Kresling periodic structure and method for implementing bandgap regulation

Abstract

This disclosure relates to a Kresling periodic structure and method for achieving bandgap control, comprising: establishing a dynamic model of the Kresling periodic structure and obtaining the bandgap characteristics of the periodic structure; normalizing the bandgap characteristics and combining the longitudinal polarization factor and the transverse polarization factor of the vibration mode of the periodic structure to obtain the longitudinal and transverse bandgap characteristics of the periodic structure; changing the panel shrinkage ratio and / or unfolding angle of the periodic structure to obtain the longitudinal and transverse bandgap characteristics of the periodic structure at different panel shrinkage ratios and / or unfolding angles; selecting the longitudinal and transverse bandgap characteristics that meet the design requirements of the periodic structure and obtaining the corresponding panel shrinkage ratio and / or unfolding angle; designing the final periodic structure based on the obtained panel shrinkage ratio and / or unfolding angle; the panel shrinkage ratio is the ratio of the radii of the circumcircles of each panel in the periodic structure, and the unfolding angle is the angular difference between each panel in the periodic structure.

Description

Technical Field

[0001] This disclosure relates to the field of spacecraft structural design, and in particular to a Kresling periodic structure and method for achieving bandgap control. Background Technology

[0002] Currently, in the field of spacecraft structural design, Kresling periodic structures can provide stable structural support for spacecraft and can achieve design requirements such as lightweight, foldable and high storage ratio.

[0003] However, the currently designed Kresling periodic structures cannot effectively control their bandgap characteristics, resulting in the existing Kresling periodic structures failing to meet the vibration isolation performance requirements of the design and thus exhibiting poor performance.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this disclosure is to provide a Kresling periodic structure and method for realizing bandgap control. This method can control the bandgap characteristics of the Kresling periodic structure in real time, so that the designed Kresling periodic structure can meet different vibration isolation requirements in real time.

[0006] This disclosure provides a method for implementing a Kresling periodic structure with bandgap modulation functionality, including:

[0007] A dynamic model of the Kresling periodic structure is established, and the bandgap characteristics of the Kresling periodic structure are obtained;

[0008] The bandgap characteristics of the Kresling periodic structure are normalized, and combined with the longitudinal polarization factor and the transverse polarization factor of the vibration mode of the Kresling periodic structure, the longitudinal bandgap characteristics and transverse bandgap characteristics of the Kresling periodic structure are obtained.

[0009] By changing the panel shrinkage ratio and / or unfolding angle of the Kresling periodic structure, the longitudinal bandgap characteristics and transverse bandgap characteristics of the Kresling periodic structure at different panel shrinkage ratios and / or unfolding angles can be obtained.

[0010] Based on the design requirements, select the longitudinal bandgap characteristics and transverse bandgap characteristics that meet the design requirements of the Kresling periodic structure, and obtain the corresponding panel shrinkage ratio and / or unfolding angle.

[0011] The final Kresling periodic structure is designed based on the obtained panel shrinkage ratio and / or unfolding angle;

[0012] Wherein, the panel shrinkage ratio is the ratio of the radii of the circumcircles of each panel in the Kresling periodic structure, and the unfolding angle is the angular difference between each panel in the Kresling periodic structure.

[0013] In one exemplary embodiment of this disclosure, establishing a dynamic model of the Kresling periodic structure and obtaining the bandgap characteristics of the Kresling periodic structure includes:

[0014] A Kresling periodic structure model is constructed, which includes two first panels arranged opposite each other, a second panel located between the two first panels, and a connecting rod connecting the first panel and the second panel. The panel shrinkage ratio is the ratio of the radius of the circumcircle of the second panel to the radius of the circumcircle of the first panel.

[0015] The Kresling periodic structure model is divided into nodes, and dynamic control equations for the displacement and nodal forces of the nodes are constructed based on the mass matrix and stiffness matrix of the Kresling periodic structure.

[0016] Based on the dynamic control equations, the propagation characteristics of elastic waves in the Kresling periodic structure are obtained, and the propagation characteristics are the bandgap characteristics of the Kresling periodic structure.

[0017] In one exemplary embodiment of this disclosure, the propagation characteristics of the elastic wave in the Kresling periodic structure are obtained according to the dynamic governing equations, including:

[0018] Apply displacement boundary condition constraints to both first panels;

[0019] Based on the applied displacement boundary conditions and the dynamic control equations, the relationship between the nodal forces of the nodes and the wave vector of the elastic wave is obtained to obtain the bandgap characteristics of the Kresling periodic structure.

[0020] In one exemplary embodiment of this disclosure, the dynamic control equation is:

[0021]

[0022] Where M is the mass matrix of the Kresling periodic structure. Let be the acceleration of the node, K be the stiffness matrix of the Kresling periodic structure, u be the displacement of the node, and f be the nodal force of the node.

[0023] In one exemplary embodiment of this disclosure, one of the two first panels is a top panel and the other is a bottom panel, and the displacement boundary condition constraint is:

[0024] u top =u bottom ·exp(-ik·2H),

[0025] Among them, u top Let u be the node displacement of the top panel. bottom The node displacement of the bottom panel. k is the wave vector, and 2H is the lattice constant.

[0026] In one exemplary embodiment of this disclosure, normalizing the bandgap characteristics of the Kresling periodic structure includes:

[0027] The frequency of the bandgap is normalized using the first formula;

[0028] The wave vector is normalized using the second formula;

[0029] The first formula is:

[0030] Ω=2Hf / (EI(2πf) 2 / ρA) 1 / 4 ,

[0031] Where Ω is the normalized frequency, 2H is the lattice constant, f is the frequency before normalization, E is the elastic modulus of the material used to construct the Kresling periodic structure, I is the moment of inertia of the link, ρ is the density of the material used to construct the Kresling periodic structure, and A is the cross-sectional area of ​​the link.

[0032] The second formula is:

[0033] k * =2Hk / π,

[0034] Where, k * 2H is the normalized wave vector, 2H is the lattice constant, and k is the wave vector before normalization.

[0035] In one exemplary embodiment of this disclosure, the Kresling periodic structure comprises multiple unit cells, each unit cell comprising multiple nodes, and the longitudinal polarization factor of the vibrational modes of the Kresling periodic structure is:

[0036]

[0037] Where, p z U is the longitudinal polarization factor of the vibrational modes of the Kresling periodic structure, V is the volume of a unit cell in the Kresling periodic structure, and u is the longitudinal polarization factor of the vibrational modes of the Kresling periodic structure. x u represents the displacement component of the node within the unit cell along the X direction. y u represents the displacement component of the node within the unit cell along the Y direction. z The displacement component of the node within the unit cell along the Z direction is defined, where the X, Y, and Z directions are perpendicular to each other.

[0038] In one exemplary embodiment of this disclosure, the step of selecting longitudinal and transverse bandgap characteristics that satisfy the design requirements of the Kresling periodic structure, and obtaining the corresponding panel shrinkage ratio and / or unfolding angle, includes:

[0039] The width of the first longitudinal bandgap of the Kresling periodic structure is selected for different panel shrinkage ratios and / or unfolding angles to meet the design requirements of the longitudinal vibration isolation performance of the Kresling periodic structure.

[0040] The width of the first transverse bandgap of the Kresling periodic structure is selected for different panel shrinkage ratios and / or unfolding angles to meet the design requirements of the transverse vibration isolation performance of the Kresling periodic structure.

[0041] Obtain the panel shrinkage ratio and / or unfolding angle that meet the design requirements for longitudinal vibration isolation performance of the Kresling periodic structure, and / or meet the design requirements for lateral vibration isolation performance of the Kresling periodic structure.

[0042] In one exemplary embodiment of this disclosure, the step of selecting longitudinal and transverse bandgap characteristics that satisfy the design requirements of the Kresling periodic structure according to design needs, and obtaining the corresponding panel shrinkage ratio and / or unfolding angle, further includes:

[0043] The center frequency of the first longitudinal bandgap of the Kresling periodic structure is selected for different panel shrinkage ratios and / or unfolding angles to update the panel shrinkage ratios and / or unfolding angles that meet the design requirements for the longitudinal vibration isolation performance of the Kresling periodic structure.

[0044] The center frequency of the first transverse bandgap of the Kresling periodic structure is selected for different panel shrinkage ratios and / or unfolding angles to update the panel shrinkage ratio and / or unfolding angle to meet the design requirements of the transverse vibration isolation performance of the Kresling periodic structure.

[0045] This disclosure also provides a Kresling periodic structure for implementing bandgap control, wherein the Kresling periodic structure is a Kresling periodic structure designed using the method described above for implementing bandgap control.

[0046] The technical solution provided in this disclosure can achieve the following beneficial effects:

[0047] The method for implementing bandgap control of the Kresling periodic structure provided in this disclosure can utilize the panel shrinkage ratio and / or unfolding angle of the Kresling periodic structure to achieve rapid and real-time control of the bandgap characteristics of the Kresling periodic structure according to the control objectives in different design requirements, while maintaining the unfoldable performance of the Kresling periodic structure, and can reduce the cost of control.

[0048] Meanwhile, this disclosure obtains the longitudinal and transverse bandgap characteristics of the Kresling periodic structure through the polarization factor, thereby enabling separate study of the longitudinal and transverse bandgap characteristics. This improves the accuracy of controlling the bandgap characteristics of the Kresling periodic structure, making the controlled Kresling periodic structure more in line with design requirements.

[0049] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0050] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0051] Figure 1 A flowchart illustrating a Kresling periodic structure for implementing bandgap modulation functionality according to an exemplary embodiment of the present disclosure is shown.

[0052] Figure 2A schematic diagram of a Kresling periodic structure according to an exemplary embodiment of the present disclosure is shown;

[0053] Figure 3 A schematic diagram of a Kresling periodic structure according to another exemplary embodiment of the present disclosure is shown;

[0054] Figure 4 A schematic diagram of a Kresling periodic structure according to yet another exemplary embodiment of the present disclosure is shown;

[0055] Figure 5 A schematic diagram of a Kresling periodic structure according to yet another exemplary embodiment of the present disclosure is shown;

[0056] Figure 6 A schematic diagram of bandgap characteristics characterized by longitudinal polarization factor according to an exemplary embodiment of the present disclosure is shown;

[0057] Figure 7 A schematic diagram of the bandgap characteristics characterized by the transverse polarization factor according to an exemplary embodiment of the present disclosure is shown;

[0058] Figure 8 A schematic diagram illustrating the effect of panel shrinkage ratio on longitudinal bandgap distribution according to an exemplary embodiment of the present disclosure is shown.

[0059] Figure 9 A schematic diagram illustrating the effect of panel shrinkage ratio on lateral bandgap distribution according to an exemplary embodiment of the present disclosure is shown;

[0060] Figure 10 A schematic diagram illustrating the effect of the unfolding angle on the longitudinal bandgap distribution according to an exemplary embodiment of the present disclosure is shown;

[0061] Figure 11 A schematic diagram illustrating the effect of the unfolding angle on the longitudinal bandgap distribution according to an exemplary embodiment of the present disclosure is shown. Detailed Implementation

[0062] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, they are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The same reference numerals in the drawings denote the same or similar structures, and therefore their detailed description will be omitted.

[0063] Although relative terms such as "up" and "down" are used in this specification to describe the relative relationship of one component of an icon to another, these terms are used only for convenience, such as according to the orientation of the examples shown in the accompanying drawings. It is understood that if the device of the icon is flipped upside down, the component described as "up" will become the component described as "down." When a structure is "up" of another structure, it may mean that the structure is integrally formed on the other structure, or that the structure is "directly" mounted on the other structure, or that the structure is "indirectly" mounted on the other structure through another structure.

[0064] The terms “a,” “one,” “the,” and “the” are used to indicate the existence of one or more elements / components / etc.; the terms “including” and “having” are used to indicate an open-ended inclusion meaning and that there may be other elements / components / etc. in addition to the listed elements / components / etc.; the terms “first” and “second” are used only as markers and are not a limitation on the number of objects.

[0065] In the field of spacecraft structural design, activities such as satellite separation, thermal shock, deployment of robotic arms, and solar array deployment can all cause spacecraft to vibrate and severely affect their normal operation. For example, low-frequency vibration is a major vibration characteristic of spacecraft and is difficult to isolate and suppress. Therefore, studying the low-frequency vibration isolation performance of spacecraft has always been an urgent problem to be solved in engineering technology. Kresling periodic structures are composite structures composed of artificially designed micro-units arranged periodically, and possess unique mechanical properties due to the careful design and precise arrangement of their constituent units. Studies have shown that Kresling periodic structures have bandgap characteristics, meaning that elastic waves in certain frequency ranges cannot pass through the structure; this frequency range is called the bandgap.

[0066] In addition to the crucial requirement of vibration isolation, high foldability is increasingly attracting the attention of engineers for spacecraft. Kresling periodic structures, due to their complex geometric transformations, can provide stable support for spacecraft while achieving optimized structural design within a limited space. Therefore, Kresling periodic structures can provide stable structural support for spacecraft and meet the design requirements of lightweight, foldable, and high foldability.

[0067] However, the inventors of this disclosure have discovered that current Kresling periodic structures often require the addition of physical fields, additional resonators, or significant alterations to the original configuration of the structure to achieve bandgap tuning. These three tuning methods change the original operating constraints of the system and incur significant economic costs or limit the deployable behavior of the structure itself during use.

[0068] Therefore, in order to solve the technical problem discovered by the inventor of this disclosure, he spent a great deal of time and effort, and finally invented a method for realizing the bandgap control function of a Kresling periodic structure, such as... Figure 1 As shown, the method includes the following steps:

[0069] S10. Establish the dynamic model of the Kresling periodic structure and obtain the bandgap characteristics of the Kresling periodic structure.

[0070] S20. The bandgap characteristics of the Kresling periodic structure are normalized, and combined with the longitudinal polarization factor and the transverse polarization factor of the vibration mode of the Kresling periodic structure, the longitudinal bandgap characteristics and transverse bandgap characteristics of the Kresling periodic structure are obtained.

[0071] S30. Change the panel shrinkage ratio and / or unfolding angle θ of the Kresling periodic structure to obtain the longitudinal bandgap characteristics and transverse bandgap characteristics of the Kresling periodic structure at different panel shrinkage ratios and / or unfolding angles θ.

[0072] S40. Based on the design requirements, select the longitudinal bandgap characteristics and transverse bandgap characteristics that meet the design requirements of the Kresling periodic structure, and obtain the corresponding panel shrinkage ratio and / or unfolding angle θ.

[0073] S50. Design the final Kresling periodic structure based on the obtained panel shrinkage ratio and / or unfolding angle θ.

[0074] Wherein, the panel shrinkage ratio is the ratio of the radii of the circumcircles of each panel in the Kresling periodic structure, and the unfolding angle θ is the angular difference between each panel in the Kresling periodic structure.

[0075] The method for implementing bandgap control of the Kresling periodic structure provided in this disclosure, compared with the prior art, can utilize the panel shrinkage ratio and / or unfolding angle θ of the Kresling periodic structure to achieve rapid and real-time control of the bandgap characteristics of the Kresling periodic structure according to the control objectives in different design requirements, while maintaining the unfoldable performance of the Kresling periodic structure, and can reduce the cost of control.

[0076] Meanwhile, this disclosure obtains the longitudinal and transverse bandgap characteristics of the Kresling periodic structure through the polarization factor, thereby enabling separate study of the longitudinal and transverse bandgap characteristics. This improves the accuracy of controlling the bandgap characteristics of the Kresling periodic structure, making the controlled Kresling periodic structure more in line with design requirements.

[0077] The following is a detailed explanation of each of the above steps:

[0078] In step S10, a dynamic model of the Kresling periodic structure can be established, and the bandgap characteristics of the Kresling periodic structure can be obtained. Specifically, a Kresling periodic structure model can be constructed. For example... Figures 2 to 5 As shown, the Kresling periodic structure model may include two first panels 1 arranged opposite each other, a second panel 2 located between the two first panels 1, and a connecting rod 3 connecting the first panel 1 and the second panel 2. The panel shrinkage ratio can be the ratio of the circumcircle radius of the second panel 2 to the circumcircle radius of the first panel 1, that is:

[0079] β = R2 / R1,

[0080] Where β is the panel shrinkage ratio, R1 is the circumcircle radius of the first panel 1, and R2 is the circumcircle radius of the second panel 2.

[0081] In one embodiment, the orthographic projection shape of the first panel 1 can be hexagonal, but it is not limited to this. The orthographic projection shape of the first panel 1 can also be triangle, quadrilateral, pentagon, etc., which can be selected and set according to the actual situation. All of these are within the protection scope of this disclosure.

[0082] The orthographic projection shape of the second panel 2 can be hexagonal, but is not limited to this. The orthographic projection shape of the second panel 2 can also be triangle, quadrilateral, pentagon, etc., and can be selected and set according to the actual situation. All of these are within the protection scope of this disclosure.

[0083] In one embodiment, the orthographic shape of the first panel 1 and the orthographic shape of the second panel 2 may be the same, but are not limited thereto.

[0084] In one embodiment, the Kresling periodic structure model can be divided into nodes, and dynamic control equations for the displacement and nodal forces of the nodes can be constructed based on the mass matrix and stiffness matrix of the Kresling periodic structure.

[0085] For example, the finite element method can be used to mesh and add nodes to a Kresling periodic structure model, yielding the mass matrix and the mass matrix of the Kresling periodic structure. It should be noted that a Kresling periodic structure can include multiple unit cells, and each unit cell can contain multiple nodes.

[0086] The above dynamic governing equations can be:

[0087]

[0088] Where M is the mass matrix of the Kresling periodic structure. Let be the acceleration of the node, K be the stiffness matrix of the Kresling periodic structure, u be the displacement of the node, and f be the nodal force of the node.

[0089] In one embodiment, the propagation characteristics of elastic waves in a Kresling periodic structure can be obtained based on the dynamic governing equations. These propagation characteristics can be the bandgap characteristics of the Kresling periodic structure.

[0090] Specifically, displacement boundary conditions can be applied to the two first panels 1. Based on the applied displacement boundary conditions and the dynamic control equations, the relationship between the nodal forces of the nodes and the wave vectors of the elastic waves can be obtained to obtain the bandgap characteristics of the Kresling periodic structure.

[0091] In one embodiment, one of the two first panels 1 can be the top panel and the other can be the bottom panel, and the aforementioned displacement boundary condition constraints can be:

[0092] u top =u bottom ·exp(-ik·2H),

[0093] Among them, u top Let u be the node displacement of the top panel. bottom The node displacement of the bottom panel. k is the wave vector, and 2H is the lattice constant.

[0094] In step S20, the bandgap characteristics of the Kresling periodic structure can be normalized, and the longitudinal polarization factor and the transverse polarization factor of the Kresling periodic structure vibration mode can be combined to obtain the longitudinal bandgap characteristics and transverse bandgap characteristics of the Kresling periodic structure.

[0095] Specifically, the frequency of the bandgap can be normalized using the first formula, and the wave vector can be normalized using the second formula.

[0096] The first formula can be:

[0097] Ω=2Hf / (EI(2πf) 2 / ρA) 1 / 4 ,

[0098] Where Ω is the normalized frequency, 2H is the lattice constant, f is the frequency before normalization, E is the elastic modulus of the material used to construct the Kresling periodic structure, I is the moment of inertia of link 3, ρ is the density of the material used to construct the Kresling periodic structure, and A is the cross-sectional area of ​​link 3.

[0099] The second formula can be:

[0100] k * =2Hk / π,

[0101] Where, k * 2H is the normalized wave vector, 2H is the lattice constant, and k is the wave vector before normalization.

[0102] In one embodiment, the longitudinal polarization factor of the above-mentioned Kresling periodic structure vibration mode can be:

[0103]

[0104] Where, p z U is the longitudinal polarization factor of the vibrational modes of the Kresling periodic structure, V is the volume of a unit cell in the Kresling periodic structure, and u is the longitudinal polarization factor of the vibrational modes of the Kresling periodic structure. x u represents the displacement component of the nodes within the unit cell along the X direction. y u represents the displacement component of the nodes within the unit cell along the Y direction. z Let X be the displacement component of the node within the unit cell along the Z direction, where the X, Y, and Z directions are perpendicular to each other.

[0105] The transverse polarization factor of the above Kresling periodic structure vibration modes can be:

[0106]

[0107] Where, p x is the transverse polarization factor of the vibration modes of the Kresling periodic structure.

[0108] In one embodiment, this disclosure may take p z Dispersion curve data with a value >0.2 are used as longitudinal bandgap characteristics of Kresling periodic structures, such as... Figure 6As shown, the shaded area represents the region covered by the longitudinal bandgap, meaning that elastic waves cannot propagate within the bandgap range of this Kresling periodic structure.

[0109] Similarly, this disclosure may take p x Dispersion curve data with a value >0.2 are used as the transverse bandgap structure of the Kresling periodic structure, such as... Figure 7 As shown, the shaded area represents the region covered by the longitudinal bandgap, meaning that elastic waves cannot propagate within the bandgap range of this Kresling periodic structure.

[0110] In step S30, the panel shrinkage ratio and / or unfolding angle θ of the Kresling periodic structure can be changed to obtain the longitudinal bandgap characteristics and transverse bandgap characteristics of the Kresling periodic structure at different panel shrinkage ratios and / or unfolding angles θ.

[0111] Specifically, the size or shape of the first panel 1 and / or the second panel 2 can be changed to alter the circumradius of the first panel 1 and / or the second panel 2, thereby changing the panel shrinkage ratio of the Kresling periodic structure. Additionally, the first panel 1 or the second panel 2 can be rotated to change the relative position between them, thus altering the unfolding angle θ of the Kresling periodic structure.

[0112] The Kresling periodic structure can be analyzed and calculated for different panel shrinkage ratios and / or unfolding angles θ, thereby obtaining the influence of panel shrinkage ratios and / or unfolding angles θ on the longitudinal and transverse bandgap characteristics of the Kresling periodic structure.

[0113] For example, such as Figure 8 As shown, when the panel shrinkage ratio increases, the width of the first longitudinal bandgap of the Kresling periodic structure gradually decreases and disappears. Therefore, it can be seen that the longitudinal low-frequency vibration isolation performance of the Kresling periodic structure decreases with the increase of the panel shrinkage ratio and increases with the decrease of the panel shrinkage ratio.

[0114] Similarly, as Figure 9 As shown, when the panel shrinkage ratio increases, the width of the two transverse band gaps of the Kresling periodic structure gradually decreases and disappears. Therefore, it can be seen that the transverse low-frequency vibration isolation performance of the Kresling periodic structure decreases with the increase of the panel shrinkage ratio and increases with the decrease of the panel shrinkage ratio.

[0115] Therefore, when the panel shrinkage ratio is small, the Kresling periodic structure has good low-frequency vibration isolation performance.

[0116] Similarly, such as Figure 10As shown, the center frequency of the longitudinal bandgap of the Kresling periodic structure gradually decreases as the unfolding angle θ increases. Therefore, it can be concluded that the longitudinal low-frequency vibration isolation performance of the Kresling periodic structure is enhanced as the unfolding angle θ increases.

[0117] Similarly, as Figure 11 As shown, the center frequency of the transverse bandgap of the Kresling periodic structure gradually decreases as the unfolding angle θ increases. Therefore, it can be concluded that the transverse low-frequency vibration isolation performance of the Kresling periodic structure is enhanced as the unfolding angle θ increases.

[0118] Therefore, when the unfolding angle θ is large, the Kresling periodic structure has good low-frequency vibration isolation performance.

[0119] In step S40, the longitudinal bandgap characteristics and transverse bandgap characteristics that meet the design requirements of the Kresling periodic structure can be selected according to the design requirements, and the corresponding panel shrinkage ratio and / or unfolding angle θ can be obtained.

[0120] Specifically, the width of the first longitudinal bandgap of the Kresling periodic structure can be selected for different panel shrinkage ratios and / or unfolding angles θ to meet the design requirements of the longitudinal vibration isolation performance of the Kresling periodic structure. Furthermore, the width of the first transverse bandgap of the Kresling periodic structure can be selected for different panel shrinkage ratios and / or unfolding angles θ to meet the design requirements of the transverse vibration isolation performance of the Kresling periodic structure.

[0121] Furthermore, the panel shrinkage ratio and / or unfolding angle θ that meet the design requirements for longitudinal vibration isolation performance of the Kresling periodic structure, and / or the design requirements for lateral vibration isolation performance of the Kresling periodic structure, can be obtained.

[0122] For example, when the design requirement is to improve the low-frequency vibration isolation performance of a Kresling periodic structure, the panel shrinkage ratio and / or unfolding angle θ corresponding to the wider first longitudinal bandgap can be selected to improve the longitudinal vibration isolation performance of the Kresling periodic structure. The panel shrinkage ratio and / or unfolding angle θ corresponding to the wider first transverse bandgap can also be selected to improve the transverse vibration isolation performance of the Kresling periodic structure.

[0123] Furthermore, the center frequency of the first longitudinal bandgap of the Kresling periodic structure can be selected for different panel shrinkage ratios and / or unfolding angles θ to update the panel shrinkage ratio and / or unfolding angle θ that meet the design requirements for the longitudinal vibration isolation performance of the Kresling periodic structure; similarly, the center frequency of the first transverse bandgap of the Kresling periodic structure can be selected for different panel shrinkage ratios and / or unfolding angles θ to update the panel shrinkage ratio and / or unfolding angle θ that meet the design requirements for the transverse vibration isolation performance of the Kresling periodic structure. This configuration can further improve the accuracy of controlling the bandgap characteristics of the Kresling periodic structure, making the controlled Kresling periodic structure more in line with design requirements.

[0124] The center frequency of the bandgap can be:

[0125]

[0126] Among them, Ω c Ω1 is the center frequency of the bandgap, Ω2 is the starting frequency of the bandgap, and Ω3 is the cutoff frequency of the bandgap.

[0127] The width of the band gap can be:

[0128] Ω w =|Ω2-Ω1|,

[0129] Among them, Ω w The width of the band gap.

[0130] In step S50, the final Kresling periodic structure can be designed based on the obtained panel shrinkage ratio and / or unfolding angle θ. Designing the final Kresling periodic structure using the aforementioned panel shrinkage ratio and / or unfolding angle θ satisfies the vibration isolation performance requirements of the design.

[0131] This disclosure also provides a Kresling periodic structure for implementing bandgap control. This Kresling periodic structure can be designed using the method described above for implementing bandgap control.

[0132] It should be noted that the specific steps and beneficial effects of the method for realizing the bandgap control function of the Kresling periodic structure have been described in detail in the previous topic. Therefore, the method for realizing the bandgap control function of the Kresling periodic structure will not be repeated in this topic; please refer to the description in the previous topic.

[0133] The Kresling periodic structure disclosed herein, designed using the method described above for achieving bandgap control, can accurately control the bandgap characteristics of the Kresling periodic structure without affecting its expandability.

[0134] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This disclosure is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A method for implementing a Kresling periodic structure with bandgap modulation function, characterized in that, include: A dynamic model of the Kresling periodic structure is established, and the bandgap characteristics of the Kresling periodic structure are obtained; The bandgap characteristics of the Kresling periodic structure are normalized, and combined with the longitudinal polarization factor and the transverse polarization factor of the vibration mode of the Kresling periodic structure, the longitudinal bandgap characteristics and transverse bandgap characteristics of the Kresling periodic structure are obtained. By changing the panel shrinkage ratio and / or unfolding angle of the Kresling periodic structure, the longitudinal bandgap characteristics and transverse bandgap characteristics of the Kresling periodic structure at different panel shrinkage ratios and / or unfolding angles can be obtained. Based on the design requirements, select the longitudinal bandgap characteristics and transverse bandgap characteristics that meet the design requirements of the Kresling periodic structure, and obtain the corresponding panel shrinkage ratio and / or unfolding angle. The final Kresling periodic structure is designed based on the obtained panel shrinkage ratio and / or unfolding angle; Wherein, the panel shrinkage ratio is the ratio of the radii of the circumcircles of each panel in the Kresling periodic structure, and the unfolding angle is the angular difference between each panel in the Kresling periodic structure.

2. The method for realizing the bandgap control function of the Kresling periodic structure according to claim 1, characterized in that, The establishment of the dynamic model of the Kresling periodic structure and the acquisition of the bandgap characteristics of the Kresling periodic structure include: A Kresling periodic structure model is constructed, which includes two first panels arranged opposite each other, a second panel located between the two first panels, and a connecting rod connecting the first panel and the second panel. The panel shrinkage ratio is the ratio of the radius of the circumcircle of the second panel to the radius of the circumcircle of the first panel. The Kresling periodic structure model is divided into nodes, and dynamic control equations for the displacement and nodal forces of the nodes are constructed based on the mass matrix and stiffness matrix of the Kresling periodic structure. Based on the dynamic control equations, the propagation characteristics of elastic waves in the Kresling periodic structure are obtained, and the propagation characteristics are the bandgap characteristics of the Kresling periodic structure.

3. The method for realizing the bandgap control function of the Kresling periodic structure according to claim 2, characterized in that, Based on the aforementioned dynamic governing equations, the propagation characteristics of elastic waves in the Kresling periodic structure are obtained, including: Displacement boundary condition constraints are applied to the two first panels; Based on the applied displacement boundary conditions and the dynamic control equations, the relationship between the nodal forces of the nodes and the wave vector of the elastic wave is obtained to obtain the bandgap characteristics of the Kresling periodic structure.

4. The method for realizing the bandgap control function of the Kresling periodic structure according to claim 2, characterized in that, The governing equations for the dynamics are: Where M is the mass matrix of the Kresling periodic structure. Let be the acceleration of the node, K be the stiffness matrix of the Kresling periodic structure, u be the displacement of the node, and f be the nodal force of the node.

5. The method for realizing the bandgap control function of the Kresling periodic structure according to claim 3, characterized in that, One of the two first panels is the top panel, and the other is the bottom panel. The displacement boundary condition constraint is as follows: you top You bottom ·exp(-ik·2H), Among them, u top Let u be the node displacement of the top panel. bottom The node displacement of the bottom panel. k is the wave vector, and 2H is the lattice constant.

6. The method for realizing the bandgap control function of the Kresling periodic structure according to claim 3, characterized in that, Normalizing the bandgap characteristics of the Kresling periodic structure includes: The frequency of the bandgap is normalized using the first formula; The wave vector is normalized using the second formula; The first formula is: Ω=2Hf / (EI(2πf) 2 / pA) 1 / 4 , Where Ω is the normalized frequency, 2H is the lattice constant, f is the frequency before normalization, E is the elastic modulus of the material used to construct the Kresling periodic structure, I is the moment of inertia of the link, ρ is the density of the material used to construct the Kresling periodic structure, and A is the cross-sectional area of ​​the link. The second formula is: k * =2Hk / π, Where, k * 2H is the normalized wave vector, 2H is the lattice constant, and k is the wave vector before normalization.

7. The method for realizing the bandgap control function of the Kresling periodic structure according to claim 2, characterized in that, The Kresling periodic structure comprises multiple unit cells, each unit cell containing multiple nodes. The longitudinal polarization factor of the vibrational modes of the Kresling periodic structure is: Where, p z U is the longitudinal polarization factor of the vibrational modes of the Kresling periodic structure, V is the volume of a unit cell in the Kresling periodic structure, and u is the longitudinal polarization factor of the vibrational modes of the Kresling periodic structure. x u represents the displacement component of the node within the unit cell along the X direction. y u represents the displacement component of the node within the unit cell along the Y direction. z The displacement component of the node within the unit cell along the Z direction is given, where the X, Y, and Z directions are perpendicular to each other.

8. The method for realizing the bandgap control function of the Kresling periodic structure according to claim 1, characterized in that, The step of selecting longitudinal and transverse bandgap characteristics that meet the design requirements of the Kresling periodic structure, and obtaining the corresponding panel shrinkage ratio and / or unfolding angle, includes: The width of the first longitudinal bandgap of the Kresling periodic structure is selected for different panel shrinkage ratios and / or unfolding angles to meet the design requirements of the longitudinal vibration isolation performance of the Kresling periodic structure. The width of the first transverse bandgap of the Kresling periodic structure is selected for different panel shrinkage ratios and / or unfolding angles to meet the design requirements of the transverse vibration isolation performance of the Kresling periodic structure. Obtain the panel shrinkage ratio and / or unfolding angle that meet the design requirements for longitudinal vibration isolation performance of the Kresling periodic structure, and / or meet the design requirements for lateral vibration isolation performance of the Kresling periodic structure.

9. The method for realizing the bandgap control function of the Kresling periodic structure according to claim 8, characterized in that, The step of selecting longitudinal and transverse bandgap characteristics that meet the design requirements of the Kresling periodic structure, and obtaining the corresponding panel shrinkage ratio and / or unfolding angle, further includes: The center frequency of the first longitudinal bandgap of the Kresling periodic structure is selected for different panel shrinkage ratios and / or unfolding angles to update the panel shrinkage ratios and / or unfolding angles that meet the design requirements for the longitudinal vibration isolation performance of the Kresling periodic structure. The center frequency of the first transverse bandgap of the Kresling periodic structure is selected for different panel shrinkage ratios and / or unfolding angles to update the panel shrinkage ratio and / or unfolding angle to meet the design requirements of the transverse vibration isolation performance of the Kresling periodic structure.

10. A Kresling periodic structure for achieving bandgap modulation, characterized in that, The Kresling periodic structure is a Kresling periodic structure designed using the method of realizing bandgap control function of the Kresling periodic structure according to any one of claims 1 to 9.

Images