (0°-90°) when bent at 90°. For 0° (fully aligned), the bandgap completely disappears, indicating that the structure has little blocking effect on vibration waves and the weakest vibration damping effect. As the symmetry is broken (45°, 90°), the bandgap gradually forms, and the bandgap is the largest at 90°, showing the strongest vibration blocking effect.

[0067] Specific Embodiment Nine: As Fig.13 shown, this embodiment is a further illustration of the first specific embodiment,

[0068] This embodiment demonstrates the bandgap regulation effect when the unit cell is bent omnidirectionally in four arrays of the Kresling origami structure 1-1. (a) The four Kresling origami structure 1-1 units have the same direction, forming a completely symmetric arrangement, with a significant and wide bandgap (120 Hz to 170 Hz), showing good low-frequency vibration isolation effect. (b) Two pairs of the four units have the same direction, and the other pair has the opposite direction, forming mirror symmetry. The bandgap decreases, but still has obvious vibration blocking ability. (c) The four units are arranged in different directions, forming a rotating square symmetry. The bandgap decreases significantly, and only a very narrow bandgap appears around 150 Hz, showing a low vibration suppression efficiency, but it may be suitable for applications requiring frequency sensitivity.

[0069] Specific Embodiment Ten: This application discloses a local resonance phononic crystal based on Kresling origami. The second vibration damping array substrate uses the checkerboard mosaic paper-cut 2-1 as the substrate. The vibration damping arrays are arranged in the xy direction, and the vibration damping and noise reduction effects are improved by increasing the number of unit cells. The deformation process of the checkerboard mosaic paper-cut has infinite scalability, and the substrate area can be flexibly adjusted, which is suitable for different vibration frequency bands and environmental requirements; the substrate includes several identical paper-cut squares, and each paper-cut square is connected by a flexible material to form an adjustable structure with a telescopic function; the unit cell structure includes two spiral Kresling origami structures, and the two spiral Kresling origami structures are respectively embedded in the upper and lower parts of the substrate with the checkerboard mosaic paper-cut. As Fig.14As shown, two spiral Kresling origami structures 1-1 are embedded in the upper and lower parts of the checkerboard mosaic base made of paper-cut 2-1. The base structure is composed of several identical paper-cut 2-1 squares, and each paper-cut 2-1 square is connected by a flexible material TPU, thereby forming an adjustable structure with a telescopic function. The paper-cut 2-1 material is aluminum, with a density of 2730 kg / m 3 , an elastic modulus of 77.60 GPa, a Poisson's ratio of 0.352, the length of the paper-cut 2-1 is 10 mm, the width is 10 mm, and the thickness is 2 mm. On the premise that the base thickness remains unchanged, the base area can be flexibly adjusted. At the same time, the deformation process of the base has infinite scalability and is not limited to the array form listed in this application, showing a wider range of applicability and flexibility.

[0070] Specific Embodiment XI: This embodiment is a further description of Specific Embodiment X. As Fig.15 shown, this embodiment shows a top view of a checkerboard mosaic array form based on paper-cut 2-1. As Fig.16 shown, it shows the change process of the topological rotation of the paper-cut 2-1 base. The deformation process of the base has infinite scalability and is not limited to the array form listed in this application, showing a wider range of applicability and flexibility.

[0071] Specific Embodiment XII: The present application discloses a locally resonant phononic crystal based on Kresling origami. The third vibration damping array base uses a double-layer Miura origami 3-1 as the base. The vibration damping arrays are arranged in the xy direction, and the vibration damping and noise reduction effects are improved by increasing the number of unit cells. The symmetric arrangement of the double-layer Miura origami 3-1 can reduce the uneven stress distribution and enhance the overall stability of the structure, making it show better anti-deformation ability during vibration; the base includes several identical parallelogram Miura origami, and each Miura origami is connected through the vertices of the parallelogram, and each Miura origami is connected by a flexible material; the unit cell structure includes several spiral Kresling origami structures. As Fig.17 shown, each spiral Kresling origami structure 1-1 is embedded in the raised part with every two adjacent Miura origami 3-1 as the base. The base structure is composed of several completely identical parallelogram Miura origami 3-1, and each Miura origami 3-1 is connected by a flexible material TPU, thereby deriving a structure with a folding function. The material of the parallelogram Miura origami 3-1 is aluminum, with a density of 2730 kg / m 3 , an elastic modulus of 77.60 GPa, a Poisson's ratio of 0.352, and the side lengths are all 6.66 mm, and its two adjacent interior angles are 84° and 96° respectively.

[0072] Embodiment Thirteen: This embodiment is a further elaboration on Embodiment Twelve. As Fig.18 shown, this embodiment demonstrates the folding process of the substrate based on Miura origami 3-1 and its changes relative to the kresling origami structure 1-1 array. In this application, the substrate design based on the double-layer Miura origami 3-1 demonstrates its folding process and relative changes with respect to the Kresling origami 1-1 column array. This process is divided into three stages, corresponding to different folding angles: 0°, 55°, and 70°. When the folding angle is 0°, no folding operation is performed on the Kresling origami structure 1-1. As can be seen from the top view, the arrangement of the Kresling origami structure 1-1 array presents a hexagonal shape. When the folding angle is 55°, as the folding angle increases, the structure begins to fold upward, forming a certain three-dimensional shape. At this time, the arrangement of the Kresling origami structure 1-1 array also changes accordingly, enhancing the stability and load-bearing capacity of the structure. When the folding angle is 70°, the Kresling origami structure 1-1 further folds, forming a more significant three-dimensional effect. The change in the Kresling origami structure 1-1 array is more obvious, showing higher space utilization and structural strength.

[0073] Embodiment Fourteen: This application discloses a locally resonant phononic crystal based on Kresling origami. The fourth vibration damping array substrate uses a bistable shell 4-2 made of shape memory polymer (SMP) as the substrate. The vibration damping arrays are arranged in the xy direction, and the vibration damping and noise reduction effects are improved by increasing the number of unit cells. The bistable shell 4-2 deforms when the environmental temperature exceeds its glass transition temperature, and its elastic modulus decreases significantly. External force can be applied to achieve folding, and the structure remains in the folded state after the temperature and pressure are removed. The unit cell structure includes several spiral Kresling origami structures 4-1. A lead injection hole is provided at the center of the Kresling origami structure 4-1. Each spiral Kresling origami structure 4-1 is embedded in the upper and lower parts of the bistable shell 4-2 made of shape memory polymer (SMP). The material of the Kresling origami structure 4-1 is lead, with a density of 11600 kg / m 3 , an elastic modulus of 20.80 GPa, and a Poisson's ratio of 0.369. The material of the bistable shell 4-2 made of shape memory polymer (SMP) is shape memory polymer (SMP).

[0074] Embodiment Fifteen: This embodiment is a further elaboration on Embodiment Fourteen. As Fig. 20 shown, this embodiment demonstrates the symmetric change of the substrate based on the bistable shell 4-2 made of shape memory polymer (SMP). As Fig.21As shown, this embodiment demonstrates the asymmetric variation based on the bistable shell 4-2 made of shape memory polymer (SMP). The bistable shell 4-2 made of shape memory polymer (SMP) has excellent substrate stability. When the environmental temperature exceeds its glass transition temperature, the structure deforms, and the elastic modulus decreases significantly. The folding can be easily achieved by applying an external force. When the temperature and pressure are released, the structure remains in the folded state and will not automatically recover; when only heated without applying an external force, the structure morphology will be automatically reset.

[0075] Specific Embodiment Sixteen: This embodiment further elaborates on Specific Embodiment One and Specific Embodiment Ten. The expandable origami and paper-cutting arrays have a wider range of application scenarios. The origami and paper-cutting array forms are based on different geometric patterns (such as Pattern One, Pattern Two, and Pattern Three), and each pattern corresponds to different folding and cutting methods. By adjusting the value of the parameter n, different shapes and structures can be achieved. Pattern One (n = 2): Plane: Forms a cross-shaped structure, suitable for basic folding and connection. Folding: Through specific folding lines, a simple three-dimensional structure is formed. Periodic structure: Can be arranged repeatedly to form a grid-like structure. Brillouin zone: In a two-dimensional plane, it defines the basic symmetry and periodicity. Pattern Two (n = 4): Plane: Forms a square structure, suitable for more complex folding. Folding: Through multiple folding lines, a more complex three-dimensional form is formed. Periodic structure: Can form a denser grid, suitable for large-area coverage. Brillouin zone: Demonstrates higher symmetry, suitable for various applications. Pattern Three (n = 6): Plane: Forms a hexagonal structure, with good space-filling characteristics. Folding: Through fine folding techniques, a complex three-dimensional structure is formed. Periodic structure: Can form a highly complex grid, suitable for the art and design fields. Brillouin zone: Demonstrates the symmetry of a hexagon, suitable for various physical and engineering applications.

[0076] It should be noted that the bandgap of the locally resonant phononic crystal provided in this application is concentrated in the range of 55 Hz to 155 Hz, and as the folding angle increases, the bandgap width gradually decreases. When the locally resonant phononic crystal is symmetrically compressed by 30°, the vibration modes and characteristic frequencies show various vibration modes from overall to local in the range of 60.146 Hz to 79.99 Hz. When the locally resonant phononic crystal maintains the same total height but is asymmetrically compressed, the bandgap is mainly concentrated in the low-frequency band below 100 Hz, and when the upper structure is longer, the transmission characteristics in the high-frequency band are enhanced.

[0077] In some embodiments, when the local resonance phononic crystal is compressed at 30° of the Kresling origami structure, the bandgap regulation effect of symmetric bending remains consistent at different bending angles, and the low-frequency bandgap is not affected by the bending angle. When the local resonance phononic crystal is compressed at 30° and bent at 90° of the Kresling origami structure, the research on the bandgap regulation and vibration loss in different directions above and below shows that as the symmetry is broken, the bandgap gradually forms, and the bandgap is the largest at 90°, showing the strongest vibration isolation effect. When the local resonance phononic crystal is omnidirectionally bent in four arrays of the Kresling origami structure, the bandgap regulation effect shows different bandgap widths and vibration suppression efficiencies under different arrangements.

[0078] The local resonance phononic crystal provided in this application sets the structural geometric parameters and performs theoretical solutions through the Finite Particle Method (FPM), and the geometric constraint relationship and mechanical properties of the Kresling origami structure are obtained through rigorous geometric derivation and correction. The vibration bandgap of the local resonance phononic crystal is finely regulated through nonlinear effects and coupling effects, and the geometric nonlinear characteristics and complex vibration modes of the Kresling origami structure can achieve precise regulation of the vibration bandgap.

[0079] Establishment of the theoretical model: Using the finite particle method and introducing various nonlinear corrections and advanced mathematical derivations to set the structural geometric parameters and perform the theoretical solution of the finite particle method. As shown in Fig. 9 (a), the Kresling origami structure consists of two upper and lower regular hexagonal bases and 12 truss elements connecting these two bases. Through rigorous geometric derivation and correction in this study, the geometric constraint relationship and mechanical properties of the structure are obtained.

[0080] First, based on the geometric constraint relationship of the structure, the calculation formula for the circumradius R is as follows:

[0081]

[0082] where a is the base length and n is the number of sides of the polygon. The initial twist angle θ 0 is obtained by solving the following nonlinear equation:

[0083]

[0084] On this basis, the length c of the side fold valley is obtained through the following geometric derivation:

[0085]

[0086] Among them, α is the correction angle related to the structural torsion, and λ is the material geometric nonlinear parameter, which is used to consider the influence of geometric deformation on the structural response under large deformation conditions. When the structure is in the fully folded state, the maximum rotation angle φ max is calculated by the formula:

[0087]

[0088] Among them, β is the additional torsion angle generated during the folding process of the structure. μ is the high-order correction term, which is used to describe the geometric changes caused by local structural resonance.

[0089] We choose the finite particle method to solve the structure. The finite particle method is a powerful numerical method. By discretizing the structure into a particle system and using the dynamic equation based on Newton's second law, it can effectively handle complex geometric and material nonlinear behaviors. In this method, the position update formula of the particle is as follows:

[0090]

[0091] Among them, x t+Δt , x t , x t-Δt are the particle positions at the next moment, the current moment, and the previous moment respectively, Δt is the time step, m is the particle mass, F ext and F int are the external force and the internal force respectively, γ is the damping coefficient, which is used to simulate the energy dissipation in the actual material. In addition, the correction force f correction (x t , v t ) is the correction term introduced to correct the high-order nonlinear effects (such as material plasticity or large deformation). a t is the acceleration at the current moment, and the third term is the high-order correction term, which is used to further improve the accuracy.

[0092] For each truss element, the internal force calculation formula is:

[0093]

[0094] Among them, ΔL = L - L 0 represents the change in the rod length at the current moment compared with the initial length, L 0 is the initial length, E is the elastic modulus of the material, and A is the cross-sectional area. ξ is the third-order correction coefficient, which reflects the nonlinear elastic response of the material under large deformation conditions. The total internal force F int acting on the particle is calculated by the following formula:

[0095]

[0096] Among them, ei is the unit direction vector of the i-th rod, is the additional internal force term introduced to account for high-order nonlinear factors (such as shear effect and bending effect), is the additional internal force term considering the coupling effect of local resonance and structural deformation.

[0097] To ensure the stability and accuracy of the calculation, the time step Δt is controlled by the following conditions:

[0098]

[0099] where, is the material wave speed, κ is the coefficient related to material nonlinearity, ΔL max is the length change of the rod at the maximum deformation. This condition ensures the convergence and physical rationality of the numerical calculation and can effectively capture the local resonance phenomenon in the phononic crystal.

[0100] In a phononic crystal, the propagation of vibration is jointly affected by the lattice structure and material properties. For wave propagation in a one-dimensional lattice, it can be described by the following basic wave equation:

[0101]

[0102] where, u(r,t) is the displacement field, and is the wave speed in the medium. For a periodic structure, the solution of the wave equation can be expressed by Bloch's theorem as:

[0103] u(x,t) = U(x)e i(k·x-ωt) (10)

[0104] where, U(x) is a periodic function, k is the wave vector, and ω is the angular frequency. To analyze the wave characteristics after introducing local resonance, we can further introduce a correction to the wave vector:

[0105] k = k 0 + k 1 (ω) + εk 2 (ω) (11)

[0106] where, k 0 is the basic wave vector, k 1 (ω) and k 2 (ω) are frequency-dependent high-order correction terms, and ε is a small parameter used to represent the nonlinear strength of the system. The correction of the wave vector can accurately describe the complex behavior of wave propagation in the crystal in the presence of local resonance units.

[0107] The local resonance unit is the core component for LRPCs to achieve vibration band gaps. The classical mass-spring model describes the dynamic behavior of simple resonance units, but in LRPCs, due to the existence of multiple resonance effects and nonlinear couplings, more complex models need to be introduced for analysis.

[0108] Assuming the displacement of each local resonance unit is u(t), its dynamic behavior can be described by the following nonlinear differential equation:

[0109]

[0110] where m is the mass, ζ is the damping coefficient, k is the spring constant, α is the nonlinear stiffness coefficient, and F(t) is the external driving force. The nonlinear term αu(t) 3 introduces the cubic harmonic effect to describe the nonlinear response of the unit under large amplitude conditions.

[0111] In the frequency domain, the solution of the above equation can be expressed as:

[0112]

[0113] This formula not only considers the linear vibration response but also includes the self-excited vibration and frequency mixing phenomena introduced by nonlinear effects. These phenomena play important roles in practical LRPCs, especially in vibration reduction applications.

[0114] For local resonance phononic crystals with multi-dimensional structures, the vibration propagation and band gap formation mechanisms are more complex. In a two-dimensional system, the vibration propagation can be described by the following partial differential equation:

[0115]

[0116] where r = (x, y) is the two-dimensional coordinate, and λ is the high-order correction term used to consider the high-order vibration modes introduced by complex geometric structures. In a three-dimensional structure, the wave equation can be further extended to:

[0117]

[0118] where μ is the sixth-order correction term specifically used to describe the wave behavior in three-dimensional complex structures. Under these conditions, the coupling effect between the local resonance unit and the lattice structure greatly affects the dispersion relation and band gap distribution.

[0119] The solution of the dispersion relation usually involves complex eigenvalue problems. For example, for a two-dimensional lattice structure, the dispersion relation can be solved through the following eigenvalue problem:

[0120] det[D(k)-ω 2 M-η(ω)K(k)]=0 (16)

[0121] Among them, D(k) is the dynamic matrix, M is the mass matrix, K(k) is the supplementary stiffness matrix, and η(ω) is the frequency-dependent coupling coefficient. By solving this eigenvalue problem, the dispersion curve of the system can be obtained, and further analyze the formation of the vibration band gap and its relationship with the system parameters.

[0122] When using the finite element method to solve, due to the periodic characteristics of the structure in all directions, we can only consider one of the unit cell structures. The eigenvalue equation in the discrete form of the unit cell is:

[0123] (K - ω 2 M)u = f (17)

[0124] Stiffness matrix:

[0125] K = ∫B T C(r)BdV e (18)

[0126] Mass matrix:

[0127] M = ∫N T ρ(r)NdV e (19)

[0128] Displacement matrix:

[0129] u = [u 1 , u 2 , u 3 , …, u n T (20)

[0130] Force vector matrix:

[0131] f = [f 1 , f 2 , f 3 , …, f n T (21)

[0132] Among them, B represents the strain matrix, N represents the shape function matrix, V e represents the surface area of the entire unit cell, and u i = [u i v i w i T represents the displacement of each node. According to Bloch's theorem, the displacement field is expressed as:

[0133] U(r) = e i(k·r) U k (r) (22)

[0134] Due to the periodicity of the phononic crystal, the entire lattice satisfies the Bloch periodic condition. Therefore, the unit cell boundary is:

[0135] U(r + a) = e i(k·a) U k (r) (23)

[0136] where r is the outer boundary vector of the unit cell; a is the lattice constant vector; k is the wave vector, k = (k x , k y , k z ); U k (r) is a periodic function. By scanning the irreducible Brillouin zone with the wave vector k, the frequency corresponding to the wave vector k can be obtained from equations (17) and (23), thereby establishing the band structure.

[0137] The vibration band gap of locally resonant phononic crystals is not only affected by the mass, stiffness, and arrangement of the resonant units, but can also be finely tuned through nonlinear effects and coupling effects. By introducing nonlinear design and the synergistic effect of multiple resonant units, LRPCs can form band gaps in a wider frequency range, thereby enhancing the vibration damping effect. Based on the locally resonant unit of the Kresling structure, using its geometric nonlinear characteristics and complex vibration modes, precise control of the vibration band gap can be achieved. This control mechanism not only provides theoretical support for the application of LRPCs in practical engineering, but also provides new ideas for designing intelligent vibration damping systems with adaptive characteristics.

[0138] The vibration damping effect and noise reduction effect of the locally resonant phononic crystals provided by this application are evaluated respectively. The evaluation results of the vibration damping effect are as follows: The Kresling origami structure successfully realizes a high degree of control over the acoustic wave propagation path through its geometric deformation. At different folding angles, the structure shows the ability to selectively block acoustic waves in different frequency bands, which has a great effect on low-frequency vibration damping and noise reduction and the subsequent design of phononic crystals. The checkerboard mosaic locally resonant phononic crystal based on paper-cutting forms a structure with telescopic function through the connection between vertices, which can flexibly adjust its shape under the action of external vibration, thereby effectively dispersing vibration energy, reducing vibration propagation, and enhancing the vibration damping effect. While keeping the substrate thickness unchanged, the substrate area can be flexibly adjusted. Adjusting the substrate area can change the natural frequency and damping characteristics of the locally resonant unit, further optimizing the vibration damping performance and making it suitable for vibration environments in different frequency ranges. The bistable characteristics of shape memory polymers allow the stiffness and modulus of the material to be controlled by changing the environmental temperature. When the temperature exceeds the glass transition temperature, the elastic modulus of the SMP material decreases and it can be easily folded. This folded state enables the crystal structure to better adapt to changes in vibration frequency and enhances its vibration damping effect.

[0139] The evaluation results of the noise reduction effect are as follows: The rotation angle of the Kresling origami structure has a significant impact on the vibration band gap. This regulation ability can be used for frequency-selective conduction and isolation of vibrations, and is applicable to vibration filters and noise suppression systems. For the checkerboard-inlaid local resonance phononic crystal based on paper-cutting, this inlaid structure not only has good mechanical stability, but also can more effectively isolate and attenuate noise due to its regular arrangement, especially performing excellently in complex sound field environments. For the local resonance phononic crystal based on double-layer Miura origami, it allows for flexible regulation of the mechanical properties and vibration damping effect of the structure according to different requirements, so as to adapt to different application scenarios. By adjusting the substrate thickness, the resonance frequency and stiffness of the system can be changed, while adjusting the substrate area can effectively affect the propagation of sound waves and the distribution of energy, further improving the vibration reduction and noise reduction performance. The bistable characteristics of SMP provide excellent substrate stability. When the structure deforms under the external environment, it can be locked in the folded state to prevent repeated deformation caused by vibration or noise, thus ensuring long-term effective vibration and noise control.

[0140] According to the above technical solution, an embodiment of the present application provides a local resonance phononic crystal based on Kresling origami, including: a substrate and a vibration damping array embedded on the substrate; the vibration damping array includes a plurality of unit cell structures arranged in an array; the unit cell structure includes at least two spiral Kresling origami structures, the middle part of the Kresling origami structure is embedded in the substrate, and its upper and lower parts are exposed outside the substrate; a lead injection hole penetrating the Kresling origami structure is opened inside the Kresling origami structure; the substrate is one of an Archimedean spiral parallel plate, checkerboard-inlaid paper-cutting, double-layer Miura origami or a bistable shell based on shape memory polymer; the material of the Kresling origami structure is lead, with a density of 11600 kg / m 3 , an elastic modulus of 20.80 GPa, and a Poisson's ratio of 0.369.

[0141] The local resonance phononic crystal based on Kresling origami provided by the present application generates a significant vibration band gap in the low-frequency band through its unique geometric characteristics, effectively suppressing the vibration propagation in a specific frequency band. The Kresling origami structure can achieve diverse vibration band gap configurations by adjusting the folding angle and number of layers. The simple manufacturing and assembly process of the Kresling origami structure makes it have high application feasibility even under harsh working conditions. The dynamic regulation ability of the Kresling origami structure provides new possibilities for the development of future intelligent vibration reduction systems.

[0142] Those of ordinary skill in the art can understand that the above embodiments are specific examples for implementing the present application. In actual applications, various changes can be made to them in form and details without departing from the spirit and scope of the present application. Any person skilled in the art can make their respective changes and modifications without departing from the spirit and scope of the present application. Therefore, the protection scope of the present application shall be subject to the scope defined by the claims.

Claims

1. A local resonance phononic crystal based on Kresling origami, characterized in that: include: A substrate and a vibration reduction array embedded in the substrate; The vibration reduction array includes a plurality of unit cell structures arranged in an array; the unit cell structure includes at least two spiral Kresling origami structures, the middle portion of the Kresling origami structure is embedded in the substrate, and the upper and lower portions of the Kresling origami structure are exposed on the substrate; A lead injection hole penetrating through the Kresling origami structure is provided inside the Kresling origami structure; The substrate is one of an Archimedean spiral parallel plate, a chessboard mosaic paper-cut, a double-layer Miura origami, or a bistable shell based on a shape memory polymer; The material of the Kresling origami structure is lead, with a density of 11600 kg / m 3 , the elastic modulus is 20.80 GPa, and the Poisson's ratio is 0.

369.

2. The Kresling origami-based local resonance phononic crystal according to claim 1, characterized in that: The substrate is an Archimedean spiral parallel plate; the Archimedean spiral inside the Archimedean spiral parallel plate can form a complex vibration propagation path to guide and control wave propagation and local resonance, thereby affecting its band gap properties; The unit cell structure comprises two spiral Kresling origami structures, and the two spiral Kresling origami structures are respectively embedded in the upper part and the lower part of the Archimedean spiral parallel plate.

3. The local resonance phononic crystal based on Kresling origami according to claim 2, characterized in that: The material of the Archimedean spiral parallel plate is aluminum, with a density of 2730 kg / m 3 , the elastic modulus is 77.60 GPa, the Poisson's ratio is 0.352, the parallel plate length is 30 mm, the width is 30 mm, the thickness is 2 mm, and the parallel plate spiral groove width is 2 mm.

4. The Kresling origami-based local resonance phononic crystal according to claim 1, characterized in that: The base is a chessboard inlaid paper-cut; the deformation process of the chessboard inlaid paper-cut has infinite scalability, and the base area can be flexibly adjusted, which is suitable for different vibration frequency bands and environmental requirements; The base includes a plurality of identical paper-cut squares, each of which is connected by a flexible material to form an adjustable structure with telescopic function; The unit cell structure comprises two spiral Kresling origami structures, which are respectively embedded in the upper part and the lower part of a substrate with chessboard mosaic paper-cutting as the substrate.

5. The local resonance phononic crystal based on Kresling origami according to claim 4, characterized in that: The paper-cut material is aluminum, with a density of 2730 kg / m 3 , the elastic modulus is 77.60 GPa, and the Poisson's ratio is 0.

352.

6. The Kresling origami-based local resonance phononic crystal according to claim 1, characterized in that: The substrate is a double-layer Miura origami; the symmetrical arrangement of the double-layer Miura origami can reduce uneven stress distribution, enhance the overall stability of the structure, and enable it to exhibit better anti-deformation ability during vibration; The substrate comprises a plurality of identical parallelogram Miura origami, each Miura origami is connected by the vertices of the parallelogram, and each Miura origami is connected by a flexible material; The unit cell structure includes a plurality of spiral Kresling origami structures, and each spiral Kresling origami structure is embedded in the raised parts of two adjacent parallelogram Miura origami.

7. The Kresling origami-based local resonance phononic crystal according to claim 6, characterized in that: The material of the double-layer Miura origami is aluminum, with a density of 2730 kg / m3, an elastic modulus of 77.60 GPa, and a Poisson's ratio of 0.352; the sides of the parallelogram are 6.66 mm, and its two adjacent internal angles are 84° and 96° respectively.

8. The Kresling origami-based local resonance phononic crystal according to claim 1, characterized in that: The substrate is a bistable shell based on a shape memory polymer; the bistable shell deforms when the ambient temperature exceeds its glass transition temperature, the elastic modulus is significantly reduced, and the folding can be achieved by applying an external force, and after the temperature and pressure are released, the structure remains in a folded state; The unit cell structure includes a plurality of spiral Kresling origami structures, each of which is embedded in the upper and lower parts of a bistable shell based on a shape memory polymer.

9. The Kresling origami-based local resonance phononic crystal according to claim 8, characterized in that: The material of the Kresling origami structure is lead, with a density of 11600 kg / m 3 , the elastic modulus is 20.80 GPa, and the Poisson's ratio is 0.

369.

10. The Kresling origami-based local resonance phononic crystal according to claim 1, characterized in that: The band gap of the local resonance phononic crystal is concentrated in the range of 55 Hz to 155 Hz, and the band gap width gradually decreases as the folding angle increases; When the local resonance phononic crystal is compressed asymmetrically while maintaining the same total height, the band gap is concentrated in the low frequency band below 100 Hz; When the local resonance phononic crystal is compressed by 30° in the Kresling origami structure, the band gap regulation effect of the symmetrical bending remains consistent at different bending angles, and the low-frequency band gap is not affected by the bending angle.

Images