Prediction method for high-frequency angular modes in two-dimensional honeycomb elastic plates

Abstract

The present application provides a prediction method, device, medium and equipment for high-frequency angular modes in a two-dimensional honeycomb elastic plate, which relates to the field of elastic phononic crystals. The method calculates an internal and external mode hybrid energy band diagram based on a two-dimensional phononic crystal plate, and determines multiple energy bands associated with band gaps from the internal and external mode hybrid energy band diagram; obtains the rhombic Brillouin zone corresponding to a unit cell of the two-dimensional phononic crystal plate; sweeps the rhombic Brillouin zone to obtain displacement wave functions; selects multiple target wave functions related to the multiple energy bands associated with band gaps from the displacement wave functions; calculates the Berry phase according to the multiple target wave functions, and calculates the bulk polarization value according to the Berry phase; determines the angular mode of the unit cell based on the bulk polarization value. In this way, the influence of the in-plane energy bands in the internal and external mode hybrid energy band diagram can be weakened, the frequency range of angular mode prediction is ensured, and thus the prediction of high-frequency angular modes in the in-plane and out-of-plane polarization hybrid energy bands can be realized.

Description

Technical Field

[0001] The present application relates to the field of elastic phononic crystals, and in particular, to a prediction method, device, medium, and equipment for high-frequency angular modes in a two-dimensional honeycomb elastic plate. Background Art

[0002] Currently, predicting angular modes in a honeycomb elastic plate requires performing bulk polarization calculations on the structural unit cell and locating the Wannier center. Furthermore, based on the Wannier center, the positions where angular modes appear are determined. However, in the related art, for elastic waves with out-of-plane polarization, the wave functions in the first and second energy bands with low in-plane and out-of-plane polarization mixing are usually calculated to determine the angular modes. However, for angular modes in the high-frequency range, it is difficult to calculate them through the related art.

[0003] It should be noted that the information disclosed in the above background art section is only used to enhance the understanding of the background of the present application, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0004] The purpose of the present application is to provide a prediction method, device, medium, and equipment for high-frequency angular modes in a two-dimensional honeycomb elastic plate. By sweeping the rhombic Brillouin zone, displacement wave functions can be obtained, and multiple target wave functions related to the energy bands associated with multiple band gaps can be selected from the displacement wave functions, weakening the influence of the in-plane energy bands in the in-out mode hybrid energy band diagram, ensuring the frequency range of angular mode prediction, and thus realizing the prediction of high-frequency angular modes in the in-out polarization hybrid energy bands.

[0005] Other features and advantages of the present application will become apparent through the following detailed description, or will be partially learned through the practice of the present application.

[0006] According to one aspect of the present application, a prediction method for high-frequency angular modes in a two-dimensional honeycomb elastic plate is provided. The method includes:

[0007] Calculating an in-out mode hybrid energy band diagram based on a two-dimensional phononic crystal plate, and determining multiple energy bands associated with band gaps from the in-out mode hybrid energy band diagram;

[0008] Obtaining the rhombic Brillouin zone corresponding to the unit cell of the two-dimensional phononic crystal plate;

[0009] Sweeping the rhombic Brillouin zone to obtain displacement wave functions;

[0010] Selecting multiple target wave functions related to the multiple energy bands associated with band gaps from the displacement wave functions;

[0011] Calculating the Berry phase based on the multiple target wave functions, and calculating the bulk polarization value based on the Berry phase;

[0012] Determine the unit cell angular mode based on the volume polarization value.

[0013] In an exemplary embodiment of the present application, according to the internal and external mode hybrid energy band diagram corresponding to the two-dimensional phononic crystal plate, it includes:

[0014] Obtain the structural parameters of the unit cell in the two-dimensional phononic crystal plate and the wave numbers scanned in the reciprocal space;

[0015] Establish the dynamic equation of the two-dimensional phononic crystal plate according to the structural parameters and the reciprocal space, and obtain the frequency values corresponding to the wave numbers;

[0016] Determine the internal and external mode hybrid energy band diagram corresponding to the two-dimensional phononic crystal plate based on the correspondence between the wave numbers and the frequency values.

[0017] In an exemplary embodiment of the present application, determine multiple energy bands associated with the band gap from the internal and external mode hybrid energy band diagram, including:

[0018] Determine multiple out-of-plane energy band positions associated with the band gap according to the out-of-plane band gap positions in the internal and external mode hybrid energy band diagram.

[0019] In an exemplary embodiment of the present application, it further includes:

[0020] Calculate the polarization factor corresponding to each point in the internal and external mode hybrid energy band diagram according to the unit cell displacement field;

[0021] Determine the in-plane mode and out-of-plane mode in the internal and external mode hybrid energy band diagram according to the comparison between the polarization factor of each point and the preset threshold.

[0022] In an exemplary embodiment of the present application, sweep the rhombic Brillouin zone to obtain the displacement wave function, including:

[0023] Select the relevant in-plane and out-of-plane modes corresponding to the wave numbers in the rhombic Brillouin zone according to the associated energy band selection rule and the relevant out-of-plane energy band positions to obtain the displacement wave function.

[0024] In an exemplary embodiment of the present application, select multiple target wave functions related to the multiple energy bands associated with the band gap from the displacement wave function, including:

[0025] Select multiple target wave functions related to the multiple energy bands associated with the band gap from the displacement wave function according to the orders respectively corresponding to the multiple energy bands associated with the band gap.

[0026] In an exemplary embodiment of the present application, calculate the Berry phase according to the multiple target wave functions, including:

[0027] Calculate the normalized wave functions respectively corresponding to the multiple target wave functions according to the unit cell displacement field;

[0028] Calculate the normalized out-of-plane wave function based on the normalized wave function;

[0029] Calculate the Berry phase based on the normalized out-of-plane wave function.

[0030] According to one aspect of the present application, there is provided a prediction device for high-frequency angular modes in a two-dimensional honeycomb elastic plate, characterized by including:

[0031] A band determination unit for calculating an in-out mode hybrid band diagram based on a two-dimensional phononic crystal plate and determining multiple bands associated with band gaps from the in-out mode hybrid band diagram;

[0032] A rhombic Brillouin zone determination unit for obtaining the rhombic Brillouin zone corresponding to a unit cell in the two-dimensional phononic crystal plate;

[0033] A displacement wave function acquisition unit for sweeping the rhombic Brillouin zone to obtain a displacement wave function;

[0034] A target wave function acquisition unit for selecting multiple target wave functions related to the multiple bands associated with band gaps from the displacement wave function;

[0035] A bulk polarization value calculation unit for calculating the Berry phase based on the multiple target wave functions and calculating the bulk polarization value according to the Berry phase;

[0036] A unit cell angular mode determination unit for determining the unit cell angular mode based on the bulk polarization value.

[0037] In an exemplary embodiment of the present application, the band determination unit, according to the in-out mode hybrid band diagram corresponding to the two-dimensional phononic crystal plate, includes:

[0038] Obtain the structural parameters of the unit cell in the two-dimensional phononic crystal plate and the wave numbers swept in the reciprocal space;

[0039] Establish a dynamic equation of the two-dimensional phononic crystal plate according to the structural parameters and the reciprocal space to obtain the frequency values corresponding to the wave numbers;

[0040] Determine the in-out mode hybrid band diagram corresponding to the two-dimensional phononic crystal plate based on the correspondence between the wave numbers and the frequency values.

[0041] In an exemplary embodiment of the present application, the band determination unit determines multiple bands associated with band gaps from the in-out mode hybrid band diagram, including:

[0042] Determine multiple out-of-plane band positions associated with band gaps according to the out-of-plane band gap positions in the in-out mode hybrid band diagram.

[0043] In an exemplary embodiment of the present application, it further includes:

[0044] A mode determination unit, configured to calculate polarization factors corresponding to points in the in - plane and out - of - plane mode hybrid band diagram according to the unit cell displacement field; and determine the in - plane mode and out - of - plane mode in the in - plane and out - of - plane mode hybrid band diagram according to the comparison between the polarization factors of each point and a preset threshold.

[0045] In an exemplary embodiment of the present application, the displacement wave function acquisition unit sweeps the rhombic Brillouin zone to obtain a displacement wave function, including:

[0046] According to the associated band selection rule and according to the relevant out - of - plane band positions, relevant in - plane and out - of - plane modes corresponding to the wave numbers in the rhombic Brillouin zone are selected to obtain a displacement wave function.

[0047] In an exemplary embodiment of the present application, the target wave function acquisition unit selects a plurality of target wave functions related to multiple band - gap associated bands from the displacement wave function, including:

[0048] According to the orders respectively corresponding to multiple bands associated with the band gap, a plurality of target wave functions related to multiple band - gap associated bands are selected from the displacement wave function.

[0049] In an exemplary embodiment of the present application, the bulk polarization value calculation unit calculates the Berry phase according to a plurality of target wave functions, including:

[0050] Calculate the normalized wave functions respectively corresponding to a plurality of target wave functions according to the unit cell displacement field;

[0051] Calculate the normalized out - of - plane wave function based on the normalized wave function;

[0052] Calculate the Berry phase based on the normalized out - of - plane wave function.

[0053] According to one aspect of the present application, there is provided a computer - readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the method of any one of the above is implemented.

[0054] According to one aspect of the present application, there is provided an electronic device, including: a processor; and a memory for storing executable instructions of the processor; wherein, the processor is configured to execute the method of any one of the above by executing the executable instructions.

[0055] The exemplary embodiments of the present application may have some or all of the following beneficial effects:

[0056] In the prediction method for high-frequency angular modes in a two-dimensional honeycomb elastic plate provided by an exemplary embodiment of the present application, an internal and external mode hybrid energy band diagram can be calculated based on the two-dimensional phononic crystal plate, and multiple energy bands associated with the band gap can be determined from the internal and external mode hybrid energy band diagram; obtain the rhombic Brillouin zone corresponding to the unit cell of the two-dimensional phononic crystal plate; sweep the rhombic Brillouin zone to obtain the displacement wave function; select multiple target wave functions related to the multiple energy bands associated with the band gap from the displacement wave function; calculate the Berry phase based on the multiple target wave functions, and calculate the bulk polarization value based on the Berry phase; determine the unit cell angular mode based on the bulk polarization value. This can weaken the influence of the in-plane energy bands in the internal and external mode hybrid energy band diagram, ensure the frequency range of angular mode prediction, and thus achieve high-frequency angular mode prediction in the in-plane and out-of-plane polarization hybrid energy bands.

[0057] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings herein are incorporated into the specification and form a part of the specification, showing embodiments consistent with the present application, and are used together with the specification to explain the principles of the present application. Obviously, the accompanying drawings in the following description are only some embodiments of the present application, and those of ordinary skill in the art can obtain other drawings without creative efforts based on these drawings.

[0059] Figure 1 Schematically shows a flowchart of a method for predicting high-frequency angular modes in a two-dimensional honeycomb elastic plate according to an embodiment of the present application;

[0060] Figure 2 Schematically shows a schematic diagram of a two-dimensional phononic crystal plate according to an embodiment of the present application;

[0061] Figure 3 Schematically shows a schematic diagram of a unit cell structure according to an embodiment of the present application;

[0062] Figure 4 Schematically shows a schematic diagram of the reciprocal space according to an embodiment of the present application;

[0063] Figure 5 Schematically shows a schematic diagram of the internal and external mode hybrid energy bands corresponding to a two-dimensional phononic crystal plate according to an embodiment of the present application;

[0064] Figure 6 Schematically shows a schematic diagram of the rhombic Brillouin zone corresponding to a unit cell according to an embodiment of the present application;

[0065] Figure 7 Schematically shows a schematic diagram of the Wannier curve according to an embodiment of the present application;

[0066] Figure 8 Schematically shows a schematic diagram of simulation analysis according to an embodiment of the present application;

[0067] Figure 9 Schematically shows a structural block diagram of a prediction device for high-frequency angular modes in a two-dimensional honeycomb elastic plate according to an embodiment of the present application;

[0068] Figure 10 Schematically shows a schematic diagram of the structure of a computer system of an electronic device suitable for implementing the embodiments of the present application. Detailed implementation manners

[0069] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this application will be more complete and comprehensive, and will fully convey the concept of the example embodiments to those skilled in the art. The features, structures, or characteristics described can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of the embodiments of the present application. However, those skilled in the art will realize that the technical solutions of the present application can be practiced without one or more of the specific details, or other methods, components, devices, steps, etc. can be adopted. In other cases, well-known technical solutions are not shown or described in detail to avoid obscuring the various aspects of the present application.

[0070] In addition, the accompanying drawings are only schematic illustrations of the present application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus their repeated description will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0071] Please refer to Figure 1 , Figure 1 Schematically shows a flowchart of a prediction method for high-frequency angular modes in a two-dimensional honeycomb elastic plate according to an embodiment of the present application. As Figure 1 shown, the prediction method for high-frequency angular modes in a two-dimensional honeycomb elastic plate may include: step S110 to step S160.

[0072] Step S110: Calculate an internal and external mode hybrid energy band diagram according to a two-dimensional phononic crystal plate, and determine multiple energy bands associated with the band gap from the internal and external mode hybrid energy band diagram.

[0073] Step S120: Obtain the rhombic Brillouin zone corresponding to the unit cell in the two-dimensional phononic crystal plate.

[0074] Step S130: Sweep the rhombic Brillouin zone to obtain the displacement wave function.

[0075] Step S140: Select multiple target wave functions from the displacement wave function that are related to multiple energy bands associated with multiple band gaps.

[0076] Step S150: Calculate the Berry phase based on the multiple target wave functions, and calculate the bulk polarization value based on the Berry phase.

[0077] Step S160: Determine the unit cell corner mode based on the bulk polarization value.

[0078] Implementation Figure 1 Implementing the method shown can weaken the influence of the in-plane energy bands in the in-out mode hybrid energy band diagram, ensure the frequency range of the corner mode prediction, and thus achieve high-frequency corner mode prediction in the in-out polarization hybrid energy bands.

[0079] Next, the above steps of the present exemplary embodiment will be described in more detail.

[0080] Step S110: Calculate the in-out mode hybrid energy band diagram based on the two-dimensional phononic crystal plate, and determine multiple energy bands associated with the band gaps from the in-out mode hybrid energy band diagram.

[0081] Among them, the two-dimensional phononic crystal plate can be obtained based on 3D printing, and has wave propagation characteristics such as energy absorption, negative Poisson's ratio, seismic shielding, elastic wave control, and negative refraction. The two-dimensional phononic crystal plate can be designed as a combination of the smallest honeycomb hexagonal phononic crystal unit cells and break its six-fold rotational symmetry. In the band gap of the high-order topological insulator, there are corner modes with energy concentration at the corners of the unit cell structure. Based on the independence between the corner modes and the structural defects, it is beneficial for open-structural design.

[0082] For the two-dimensional phononic crystal plate, please refer to Figure 2 , Figure 2 which schematically shows a diagram of a two-dimensional phononic crystal plate according to an embodiment of the present application. Referring to Figure 2 it can be seen that the two-dimensional phononic crystal plate is composed of multiple unit cell structures. For one of the unit cell structures, please refer to Figure 3 , Figure 3 which schematically shows a diagram of the unit cell structure according to an embodiment of the present application. Referring to Figure 2It can be seen that the unit cell structure can include six resonators connected to the truss of the unit cell structure (i.e., the frame of the unit cell structure) by thin rods. The sizes of adjacent resonators are different, and the sizes of the separated resonators are the same. Among them, it can be understood that the unit cell structure contains three type-I resonators and three type-II resonators. The radius r1 of the type-I resonator is greater than the radius r2 of the type-II resonator O2. The center of the type-I resonator can be denoted as O1, and the center of the type-II resonator can be denoted as O2. In addition, the deviation distance of the resonator from the symmetry axis of the unit cell structure can be denoted as b. The a1 vector and the a2 vector represent the lattice displacement vectors in real space. a represents the lengths of the a1 vector and the a2 vector. d represents the length of the thin rod, s represents the width of the thin rod, w represents the width of the truss, and A can be a position point that is simultaneously on the symmetry axis and the truss of the unit cell structure.

[0083] As an alternative embodiment, according to the internal and external mode hybrid band diagram corresponding to the two-dimensional phononic crystal plate, it includes: obtaining the structural parameters of the unit cell in the two-dimensional phononic crystal plate and the wave numbers swept in the reciprocal space; establishing the dynamic equation of the two-dimensional phononic crystal plate based on the structural parameters and the reciprocal space to obtain the frequency values corresponding to the wave numbers; and determining the internal and external mode hybrid band diagram corresponding to the two-dimensional phononic crystal plate based on the corresponding relationship between the wave numbers and the frequency values. In this way, a more accurate internal and external mode hybrid band diagram can be determined, which is beneficial to improving the prediction accuracy of the angular mode.

[0084] Specifically, the structural parameters of the unit cell in the two-dimensional phononic crystal plate and the wave numbers swept in the reciprocal space can be obtained. Among them, the structural parameters include but are not limited to: Figure 2 r1, r2, O1, O2, b, a1, a2, a, d, s, w, etc. as shown. In addition, the reciprocal space corresponds to the unit cell. For the reciprocal space, reference can be made to Figure 4 , Figure 4 which schematically shows a reciprocal space diagram according to an embodiment of the present application. In Figure 4 , the shaded area is the irreducible Brillouin zone of the reciprocal space. Γ, K, and M are respectively used to represent the three vertices of the irreducible Brillouin zone. The k1 vector and the k2 vector represent the lattice displacement vectors in the reciprocal space. Furthermore, based on the structural parameters and the Γ, K, M, k1 vector, and k2 vector in the reciprocal space, the dynamic equation of the two-dimensional phononic crystal plate can be established through a preset commercial finite element software to realize the sweeping of the edge of the shaded area, so as to obtain the frequency values corresponding to each wave number (i.e., each point on the edge). Furthermore, based on the corresponding relationship between the wave numbers and the frequency values, the internal and external mode hybrid band diagram corresponding to the two-dimensional phononic crystal plate as shown in Figure 5 can be determined. In the internal and external mode hybrid band diagram, the vertical axis is used to represent the frequency values, the horizontal axis is used to represent the sweeping direction, each column in the sweeping direction can correspond to a wave number, and each column can include one or more frequency values.

[0085] In addition, in the internal and external mode hybrid energy band diagram, a shaded area for defining the bandgap characteristics may also be included. The shaded area can be defined as a frequency range, and the shaded area can be referred to as the bandgap. In the internal and external mode hybrid energy band diagram, the shapes of the points representing the frequency values include circles and rectangles. The circular points are used to represent the out-of-plane energy bands, and the rectangular points are used to represent the in-plane energy bands. Specifically, based on the expression: polarization factor p = ∫(|w| 2 dV) / ∫(|u| 2 +|v| 2 +|w| 2 )dV, the mode corresponding to each frequency value can be determined, so as to determine the above-mentioned out-of-plane energy band and in-plane energy band; where, (u, v, w) represents the displacement field in the unit cell. If p > 0.9, it is determined as the out-of-plane energy band, otherwise it is determined as the in-plane energy band.

[0086] As an alternative embodiment, multiple energy bands associated with the bandgap are determined from the internal and external mode hybrid energy band diagram, including: determining multiple out-of-plane energy band positions associated with the bandgap according to the out-of-plane bandgap position in the internal and external mode hybrid energy band diagram. This can achieve the precise selection of the out-of-plane energy band positions associated with the bandgap, thereby facilitating the improvement of the prediction accuracy for the angular mode.

[0087] Specifically, the out-of-plane bandgap position (i.e., the position of the circular points) in the internal and external mode hybrid energy band diagram can be determined to find the two energy bands closest to the bandgap edge, one closest to the upper edge of the bandgap and the other closest to the lower edge of the bandgap. Furthermore, the out-of-plane energy band position including the above two energy bands can be determined from the internal and external mode hybrid energy band diagram; it should be noted that an energy band can be composed of multiple frequency points.

[0088] As an alternative embodiment, it further includes: calculating the polarization factor corresponding to each point in the internal and external mode hybrid energy band diagram according to the unit cell displacement field; determining the in-plane mode and out-of-plane mode in the internal and external mode hybrid energy band diagram according to the comparison between the polarization factor of each point and a preset threshold (such as, 0.9). This can achieve the accurate distinction between the in-plane mode and out-of-plane mode.

[0089] Specifically, the polarization factor corresponding to each point in the internal and external mode hybrid energy band diagram can be calculated according to the unit cell displacement field (u, v, w). The points with the polarization factor greater than the preset threshold are determined as the out-of-plane energy bands, and the points with the polarization factor less than or equal to the preset threshold are determined as the in-plane energy bands.

[0090] Step S120: Obtain the rhombic Brillouin zone corresponding to the unit cell in the two-dimensional phononic crystal plate.

[0091] Specifically, the bulk polarization expression can be converted based on a preset conversion method into Among them, is used to represent the Berry phase vector potential, α represents two directions of the lattice vectors, (1 and (2 are used to sweep the frequency points related to the band gap, % α,kβ is used to represent the Berry phase obtained by sweeping along the kα loop at a fixed kβ, and L represents the projected length of the Brillouin zone along the kβ direction. However, all in-plane and out-of-plane modes are included in the Wannier bands calculated using the transformed expression, and the influence of the in-plane energy bands is not weakened, making it easy for high-frequency angular modes to be difficult to predict. The present application has improved this.

[0092] Specifically, the following steps can be implemented. First, in order to improve the operation efficiency, the Brillouin zone is deformed from Figure 4 the hexagon shown in Figure 6 to the rhombus shown in Figure 4 The hexagon shown in Figure 6 and the rhombus shown in Figure 6 correspond to the same area. Specifically, the rhombus Brillouin zone can refer to Figure 6 which schematically shows the schematic diagram of the rhombus Brillouin zone corresponding to the unit cell according to an embodiment of the present application. Figure 6 shows the rhombus Brillouin zone (represented by the dashed box) deformed from the hexagonal Brillouin zone (represented by the solid line box). For the rhombus Brillouin zone, k1 and k2 can be used to indicate the sweeping direction of the rhombus Brillouin zone.

[0093] Step S130: Sweep the rhombus Brillouin zone to obtain the displacement wave function.

[0094] Specifically, the displacement wave function can be expressed as multiple values obtained by sweeping the rhombus Brillouin zone.

[0095] As an optional embodiment, sweeping the rhombus Brillouin zone to obtain the displacement wave function includes: according to the associated energy band selection rule, and according to the relevant out-of-plane energy band position, selecting the relevant in-plane and out-of-plane modes corresponding to the wave number in the rhombus Brillouin zone to obtain the displacement wave function. This can achieve the accurate acquisition of the displacement wave function, which is beneficial to the prediction of high-frequency angular modes.

[0096] Specifically, the associated energy band selection rule is used to select the relevant in-plane and out-of-plane modes. The associated energy band selection rule can be used to characterize the selection conditions for the in-plane and out-of-plane modes, and the relevant out-of-plane energy band position can be used as the basis for the selection of the in-plane and out-of-plane modes.

[0097] Step S140: Select multiple target wave functions related to multiple band gap associated energy bands from the displacement wave function.

[0098] Specifically, the target wave functions with the same order as each band gap associated energy band can be selected from the displacement wave function.

[0099] As an alternative embodiment, multiple target wave functions related to multiple energy bands associated with band gaps are selected from the displacement wave function, including: selecting multiple target wave functions related to multiple energy bands associated with band gaps from the displacement wave function according to the orders respectively corresponding to the multiple energy bands associated with band gaps. This can increase the possibility of predicting high-frequency angular modes.

[0100] Specifically, multiple target wave functions related to multiple energy bands associated with band gaps can be selected from the displacement wave function according to the orders respectively corresponding to the multiple energy bands β1, β2, …, β m associated with band gaps, that is, β1, β2, …, β m respectively corresponding to k i , which can be used to distinguish different points.

[0101] Step S150: Calculate the Berry phase according to the multiple target wave functions, and calculate the bulk polarization value according to the Berry phase.

[0102] Specifically, the Berry phase can be calculated according to k m respectively corresponding to β1, β2, …, β ) . Based on this, the Berry phase can be further calculated. wherein can be understood as the normalized wave function, and w .k n ) is the out-of-plane energy band's normalized displacement with a polarization factor p > 0.9. Furthermore, the polarization value P ) can be calculated based on the expression . Among them, the polarization value P α is the average value of the Berry phase in the Brillouin zone. By numerical calculation α a Wannier curve with an average value of ±1 / 3 can be obtained. Specifically, reference can be made to , Figure 7 , Figure 7 which schematically shows a Wannier curve diagram according to an embodiment of the present application. As Figure 7 shown, the abscissa represents the points in the swept Brillouin zone, and the ordinate represents the Berry phase value. Taking two unit cells with opposite offset distances b as examples, the calculated bulk polarization values are P1 = (–1 / 3, –1 / 3) and P2 = (1 / 3, 1 / 3) respectively. P1 and P2 can respectively represent the positions of the Wannier centers. For unit cell 710 and unit cell 720, their corresponding angular modes are represented as highlighted vertices in the figure. Unit cell 710 corresponds to Wannier region 711, and unit cell 720 corresponds to Wannier region 721.

[0103] As an alternative embodiment, calculating the Berry phase according to multiple target wave functions includes: calculating the normalized wave functions corresponding to the multiple target wave functions respectively according to the unit cell displacement field; calculating the normalized out-of-plane wave function based on the normalized wave functions; calculating the Berry phase based on the normalized out-of-plane wave function. This can achieve determining the positions of the corner modes in the high-order topological insulator in the high-frequency range, thereby extending the research on the corner modes in the elastic plate to the high-frequency range and providing a theoretical basis for the application of elastic wave vibration energy capture.

[0104] Specifically, β1, β2, …, β can be determined according to the unit cell displacement field m respectively corresponding to k ) , and further corresponding normalized wave functions Furthermore, based on calculate the normalized out-of-plane wave function Based on the normalized out-of-plane wave function, the Berry phase can be calculated

[0105] Step S160: Determine the unit cell corner modes based on the bulk polarization value.

[0106] Specifically, simulation analysis can be performed based on the bulk polarization value to verify the existence of the unit cell corner modes. For details, refer to Figure 8 , Figure 8 which schematically shows a schematic diagram of the simulation analysis according to an embodiment of the present application. As Figure 8 shown, taking the triangular plate 810 composed of unit cells with an offset displacement b < 0 as an example, the corner modes can exist at the three corner points of the triangular plate. The eigenfrequencies of the triangular plate can be calculated by COMSOL. The modes represented by the three marked points in the structural eigenfrequency spectrum are the corner modes, which are distributed at the three corner points of the triangular plate that can accommodate the corner modes. Specifically, the corner mode at f = 3588 Hz at the top corner can be respectively shown as the highlighted corner unit cells of the triangular plates 820, 830, and 840. Based on the above process, the existence verification of the high-frequency unit cell corner modes can be achieved.

[0107] Please refer to Figure 9 , Figure 9 which schematically shows a structural block diagram of a prediction device for high-frequency corner modes in a two-dimensional honeycomb elastic plate according to an embodiment of the present application. The prediction device 900 for high-frequency corner modes in a two-dimensional honeycomb elastic plate corresponds to the Figure 1 method shown as Figure 9 shown. As shown, the prediction device 900 for high-frequency corner modes in a two-dimensional honeycomb elastic plate includes:

[0108] A band determination unit 901, configured to calculate an internal and external mode hybrid band diagram based on a two-dimensional phononic crystal plate, and determine multiple bands associated with a band gap from the internal and external mode hybrid band diagram;

[0109] A rhombic Brillouin zone determination unit 902, configured to obtain the rhombic Brillouin zone corresponding to a unit cell in the two-dimensional phononic crystal plate;

[0110] A displacement wave function acquisition unit 903, configured to sweep the rhombic Brillouin zone to obtain a displacement wave function;

[0111] A target wave function acquisition unit 904, configured to select multiple target wave functions related to the bands associated with multiple band gaps from the displacement wave function;

[0112] A bulk polarization value calculation unit 905, configured to calculate a Berry phase according to multiple target wave functions, and calculate a bulk polarization value according to the Berry phase;

[0113] A unit cell corner mode determination unit 906, configured to determine a unit cell corner mode based on the bulk polarization value.

[0114] It can be seen that implementing Figure 9 the device shown can weaken the influence of the in-plane bands in the internal and external mode hybrid band diagram, ensure the frequency range of corner mode prediction, and thus achieve high-frequency corner mode prediction in the in-plane and out-of-plane polarization hybrid bands.

[0115] In an exemplary embodiment of the present application, the band determination unit 901 includes, according to the internal and external mode hybrid band diagram corresponding to the two-dimensional phononic crystal plate:

[0116] Obtaining the structural parameters of the unit cell in the two-dimensional phononic crystal plate and the wave numbers swept in the reciprocal space;

[0117] Establishing a two-dimensional phononic crystal plate dynamics equation according to the structural parameters and the reciprocal space to obtain frequency values corresponding to the wave numbers;

[0118] Determining the internal and external mode hybrid band diagram corresponding to the two-dimensional phononic crystal plate based on the correspondence between the wave numbers and the frequency values.

[0119] It can be seen that implementing this optional embodiment can determine a more accurate internal and external mode hybrid band diagram, which is beneficial to improving the prediction accuracy of corner modes.

[0120] In an exemplary embodiment of the present application, the band determination unit 901 determines multiple bands associated with a band gap from the internal and external mode hybrid band diagram, including:

[0121] Determining multiple out-of-plane band positions associated with the band gap according to the out-of-plane band gap positions in the internal and external mode hybrid band diagram.

[0122] It can be seen that implementing this optional embodiment can achieve the accurate selection of the out-of-plane energy band position associated with the bandgap, thereby facilitating the improvement of the prediction accuracy for angular modes.

[0123] In an exemplary embodiment of the present application, it further includes:

[0124] A mode determination unit, configured to calculate the polarization factor corresponding to each point in the in-out mode hybrid energy band diagram according to the unit cell displacement field; determine the in-plane mode and the out-of-plane mode in the in-out mode hybrid energy band diagram according to the comparison between the polarization factor of each point and a preset threshold.

[0125] It can be seen that implementing this optional embodiment can achieve the accurate distinction between the in-plane mode and the out-of-plane mode.

[0126] In an exemplary embodiment of the present application, the displacement wave function acquisition unit 903 sweeps the rhombic Brillouin zone to obtain the displacement wave function, including:

[0127] According to the associated energy band selection rule and according to the relevant out-of-plane energy band position, select the relevant in-out modes corresponding to the wave numbers in the rhombic Brillouin zone to obtain the displacement wave function.

[0128] It can be seen that implementing this optional embodiment can achieve the accurate acquisition of the displacement wave function, thereby facilitating the prediction of high-frequency angular modes.

[0129] In an exemplary embodiment of the present application, the target wave function acquisition unit 904 selects multiple target wave functions related to multiple bandgap-associated energy bands from the displacement wave function, including:

[0130] According to the orders respectively corresponding to multiple energy bands associated with the bandgap, select multiple target wave functions related to multiple bandgap-associated energy bands from the displacement wave function.

[0131] It can be seen that implementing this optional embodiment can increase the possibility of predicting high-frequency angular modes.

[0132] In an exemplary embodiment of the present application, the bulk polarization value calculation unit 905 calculates the Berry phase according to multiple target wave functions, including:

[0133] Calculate the normalized wave functions respectively corresponding to multiple target wave functions according to the unit cell displacement field;

[0134] Calculate the normalized out-of-plane wave function based on the normalized wave function;

[0135] Calculate the Berry phase based on the normalized out-of-plane wave function.

[0136] It can be seen that implementing this optional embodiment can achieve determining the positions of corner modes in a high-order topological insulator within a high-frequency range, thereby extending the research on corner modes in an elastic plate to the high-frequency range and providing a theoretical basis for the application of elastic wave vibration energy capture.

[0137] It should be noted that although several modules or units of a device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiments of the present application, the features and functions of two or more of the above-described modules or units can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0138] Since each functional module of the prediction device for high-frequency corner modes in a two-dimensional honeycomb elastic plate in the exemplary embodiments of the present application corresponds to the steps of the above-described exemplary embodiments of the prediction method for high-frequency corner modes in a two-dimensional honeycomb elastic plate, for details not disclosed in the device embodiments of the present application, please refer to the embodiments of the above-described prediction method for high-frequency corner modes in a two-dimensional honeycomb elastic plate of the present application.

[0139] Please refer to Figure 10 , Figure 10 which shows a schematic structural diagram of a computer system of an electronic device suitable for implementing the embodiments of the present application.

[0140] It should be noted that Figure 10 the computer system 1000 of the shown electronic device is only an example and should not bring any limitation to the functions and usage scope of the embodiments of the present application.

[0141] As Figure 10 shown, the computer system 1000 includes a central processing unit (CPU) 1001, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 1002 or the program loaded from the storage section 1008 into the random access memory (RAM) 1003. In the RAM 1003, various programs and data required for system operation are also stored. The CPU 1001, ROM 1002, and RAM 1003 are connected to each other through a bus 1004. The input / output (I / O) interface 1005 is also connected to the bus 1004.

[0142] The following components are connected to the I / O interface 1005: an input section 1006 including a keyboard, a mouse, etc.; an output section 1007 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc. as well as a speaker, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, a modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the I / O interface 1005 as required. A removable medium 1011, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 1010 as required so that a computer program read from it is installed into the storage section 1008 as required.

[0143] Specifically, according to an embodiment of the present application, the process described in the above reference flow chart can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes program codes for executing the method shown in the flow chart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication section 1009, and / or installed from the removable medium 1011. When the computer program is executed by a central processing unit (CPU) 1001, various functions defined in the method and apparatus of the present application are executed.

[0144] As another aspect, the present application also provides a computer-readable medium, which may be included in the electronic device described in the above embodiment; or may exist separately without being assembled into the electronic device. The above computer-readable medium carries one or more programs, and when the one or more programs are executed by an electronic device, the electronic device implements the method described in the above embodiment.

[0145] It should be noted that the computer-readable medium shown in this application can be a computer-readable signal medium, a computer-readable storage medium, or any combination of the two. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of a computer-readable storage medium can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this application, a computer-readable storage medium can be any tangible medium that contains or stores a program, and this program can be used by or in combination with an instruction execution system, apparatus, or device. And in this application, a computer-readable signal medium can include a data signal propagated in a baseband or as part of a carrier wave, in which computer-readable program code is carried. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, and this computer-readable medium can send, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium can be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0146] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram can represent a module, a program segment, or a part of code, and the above module, program segment, or part of code contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks can occur in a different order than that marked in the accompanying drawings. For example, two consecutively represented blocks can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram or flowchart, as well as the combination of blocks in the block diagram or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0147] The units involved in the embodiments of the present application can be implemented in software or in hardware, and the described units can also be provided in a processor. Among them, the names of these units do not constitute a limitation on the units themselves in certain cases.

[0148] Those skilled in the art will readily conceive of other embodiments of the present application after considering the specification and practicing the invention disclosed herein. The present application is intended to cover any variations, uses, or adaptations of the present application, which follow the general principles of the present application and include the known common general knowledge or conventional technical means in the art not disclosed in the present application. The specification and the embodiments are only regarded as exemplary, and the true scope and spirit of the present application are indicated by the foregoing claims.

Claims

1. A prediction method for high-frequency angular modes in a two-dimensional honeycomb elastic plate, characterized in that, Including: Calculating an internal and external mode hybrid energy band diagram according to the two-dimensional phononic crystal plate, and determining multiple energy bands associated with the band gap from the internal and external mode hybrid energy band diagram; Obtaining the rhombic Brillouin zone corresponding to the unit cell in the two-dimensional phononic crystal plate; Scanning the rhombic Brillouin zone to obtain a displacement wave function; Selecting multiple target wave functions related to the multiple energy bands associated with the band gap from the displacement wave function; Calculating the Berry phase according to the multiple target wave functions, and calculating the bulk polarization value according to the Berry phase; Determining the unit cell angular mode based on the bulk polarization value.

2. The method according to claim 1, wherein According to the internal and external mode hybrid energy band diagram corresponding to the two-dimensional phononic crystal plate, including: Obtaining the structural parameters of the unit cell in the two-dimensional phononic crystal plate and the wave numbers scanned in the reciprocal space; Establishing a dynamic equation of the two-dimensional phononic crystal plate according to the structural parameters and the reciprocal space, and obtaining the frequency values corresponding to the wave numbers; Determining the internal and external mode hybrid energy band diagram corresponding to the two-dimensional phononic crystal plate based on the correspondence between the wave numbers and the frequency values.

3. The method according to claim 1, characterized in that Determining multiple energy bands associated with the band gap from the internal and external mode hybrid energy band diagram, including: Determining multiple out-of-plane energy band positions associated with the band gap according to the out-of-plane band gap positions in the internal and external mode hybrid energy band diagram.

4. The method according to claim 1, characterized in that, Also including: Calculating the polarization factor corresponding to each point in the internal and external mode hybrid energy band diagram according to the unit cell displacement field; Determining the in-plane mode and out-of-plane mode in the internal and external mode hybrid energy band diagram according to the comparison between the polarization factors of each point and a preset threshold.

5. The method according to claim 1, characterized in that, Scanning the rhombic Brillouin zone to obtain a displacement wave function, including: Selecting the relevant in-plane and out-of-plane modes corresponding to the wave numbers in the rhombic Brillouin zone according to the associated energy band selection rule and the relevant out-of-plane energy band positions to obtain a displacement wave function.

6. The method according to claim 1, wherein Selecting multiple target wave functions related to the multiple energy bands associated with the band gap from the displacement wave function, including: Selecting multiple target wave functions related to the multiple energy bands associated with the band gap from the displacement wave function according to the orders respectively corresponding to the multiple energy bands associated with the band gap.

7. The method according to claim 1, characterized in that Calculating the Berry phase according to the multiple target wave functions, including: Calculating the normalized wave functions respectively corresponding to the multiple target wave functions according to the unit cell displacement field; Calculating the normalized out-of-plane wave function based on the normalized wave functions; Calculating the Berry phase based on the normalized out-of-plane wave function.

8. A prediction device for high-frequency angular modes in a two-dimensional honeycomb elastic plate, characterized in that, Including: An energy band determination unit, configured to calculate an internal and external mode hybrid energy band diagram according to the two-dimensional phononic crystal plate, and determine multiple energy bands associated with the band gap from the internal and external mode hybrid energy band diagram; A rhombic Brillouin zone determination unit, configured to obtain the rhombic Brillouin zone corresponding to the unit cell in the two-dimensional phononic crystal plate; A displacement wave function acquisition unit, configured to scan the rhombic Brillouin zone to obtain a displacement wave function; A target wave function acquisition unit, configured to select multiple target wave functions related to the multiple energy bands associated with the band gap from the displacement wave function; A bulk polarization value calculation unit, configured to calculate the Berry phase according to the multiple target wave functions, and calculate the bulk polarization value according to the Berry phase; A unit cell angular mode determination unit, configured to determine the unit cell angular mode based on the bulk polarization value.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method according to any one of claims 1-7.

10. An electronic device, characterized in that, Comprising: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to execute the method according to any one of claims 1-7 by executing the executable instructions.

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