Piezoelectric defect photonic crystal plate preparation method

Abstract

The invention provides a piezoelectric defect photonic crystal plate preparation method, which comprises the following steps: determining the change range of a target band gap, and selecting a vibration reduction photonic crystal material and geometric parameters according to the change range of the target band gap; introducing a cantilever beam type line defect structure based on the optimal energy diversion effect according to the vibration reduction photonic crystal material and the geometric parameters, and determining the material and the geometric parameters of the cantilever beam type line defect structure; determining the length of piezoelectric patches fixedly connected to the upper and lower surfaces of the cantilever beam based on the corresponding relationship between the material of the cantilever beam type line defect structure and geometric parameters; and acquiring the arrangement angle of the resonance body of the cantilever beam type line defect structure, and checking the interference condition of the cantilever beam type line defect structure based on the arrangement angle to obtain the piezoelectric defect photonic crystal plate. According to the invention, too complex preparation of the piezoelectric defect photonic crystal plate caused by too many design parameters can be avoided, and flow guide can be accurately carried out on vibration energy of a specific frequency in a 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: 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; 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.

[0006] Compared with the prior art, the beneficial effects of the present invention are: by clarifying the variation range of the target band gap and introducing a cantilever beam line defect structure according to the optimal energy conduction effect, and by obtaining the design parameters of the corresponding piezoelectric defect phononic crystal plate, it is possible to avoid excessive design parameters that lead to overly complicated preparation of the piezoelectric defect phononic crystal plate, and it is also possible to accurately conduct vibration energy of a specific frequency within the low-frequency band gap range.

[0007] Furthermore, the step of selecting the vibration-damping phononic crystal material and geometric parameters according to the target band gap variation range includes: 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.

[0008] Furthermore, the cantilever beam type line defect structure is a sandwich type cantilever beam type line defect structure, and the number of line defects in the sandwich type cantilever beam type line defect structure does not exceed 1.

[0009] Furthermore, 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 linear defect structure, the method further includes: Obtaining the first-order bending modal frequency of the cantilever beam type line defect structure without an external circuit based on the modal analysis of the cantilever beam type line defect structure and the calculation of the natural frequency; 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 piece, the length of the piezoelectric piece without an external circuit is calculated.

[0010] Furthermore, 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.

[0011] Furthermore, after the step of checking the interference condition 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.

[0012] Furthermore, 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of a method for preparing a piezoelectric defect phononic crystal plate in an embodiment of the present invention; Figure 2 Schematic diagram of the structure of a phononic crystal single cell in an embodiment of the present invention; Figure 3is a schematic structural diagram of a cantilever beam type line defect in an embodiment of the present invention; Figure 4 It is a schematic diagram of a seven-period structure of a resonant body arrangement of a sandwich-type cantilever beam type line defect in an embodiment of the present invention; Figure 5 is a vibration transmissibility curve of a phononic crystal plate before a cantilever beam type line defect is introduced in an embodiment of the present invention; Figure 6 is a vibration transmissibility curve of a phononic crystal plate after a cantilever beam type line defect is introduced in an embodiment of the present invention; Figure 7 3 is a vibration mode diagram of a piezoelectric defect phononic crystal plate when the external excitation frequency is 68 Hz in an embodiment of the present invention.

[0014] The following specific implementation manner will further illustrate the present invention in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0015] In order to facilitate the understanding of the present invention, the present invention will be described more fully 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, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0016] It should be noted that when an element is referred to as being "fixed to" another element, it may be directly on the other element or there may be a central element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be a central element at the same time. The terms "vertical", "horizontal", "left", "right" and similar expressions used herein are for illustrative purposes only.

[0017] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which the present invention belongs. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0018] See also Figure 1 , which shows a method for preparing a piezoelectric defect phononic crystal plate in an embodiment of the present invention, the method comprises steps S1 to S4: S1, clarifying the variation range of the target band gap, and selecting the vibration-damping phononic crystal material and geometric parameters according to the variation range of the target band gap; Specifically, the step S1 includes steps S11 to S12: S11, design the material parameters of the vibration-damping matrix, elastic element, scatterer and the material parameters of the piezoelectric sheet; S12, designing 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; It needs to be explained that, during the design, the variation range of the target band gap should be clearly defined. In order to minimize the additional mass, the matrix material of the vibration-damping phononic crystal plate should be selected from a material with low density and low elastic modulus; the elastic element should be selected from a material with high elastic modulus; the scatterer should be selected from a material with high density, and the matrix thickness of the vibration-damping phononic crystal plate should be as small as possible; in order to maintain the isotropy of the vibration-damping effect, the positions of the elastic element and the scatterer should be located as close to the geometric center of the matrix as possible, and a cylinder is the best shape; in order to meet the low-frequency vibration reduction requirements, the radius of the scatterer should be large and the height should not be too high; the selection of the lattice constant of the matrix plate must ensure that only local resonance band gaps exist within the target band gap variation range, and no Bragg band gaps appear.

[0019] It is worth noting that in this embodiment, the band gap varies from 20 to 100 Hz, and the plate thickness 2 mm, material is steel; The base material of the vibration-damping phononic crystal plate single unit cell is organic glass, which replaces the steel material at the vibration concentration point of the bottom panel of the car, and keeps the thickness unchanged; the elastic element material is designed to be silicone, which is cylindrical in shape, with the same height as the organic glass base plate, and its center position coincides with the centroid of the base plate; the scatterer material is designed to be a lead column, which is cylindrical in shape, and its 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.

[0020] S2, 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; Specifically, the cantilever beam type line defect structure is a sandwich type cantilever beam type line defect structure, and the number of line defects in the sandwich type cantilever beam type line defect structure does not exceed one.

[0021] It needs to be explained that in order to achieve a good energy conduction effect, the periodicity of the vibration-damping phononic crystal plate should be destroyed and line defects should be introduced; in order to ensure good vibration-damping performance of the vibration-damping phononic crystal plate within the band gap range, the number of line defects should not exceed 1; in order to ensure high conduction efficiency of vertical vibration energy, the line defect form adopts a sandwich cantilever beam structure; the material of the cantilever beam should be a material with low density and low elastic modulus, and the material of the piezoelectric sheet should be a piezoelectric material with high short-circuit compliance coefficient, high constant stress dielectric constant, and high voltage electric strain constant (absolute value); the length of the cantilever beam should be less than the lattice constant, the ratio of the thickness of the piezoelectric sheet to the thickness of the base beam is approximately 1:1, and the width of the base beam (piezoelectric sheet) should be selected to ensure that the additional mass is not too large; It is worth noting that in this embodiment, the number of designed line defects is 1, the position of the line defect is located in the 4th column of the two-dimensional vibration-damping phononic crystal plate, 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 by a sandwich cantilever beam structure with a support block; The material of the middle beam and the support block of the sandwich cantilever beam is organic glass, and the material of the piezoelectric sheet 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 structure diagram of the phononic crystal single unit cell is shown in Figure 2 The structure of the cantilever beam line defect is shown in Figure 3 .

[0022] Table 1

[0023] Table 2

[0024] S3, 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 linear defect structure; Specifically, the step S3 includes step S31 to step S32: S31, obtaining the first-order bending modal frequency of the cantilever beam type line defect structure without an external circuit based on the modal analysis of the cantilever beam type line defect structure and the calculation of the natural frequency; S32, calculating the length of the piezoelectric sheet without an external circuit based on the change relationship between the first-order bending mode frequency of the cantilever beam type line defect structure and the length of the piezoelectric sheet; Wherein, 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.

[0025] It should be noted that the frequency of the vibration energy to be diverted is based on , the piezoelectric length of the sandwich cantilever beam is calculated using the formula The piezoelectric length is obtained and appropriately approximated as the piezoelectric sheet calculation parameter for energy recovery at this vibration frequency. When the frequency of the external vibration energy to be recovered is 68 Hz, the piezoelectric sheet length is approximately =0.018m.

[0026] S4, obtaining an arrangement angle of the resonant body of the cantilever beam type line defect structure, and checking the interference condition of the cantilever beam type line defect structure based on the arrangement angle to obtain a piezoelectric defect phononic crystal plate; Specifically, the step S4 includes steps S41 to S44: S41, determining the interference direction of the resonant body interference; S42, if interference occurs in the width direction of the resonator, reducing the number of cells in the x direction or the y direction; S43, if interference occurs in the length direction of the resonant body, increasing the number of cells in the x direction or the y direction; S44, if interference occurs in the width direction of the resonant body and interference occurs in the length direction of the resonant body, then increase the lattice constant of the vibration-damping phononic crystal substrate plate, and repeat the process to clarify 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; introduce a cantilever beam type line defect structure based on the optimal energy conduction effect, and determine the material and geometric parameters of the cantilever beam type line defect structure; determine the length of the piezoelectric sheet 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; obtain the arrangement angle of the resonant body 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, until a piezoelectric defect phononic crystal plate is obtained; It should be explained that, in this embodiment, the number of cells in the x direction and the y direction is set to 7 and 7 respectively. At this time, the resonant body arrangement angle of the sandwich cantilever beam type line defect is 0°, parallel to the x direction, and the schematic diagram of the seven-period structure is as follows: Figure 4 At this time, the resonant body does not interfere, the design is completed, and the design parameter results are shown in Table 3.

[0027] Table 3

[0028] Furthermore, a finite element model of a piezoelectric defect phononic crystal plate with 7×7 cells was established, and the vibration transmissibility curves of the phononic crystal plate before and after the introduction of the cantilever beam line defect were calculated using finite element software, as shown in the figure below: Figure 5 and Figure 6 , and the vibration mode diagram of the piezoelectric defect phononic crystal plate when the external excitation frequency is 68Hz is shown in Figure 7 It can be seen that the band gap range of the designed phononic crystal plate is 20~140 Hz, which includes the target vibration reduction frequency range of 20~100 Hz, verifying the low-frequency vibration reduction performance of the phononic crystal plate; after the cantilever beam line defect is introduced, the transmission rate curve of the phononic crystal plate has a passband near the frequency of 68 Hz, and when the external excitation frequency is 68 Hz, the vibration energy is concentrated on the cantilever beam line defect, indicating that the introduced cantilever beam line defect structure can realize the energy diversion function of the target excitation frequency, verifying the feasibility of the design.

[0029] In summary, the method for preparing a piezoelectric defect phononic crystal plate in the above-mentioned embodiment of the present invention, by clarifying the variation range of the target band gap and introducing a cantilever beam line defect structure according to the optimal energy conduction effect, and by obtaining the design parameters of the corresponding piezoelectric defect phononic crystal plate, can avoid excessive complexity in the preparation of the piezoelectric defect phononic crystal plate due to too many design parameters, and can also accurately conduct vibration energy of a specific frequency within the low-frequency band gap range.

[0030] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0031] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached 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; 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: 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: Obtaining the first-order bending modal frequency of the cantilever beam type line defect structure without an external circuit based on the modal analysis of the cantilever beam type line defect structure and the calculation of the natural frequency; 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 piece, the length of the piezoelectric piece without an external circuit is calculated.

5. The method for preparing a piezoelectric defect phononic crystal plate according to claim 4, characterized in that: 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.

6. 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.

7. The method for preparing a piezoelectric defect phononic crystal plate according to claim 6, 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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