A preparation method of a piezoelectric defect phononic crystal plate

Abstract

The present invention provides a method for preparing a piezoelectric defective phononic crystal plate. The method includes clarifying the variation range of the target band gap, and selecting a vibration-damping phononic crystal material and geometric parameters according to the variation range of the target band gap; introducing a cantilever beam type line defect structure based on the vibration-damping phononic crystal material and geometric parameters and based on the best energy diversion effect, and determining the material and geometric parameters of the cantilever beam type line defect structure; determining the length of the piezoelectric sheet fixedly connected to the upper and lower surfaces of the cantilever beam based on the corresponding relationship between the material and geometric parameters of the cantilever beam type line defect structure; obtaining the arrangement angle of the resonators of the cantilever beam type line defect structure, and checking the interference situation of the cantilever beam type line defect structure based on the arrangement angle to obtain a piezoelectric defective phononic crystal plate. The present invention can avoid the over-complex preparation of the piezoelectric defective phononic crystal plate caused by too many design parameters, and can also accurately divert the vibration energy of specific frequencies within the low-frequency band gap range.

Description

Technical Field

[0001] The invention relates to the technical field of phononic crystal plates, and in particular to a method for preparing a piezoelectric defect phononic crystal plate. Background Art

[0002] As a new type of material developed from photonic crystals, phononic crystals have attracted extensive attention and in-depth research from scholars at home and abroad due to their band gap characteristics, that is, the ability to suppress vibrations in a specific frequency band. They are also increasingly used in the fields of architecture, aerospace, navigation, and automobiles. However, in phononic crystals with traditional structures, vibration energy, especially low-frequency and large-amplitude vibration energy, is usually dissipated in the form of oscillator vibrations during the propagation of the phononic crystal plate, converted into heat energy, and is not utilized. Therefore, it is very important for phononic crystals to guide vibration energy while suppressing the transmission of low-frequency and large-amplitude vibrations in the matrix structure. Therefore, on the basis of the traditional spring-oscillator type local resonance phononic crystal, its periodicity is destroyed, and a sandwich piezoelectric cantilever beam line defect structure is introduced to achieve vibration energy guidance of a specific frequency in the low-frequency range.

[0003] In the prior art, the parameters that need to be designed in the design process of the piezoelectric defect phononic crystal plate mainly include the following parts: (1) Material parameters: the selection of the phononic crystal substrate, elastic element, scatterer, cantilever beam and piezoelectric material; (2) Geometric parameters: the thickness and lattice constant of the phononic crystal substrate, the center position, radius and thickness of the elastic element, the position, radius and height of the scatterer, the length, width and thickness of the cantilever beam and the piezoelectric plate. Due to the large number and complexity of the design parameters, this structure has always lacked a programmed design method. Summary of the invention

[0004] Based on this, the purpose of the present invention is to provide a method for preparing a piezoelectric defect phononic crystal plate to solve the deficiencies in the above-mentioned prior art.

[0005] The present invention provides a method for preparing a piezoelectric defect phononic crystal plate, the method comprising:

[0006] Determine the target band gap variation range, and select the vibration-damping phononic crystal material and geometric parameters according to the target band gap variation range;

[0007] Introducing a cantilever beam type line defect structure according to the vibration-damping phononic crystal material and the geometric parameters and based on the optimal energy conduction effect, and determining the material and geometric parameters of the cantilever beam type line defect structure;

[0008] Determining the length of the piezoelectric sheets fixed to the upper and lower surfaces of the cantilever beam based on the corresponding relationship between the material and geometric parameters of the cantilever beam type line defect structure;

[0009] Obtain the arrangement angle of the resonators of the cantilever beam type line defect structure, and check the interference of the cantilever beam type line defect structure based on the arrangement angle to obtain a piezoelectric defect phononic crystal plate.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: By clarifying the change range of the target bandgap and introducing a cantilever beam type line defect structure according to the best energy diversion effect, and by obtaining the design parameters of the corresponding piezoelectric defect phononic crystal plate, it is possible to avoid the overly complex preparation of the piezoelectric defect phononic crystal plate due to excessive design parameters, and it is also possible to accurately divert the vibration energy of specific frequencies within the low-frequency bandgap range.

[0011] Further, the step of selecting the vibration damping phononic crystal material and geometric parameters according to the change range of the target bandgap includes:

[0012] Design the material parameters of the vibration damping matrix, elastic element, scatterer, and the material parameters of the piezoelectric sheet;

[0013] Design the lattice constant of the matrix plate, the thickness of the elastic element, the central position of the elastic element, the radius of the elastic element, the position of the scatterer, the radius of the scatterer, the height of the scatterer, the positions of the cantilever beam and the piezoelectric sheet, the widths of the cantilever beam and the piezoelectric sheet, the lengths of the cantilever beam and the piezoelectric sheet, and the thicknesses of the cantilever beam and the piezoelectric sheet.

[0014] Further, the cantilever beam type line defect structure is a sandwich type cantilever beam type line defect structure, and the number of line defects of the sandwich type cantilever beam type line defect structure does not exceed 1.

[0015] Further, before the step of determining the length of the piezoelectric sheet fixedly connected to the upper and lower surfaces of the cantilever beam based on the corresponding relationship between the material and geometric parameters of the cantilever beam type line defect structure, the method further includes:

[0016] Based on the modal analysis of the cantilever beam type line defect structure and the calculation of the natural frequency, obtain the first-order bending modal frequency of the cantilever beam type line defect structure without an external circuit;

[0017] Based on the change relationship between the first-order bending modal frequency of the cantilever beam type line defect structure and the length of the piezoelectric sheet, obtain the length of the piezoelectric sheet without an external circuit.

[0018] Further, the calculation expression of the first-order bending modal frequency is:

[0019] ;

[0020] In the formula, represents the first-order bending modal frequency, represents the proximity factor, represents the short-circuit compliance coefficient of the piezoelectric sheet, represents the piezoelectric strain constant of the piezoelectric sheet, represents the constant strain dielectric constant of the piezoelectric sheet, represents the density of the piezoelectric sheet, 、 respectively represent the elastic modulus of the cantilever beam substrate beam and the density of the cantilever beam substrate beam, 、 respectively represent the cross-sectional area of the cantilever beam substrate beam and the centroidal moment of inertia of the central cross-section of the cantilever beam substrate beam, 、 respectively represent the cross-sectional area of the piezoelectric sheet and the centroidal moment of inertia of the central cross-section of the piezoelectric sheet, represents the length of the piezoelectric sheet;

[0021] The calculation expression for the length of the piezoelectric sheet without an external circuit is:

[0022] ;

[0023] In the formula, represents the length of the piezoelectric sheet without an external circuit, represents the frequency of the vibration energy.

[0024] Further, after the step of checking the interference of the cantilever beam type line defect structure based on the arrangement angle, the method further includes:

[0025] judging the interference direction of the resonator interference situation;

[0026] If interference occurs in the width direction of the resonator, reduce the number of unit cells in the x direction or the y direction;

[0027] If interference occurs in the length direction of the resonator, increase the number of unit cells in the x direction or the y direction.

[0028] Further, after the step of judging the interference direction of the resonator interference situation, the method further includes:

[0029] If interference occurs in the width direction of the resonator and interference occurs in the length direction of the resonator, increase the lattice constant of the vibration-damping phononic crystal substrate plate, and repeatedly execute to clarify the change range of the target bandgap, and select the vibration-damping phononic crystal material and geometric parameters according to the change range of the target bandgap; introduce a cantilever beam type line defect structure based on the best energy diversion effect, and determine the material and geometric parameters of the cantilever beam type line defect structure; determine the length of the piezoelectric sheet fixedly connected to the upper and lower surfaces of the cantilever beam based on the corresponding relationship between the material and geometric parameters of the cantilever beam type line defect structure; obtain the arrangement angle of the resonators of the cantilever beam type line defect structure, and check the interference situation of the cantilever beam type line defect structure based on the arrangement angle until a piezoelectric defect phononic crystal plate is obtained. Description of the Drawings

[0030] Figure 1 It is a flowchart of the method for preparing a piezoelectric defect phononic crystal plate in an embodiment of the present invention;

[0031] Figure 2 It is a schematic structural diagram of a phononic crystal single cell in an embodiment of the present invention;

[0032] Figure 3 It is a schematic structural diagram of a cantilever beam type line defect in an embodiment of the present invention;

[0033] Figure 4 It is a schematic diagram of a seven-period structure of the resonator arrangement of a sandwich type cantilever beam type line defect in an embodiment of the present invention;

[0034] Figure 5 It is a vibration transmission rate curve graph of a phononic crystal plate before introducing a cantilever beam type line defect in an embodiment of the present invention;

[0035] Figure 6 It is a vibration transmission rate curve graph of a phononic crystal plate after introducing a cantilever beam type line defect in an embodiment of the present invention;

[0036] Figure 7 It is a vibration mode graph of a piezoelectric defect phononic crystal plate when the external excitation frequency is 68 Hz in an embodiment of the present invention.

[0037] The following specific embodiments will further illustrate the present invention in conjunction with the above-mentioned drawings. Specific Embodiments

[0038] To facilitate the understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. Several embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, these embodiments are provided to make the disclosure of the present invention more thorough and comprehensive.

[0039] It should be noted that when an element is referred to as being "fixed to" another element, it can be directly on the other element or there can also be an intermediate element. When an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intermediate element at the same time. The terms "vertical", "horizontal", "left", "right" and similar expressions used herein are for illustrative purposes only.

[0040] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which this invention belongs. The terms used herein in the specification of this invention are only for the purpose of describing specific embodiments and are not intended to limit the invention. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0041] Please refer to Figure 1 , which shows the preparation method of a piezoelectric defect phononic crystal plate in an embodiment of the present invention. The method includes steps S1 to S4:

[0042] S1. Define the change range of the target band gap, and select the vibration damping phononic crystal material and geometric parameters according to the change range of the target band gap;

[0043] Specifically, step S1 includes steps S11 to S12:

[0044] S11. Design the material parameters of the vibration damping matrix, elastic element, scatterer and piezoelectric sheet;

[0045] S12. Design the lattice constant of the matrix plate, the thickness of the elastic element, the central position of the elastic element, the radius of the elastic element, the position of the scatterer, the radius of the scatterer, the height of the scatterer, the positions of the cantilever beam and the piezoelectric sheet, the widths of the cantilever beam and the piezoelectric sheet, the lengths of the cantilever beam and the piezoelectric sheet, and the thicknesses of the cantilever beam and the piezoelectric sheet;

[0046] It should be explained that at the beginning of the design, the change range of the target band gap should be defined. In order to minimize the additional mass, the matrix material of the vibration damping phononic crystal plate should be selected as a material with a small density and a low elastic modulus; the elastic element should be selected as a material with a high elastic modulus; the scatterer should be selected as a material with a large density, and the thickness of the matrix of the vibration damping phononic crystal plate should be as small as possible; to maintain the isotropy of the vibration damping effect, the positions of the elastic element and the scatterer should be as close as possible to the geometric center of the matrix, and the best shape is a cylinder; to meet the low-frequency vibration damping requirements, the radius of the scatterer should be larger and the height should not be too high; the selection of the lattice constant of the matrix plate should ensure that only local resonance band gaps exist within the change range of the target band gap and no Bragg band gaps will appear.

[0047] It should be noted that in this embodiment, the bandgap change range is 20~100 Hz, and the thickness of the plate member is 2 mm, and the material is steel;

[0048] The matrix material of the single crystal cell of the designed vibration-damping phononic crystal plate is plexiglass, which replaces the steel material at the vibration concentration area of the bottom plate of the car, and keeps the thickness unchanged; the elastic element material is designed as silicone, with a cylindrical shape, the height is the same as that of the plexiglass matrix plate, and the center position coincides with the centroid of the matrix plate; the scatterer material is designed as a lead column, with a cylindrical shape, and the center position coincides with the upper and lower center positions of the silicone. The specific material parameters of each component are shown in Table 1, and the geometric parameters are shown in Table 2.

[0049] S2. According to the vibration-damping phononic crystal material and the geometric parameters, and based on the best energy diversion effect, a cantilever beam type line defect structure is introduced, and the material and geometric parameters of the cantilever beam type line defect structure are determined;

[0050] Specifically, the cantilever beam type line defect structure is a sandwich type cantilever beam type line defect structure, and the number of line defects of the sandwich type cantilever beam type line defect structure does not exceed 1.

[0051] It should be explained that to achieve a good energy diversion effect, the periodicity of the vibration-damping phononic crystal plate should be destroyed and a line defect should be introduced; to ensure good vibration-damping performance of the vibration-damping phononic crystal plate within the bandgap range, the number of line defects should not exceed 1; to ensure high diversion efficiency for vertical vibration energy, the line defect form adopts a sandwich type cantilever beam structure; the material of the cantilever beam should be selected as a material with a small density and a low elastic modulus, and the piezoelectric sheet material should be selected as a piezoelectric material with a high short-circuit compliance coefficient, a high constant stress dielectric constant, and a high piezoelectric strain constant (absolute value); the length of the cantilever beam should be less than the lattice constant, the thickness ratio of the piezoelectric sheet to the thickness of the matrix beam is approximately 1:1, and the selection of the width of the matrix beam (piezoelectric sheet) needs to ensure that the additional mass is not too large;

[0052] It should be noted that in this embodiment, the number of designed line defects is 1, the position of the line defect is in the 4th column of the two-dimensional vibration-damping phononic crystal plate member, and the structural form of the line defect is that the scatterers of the lead cylinders on the upper and lower surfaces of the original elastic element are replaced with a sandwich type cantilever beam structure with support blocks;

[0053] The material of the middle beam and support blocks of the sandwich type cantilever beam is plexiglass, and the piezoelectric sheet material connected to the upper and lower surfaces is PZT-5H. The specific material parameters are shown in Table 1, and the geometric parameters are shown in Table 2. The structural diagram of the single crystal cell of the phononic crystal is as Figure 2 , and the structural diagram of the cantilever beam type line defect is as Figure 3 .

[0054] Table 1

[0055]

[0056] Table 2

[0057]

[0058] S3. Determine the length of the piezoelectric sheet fixedly connected to the upper and lower surfaces of the cantilever based on the corresponding relationship between the material and geometric parameters of the cantilever beam type line defect structure;

[0059] Specifically, the step S3 includes steps S31 to S32:

[0060] S31. Obtain the first-order bending mode frequency of the cantilever beam type line defect structure without an external circuit based on the modal analysis and natural frequency calculation of the cantilever beam type line defect structure;

[0061] S32. Obtain the length of the piezoelectric sheet without an external circuit based on the variation relationship between the first-order bending mode frequency of the cantilever beam type line defect structure and the length of the piezoelectric sheet;

[0062] Among them, the calculation expression of the first-order bending mode frequency is:

[0063] ;

[0064] In the formula, represents the first-order bending mode frequency, represents the proximity factor, represents the short-circuit compliance coefficient of the piezoelectric sheet, represents the piezoelectric strain constant of the piezoelectric sheet, represents the constant strain dielectric constant of the piezoelectric sheet, represents the density of the piezoelectric sheet, 、 respectively represent the elastic modulus and density of the cantilever beam matrix beam, 、 respectively represent the cross-sectional area and central section moment of inertia of the cantilever beam matrix beam, 、 respectively represent the cross-sectional area and central section moment of inertia of the piezoelectric sheet, represents the length of the piezoelectric sheet;

[0065] The calculation expression of the length of the piezoelectric sheet without an external circuit is:

[0066] ;

[0067] In the formula, represents the length of the piezoelectric sheet without an external circuit, represents the frequency of the vibration energy.

[0068] It should be noted that based on the frequency of the vibration energy to be diverted from the outside , the length of the piezoelectric sheet of the sandwich-type cantilever beam is obtained by using the formula and appropriately approximated, and it is used as the calculation parameter of the piezoelectric sheet for energy recovery at this vibration frequency. When the frequency of the external vibration energy to be recovered is 68 Hz, the length of the piezoelectric sheet is approximately = 0.018 m.

[0069] S4. Obtain the arrangement angle of the resonators of the cantilever beam type line defect structure, and check the interference condition of the cantilever beam type line defect structure based on the arrangement angle to obtain a piezoelectric defect phononic crystal plate;

[0070] Specifically, the step S4 includes steps S41 to S44:

[0071] S41. Judge the interference direction of the resonator interference condition;

[0072] S42. If interference occurs in the width direction of the resonator, reduce the number of unit cells in the x direction or the y direction;

[0073] S43. If interference occurs in the length direction of the resonator, increase the number of unit cells in the x direction or the y direction;

[0074] S44. If interference occurs in the width direction of the resonator and interference occurs in the length direction of the resonator, increase the lattice constant of the damping phononic crystal substrate plate member, and repeat to clarify the change range of the target band gap, and select the damping phononic crystal material and geometric parameters according to the change range of the target band gap; introduce a cantilever beam type line defect structure based on the best energy diversion effect, and determine the material and geometric parameters of the cantilever beam type line defect structure; determine the length of the piezoelectric sheet fixedly connected to the upper and lower surfaces of the cantilever beam based on the corresponding relationship between the material and geometric parameters of the cantilever beam type line defect structure; obtain the arrangement angle of the resonators of the cantilever beam type line defect structure, and check the interference condition of the cantilever beam type line defect structure based on the arrangement angle until a piezoelectric defect phononic crystal plate is obtained;

[0075] It should be explained that in this embodiment, the number of unit cells in the x direction and the y direction are set to 7 and 7 respectively. At this time, the arrangement angle of the resonators of the sandwich-type cantilever beam type line defect is 0°, parallel to the x direction. The schematic diagram of the seven-period structure is as Figure 4 , and at this time, no interference occurs in the resonators, and the design is completed. The design parameter results are shown in Table 3.

[0076] Table 3

[0077]

[0078] Furthermore, a finite element model of a piezoelectric defective phononic crystal plate with 7×7 unit cells was established. The vibration transmissibility curves of the phononic crystal plate before and after introducing the cantilever beam - type line defect were calculated using finite element software, as shown in Figure 5 and Figure 6 respectively. And the vibration mode diagram of the piezoelectric defective phononic crystal plate when the external excitation frequency is 68 Hz is shown in Figure 7 . It can be seen that the bandgap range of the designed phononic crystal plate is 20 - 140 Hz, which includes the target vibration - damping frequency range of 20 - 100 Hz, verifying the low - frequency vibration - damping performance of the phononic crystal plate. When the cantilever beam - type line defect is introduced, a pass - band appears in the transmissibility curve of the phononic crystal plate near the frequency of 68 Hz, and when the external excitation frequency is 68 Hz, the vibration energy is concentrated on the cantilever beam - type line defect, indicating that the introduced cantilever beam - type line defect structure can achieve the energy diversion function of the target excitation frequency, verifying the feasibility of the design.

[0079] In summary, the preparation method of the piezoelectric defective phononic crystal plate in the above - mentioned embodiments of the present invention can avoid the over - complexity of the preparation of the piezoelectric defective phononic crystal plate caused by excessive design parameters by clarifying the change range of the target bandgap, introducing the cantilever beam - type line defect structure according to the best energy diversion effect, and obtaining the design parameters of the corresponding piezoelectric defective phononic crystal plate. Moreover, it can accurately divert the vibration energy of specific frequencies within the low - frequency bandgap range.

[0080] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above - mentioned terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0081] The above - mentioned embodiments only represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be subject to the appended claims.

Claims

1. A method for preparing a piezoelectric defect phononic crystal plate, characterized in that: The method comprises: Determine the target band gap variation range, and select the vibration-damping phononic crystal material and geometric parameters according to the target band gap variation range; Introducing a cantilever beam type line defect structure according to the vibration-damping phononic crystal material and the geometric parameters and based on the optimal energy conduction effect, and determining the material and geometric parameters of the cantilever beam type line defect structure; Determining the length of the piezoelectric sheets fixed to the upper and lower surfaces of the cantilever beam based on the corresponding relationship between the material and geometric parameters of the cantilever beam type line defect structure; Before the step of determining the length of the piezoelectric sheets fixed to the upper and lower surfaces of the cantilever beam based on the corresponding relationship between the material and geometric parameters of the cantilever beam type line defect structure, the method further includes: Based on the modal analysis of the cantilever beam type line defect structure and the calculation of the natural frequency, the first-order bending modal frequency of the cantilever beam type line defect structure without an external circuit is obtained. The calculation expression of the first-order bending modal frequency is: ； In the formula, represents the first-order bending mode frequency, represents the proximity factor, represents the short-circuit compliance coefficient of the piezoelectric film, represents the piezoelectric strain constant of the piezoelectric sheet, represents the constant strain dielectric constant of the piezoelectric film, represents the density of the piezoelectric sheet, , They represent the elastic modulus of the cantilever beam base beam and the density of the cantilever beam base beam, respectively. , They represent the cross-sectional area of ​​the cantilever beam base beam and the central section moment of inertia of the cantilever beam base beam, respectively. , They represent the cross-sectional area of ​​the piezoelectric film and the central section moment of inertia of the piezoelectric film, respectively. represents the length of the piezoelectric film; The calculation expression of the length of the piezoelectric piece without an external circuit is: ； In the formula, Indicates the length of the piezoelectric film without external circuit. The frequency that represents the energy of vibration; Calculating the length of the piezoelectric sheet without an external circuit based on the variation relationship between the first-order bending mode frequency of the cantilever beam type line defect structure and the length of the piezoelectric sheet; The arrangement angle of the resonant body of the cantilever beam type line defect structure is obtained, and the interference condition of the cantilever beam type line defect structure is checked based on the arrangement angle to obtain a piezoelectric defect phononic crystal plate.

2. The method for preparing a piezoelectric defect phononic crystal plate according to claim 1, characterized in that: The step of selecting the vibration-damping phononic crystal material and geometric parameters according to the target band gap variation range comprises: Design the material parameters of the vibration-damping matrix, elastic element, scatterer and piezoelectric film; Design the lattice constant of the substrate, the thickness of the elastic element, the center position of the elastic element, the radius of the elastic element, the position of the scatterer, the radius of the scatterer, the height of the scatterer, the position of the cantilever beam and the piezoelectric sheet, the width of the cantilever beam and the piezoelectric sheet, the length of the cantilever beam and the piezoelectric sheet, and the thickness of the cantilever beam and the piezoelectric sheet.

3. The method for preparing a piezoelectric defect phononic crystal plate according to claim 1, characterized in that: The cantilever beam type line defect structure is a sandwich type cantilever beam type line defect structure, and the number of line defects of the sandwich type cantilever beam type line defect structure does not exceed 1.

4. The method for preparing a piezoelectric defect phononic crystal plate according to claim 1, characterized in that: After the step of checking the interference of the cantilever beam type line defect structure based on the arrangement angle, the method further includes: Determine the interference direction of the resonant body interference situation; If interference occurs in the width direction of the resonator, the number of cells in the x-direction or y-direction is reduced; If interference occurs in the length direction of the resonator, the number of cells in the x-direction or the y-direction is increased.

5. The method for preparing a piezoelectric defect phononic crystal plate according to claim 4, characterized in that: After the step of determining the interference direction of the resonant body interference, the method further includes: If interference occurs in the width direction of the resonant body and interference occurs in the length direction of the resonant body, the lattice constant of the vibration-damping phononic crystal substrate plate is increased, and the operation is repeated to clarify the range of variation of the target band gap, and the vibration-damping phononic crystal material and geometric parameters are selected according to the range of variation of the target band gap; a cantilever beam type line defect structure is introduced based on the optimal energy conduction effect, and the material and geometric parameters of the cantilever beam type line defect structure are determined; based on the correspondence between the material and geometric parameters of the cantilever beam type line defect structure, the length of the piezoelectric sheet fixed to the upper and lower surfaces of the cantilever beam is determined; the arrangement angle of the resonant body of the cantilever beam type line defect structure is obtained, and the interference of the cantilever beam type line defect structure is checked based on the arrangement angle until a piezoelectric defect phononic crystal plate is obtained.

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