CN113111551A - Lamb wave regulation and control equipment and design method thereof - Google Patents
Lamb wave regulation and control equipment and design method thereof Download PDFInfo
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Abstract
The invention relates to lamb wave regulation and control equipment and a design method thereof, wherein the lamb wave regulation and control equipment comprises a flat plate and a super-structure surface which is arranged above the flat plate and connected with the flat plate, the super-structure surface consists of a row of columns with the same bottom surface diameter and arranged at equal intervals, and the height of each column is adapted to the shape of the wave front of the needed lamb wave. Compared with the prior art, the invention arranges the super-structure surface above the flat plate, the super-structure surface is composed of a row of columns with the same bottom surface diameter and arranged at equal intervals, the regulation and control of any wave front of the anti-symmetric mode transmitted lamb wave are realized by changing the height of each column and carrying out different transmitted wave phase changes, the structure is simple, the regulation and control of the wave front can be realized only by one row of columns, the thickness of the columns is sub-wavelength thickness, the total thickness is small, and the influence on the static performance of the flat plate is small.
Description
Technical Field
The invention relates to the field of elastic wave regulation in engineering application, in particular to lamb wave regulation equipment and a design method thereof.
Background
Plate-like materials are widely used in industries such as aerospace, automotive and shipbuilding. Mechanical waves can be divided into two basic forms, transverse waves and longitudinal waves, and mechanical waves (also known as lamb waves) propagating in a flat plate with free upper and lower boundaries are mixed waves of the two basic forms. Lamb waves contain mainly the following three modes: Anti-Symmetric (A), Symmetric (S) and Shear-horizontal (SH) modes, with different modes having different orders and in different cases exciting different lamb waves. Compared with sound waves and light waves, the multi-mode characteristic of lamb waves makes the regulation of lamb waves extremely challenging. However, the realization of lamb wave regulation and control (such as deflection, focusing and the like) has important significance in the aspects of nondestructive detection, energy capture, sensing communication and the like of engineering structures.
Currently, in practical applications, lamb wave modulation of plate-shaped materials is mainly realized by means of a concept of a metamaterial or a phononic crystal. However, the mechanism of action of the metamaterial or the phononic crystal requires that the basic structure is periodically arranged, so that the elastic functional device has larger integral size and more complex structure, thereby not only limiting the application on small or highly integrated functional devices, but also being not beneficial to processing and manufacturing, and not being ideal lamb wave regulating and controlling equipment. In addition, the original mechanical properties of the flat plate need to be kept as much as possible when the lamb wave regulation and control equipment is designed, so that the flat plate structure can fully play a bearing role, and the structural design (such as a flat plate hollowed structure) in some existing lamb wave regulation and control equipment seriously affects the mechanical properties of the flat plate, which is not beneficial to practical application.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide lamb wave regulation and control equipment and a design method thereof.
The purpose of the invention can be realized by the following technical scheme:
the utility model provides a lamb wave regulation and control equipment, includes the flat board and arranges the super structure surface in the flat board top, super structure surface links to each other with the flat board, by a row of cylinder that the bottom surface diameter is the same, the equidistant range is formed, the height of each cylinder suits with the wave front shape of required lamb wave, different cylinder height corresponds different transmission wave phase change.
Further, the thickness of the pillar is a sub-wavelength thickness.
Furthermore, the cylinder and the flat plate are integrally formed and made of the same material.
Further, the cylinder and the flat plate are integrally formed through a 3D printing technology.
A design method of lamb wave regulation and control equipment comprises the following steps:
s1: obtaining the thickness of a flat plate, and generating a plurality of unit models with different geometric parameters, wherein each unit model comprises the flat plate and a single cylinder arranged above the flat plate, and the geometric parameters comprise the bottom surface diameter of the cylinder and the height of the cylinder;
s2: respectively applying exciting forces with different frequencies to each unit model, and calculating the phase change of the transmitted wave of each unit model at each frequency
And a transmission coefficient, obtaining a basic unit model, wherein the basic unit model satisfies the following conditions: phase change of transmitted wave of basic unit model at certain frequency
Is pi or-pi, and the transmission coefficient of the basic unit model at the frequency is not less than the preset transmission coefficient threshold, and the frequency is recorded as the working frequency of the basic unit model;
s3: applying an exciting force with the frequency equal to the working frequency to the basic unit model, keeping the diameter of the bottom surface of the column in the basic unit model unchanged, continuously changing the height of the column in the basic unit model and calculating the phase change of the transmitted wave of the basic unit model
And transmission coefficient until phase change of transmitted wave is obtainedTransforming
In the range of [ - π, π]A variation function of the cylinder height internally with respect to the basic cell model;
s4: acquiring a required wave front shape, acquiring continuous phase distribution of an ultra-structured surface on a flat plate according to the wave front shape, performing discrete operation on the continuous phase distribution according to the unit width to obtain discrete phase distribution, wherein each discrete point in the discrete phase distribution corresponds to a cylinder, the height of each cylinder is determined according to the phase of each discrete point, and the unit width is the distance between the central points of two adjacent cylinders and is greater than the diameter of the bottom surface of the cylinder;
s5: and manufacturing lamb wave regulating and controlling equipment based on the discrete phase distribution obtained in the step S4 and the height of each column.
Further, element models are generated in finite element software and transmitted wave phase changes of the element models are calculated
And a transmission coefficient.
Further, a perfect matching layer and a periodic condition perpendicular to the wave propagation direction are set in the cell model generated in step S1.
Further, the phase change of the transmitted wave of the cell model is calculated
And the process of transmission coefficient is as follows:
applying an excitation force in the outer direction of the plane plate on one side of the cylinder in the unit model, arranging a detection point on the other side of the cylinder in the unit model, and transmitting wave phase change
Transmission coefficient T ═ w1/w0L where w1For out-of-plane displacement measured at the detection point, w0The out-of-plane displacement measured at the detection point without columns in the unit model.
Further, the preset threshold value of the transmission coefficient is 0.4.
Compared with the prior art, the invention has the following beneficial effects:
(1) the super-structure surface is arranged above the flat plate and consists of a row of cylinders with the same bottom surface diameter and arranged at equal intervals, different transmission wave phase changes are carried out by changing the height of the cylinders, the regulation and control of any wave front of the transmission lamb waves in an anti-symmetric mode are realized, the structure is simple, the regulation and control of the wave front can be realized only by one row of cylinders, the thickness of the cylinders is sub-wavelength thickness, the total thickness is small, and the influence on the static performance of the flat plate is small.
(2) The cylinder and the flat plate are integrally formed and made of the same material, so that the connection between the super-structure surface and the flat plate is stable and reliable, and the processing and the manufacturing are facilitated.
(3) Obtaining continuous phase distribution of the wave front along the arrangement direction of the cylinders, discretizing the continuous phase distribution according to the unit width, enabling each discrete point to correspond to one cylinder, determining the height of each cylinder according to the phase of each discrete point, and enabling the obtained super-structure surface to achieve required wave front regulation and control.
Drawings
FIG. 1 is a schematic structural view of a lamb wave control device;
FIG. 2 is a schematic structural view of a nanostructured surface element;
FIG. 3 is a graph of cylinder height versus transmitted wave phase (curve) and amplitude (gray scale level) for a unit of a nanostructured surface;
FIG. 4 is a phase distribution diagram of an exemplary microstructured surface, including a continuous phase variation curve and a discrete phase distribution;
FIG. 5 shows simulation results and experimental results of a plane wave focused energy field intensity diagram in the examples.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
In the drawings, structurally identical elements are represented by like reference numerals, and structurally or functionally similar elements are represented by like reference numerals throughout the several views. The size and thickness of each component shown in the drawings are arbitrarily illustrated, and the present invention is not limited to the size and thickness of each component. Parts are exaggerated in the drawing where appropriate for clarity of illustration.
Example 1:
a lamb wave regulation device is shown in figure 1 and comprises a flat plate and a super-structure surface arranged above the flat plate, wherein the super-structure surface is connected with the flat plate, the super-structure surface is composed of a row of columns with the same bottom surface diameter, and the height of each column is adapted to the wave front shape of a required lamb wave.
The basic principle is as follows: the cylinder is a resonance cylinder, under the specific cylinder size, the resonance cylinder can be regarded as a secondary excitation source, scattered waves can be excited, the phases of the scattered waves are opposite to those of incident waves, the amplitude of the scattered waves is larger than that of the incident waves, 2 pi phase change of transmitted lamb waves can be realized by utilizing the interaction of the anti-phase scattered waves and the incident waves, and wave front regulation and control of the lamb waves in an anti-symmetric mode are achieved.
The thickness of the columns is sub-wavelength thickness, the columns are cylinders, the diameter of the bottom surfaces of the columns is 1/3 of the wavelength, and the columns in the super-structure plane are arranged at equal intervals. The cylinder and the flat plate are integrally formed and made of the same material, so that the connection between the super-structure surface and the flat plate is stable and reliable, and the processing and the manufacturing are facilitated. In this embodiment, cylinder and dull and stereotyped through 3D printing technique integrated into one piece, the material of use is 3D printing material polylactic acid (PLA).
A design method of lamb wave regulation and control equipment comprises the following steps:
s1: obtaining the thickness of a flat plate, and generating a plurality of unit models with different geometric parameters, wherein each unit model comprises the flat plate and a single cylinder arranged above the flat plate, and the geometric parameters comprise the bottom diameter of the cylinder and the height of the cylinder;
s2: respectively applying exciting forces with different frequencies to each unit model, and calculating the phase change of the transmitted wave of each unit model at each frequency
And a transmission coefficient, obtaining a basic unit model, wherein the basic unit model satisfies the following conditions: phase change of transmitted wave of basic unit model at certain frequency
Is pi or-pi, and the transmission coefficient of the basic unit model at the frequency is not less than the preset transmission coefficient threshold, and the frequency is recorded as the working frequency of the basic unit model;
s3: applying an exciting force with the frequency equal to the working frequency to the basic unit model, keeping the diameter of the bottom surface of the column in the basic unit model unchanged, continuously changing the height of the column in the basic unit model and calculating the phase change of the transmitted wave of the basic unit model
And transmission coefficient until the phase change of the transmitted wave is obtained
In the range of [ - π, π]A variation function of the cylinder height internally with respect to the basic cell model;
s4: acquiring a required wave front shape, acquiring continuous phase distribution of an ultra-structured surface on a flat plate according to the wave front shape, performing discrete operation on the continuous phase distribution according to the unit width to obtain discrete phase distribution, wherein each discrete point in the discrete phase distribution corresponds to a cylinder, the height of each cylinder is determined according to the phase of each discrete point, and the unit width is the distance between the central points of two adjacent cylinders and is greater than the diameter of the bottom surface of the cylinder;
s5: and manufacturing lamb wave regulating and controlling equipment based on the discrete phase distribution obtained in the step S4 and the height of each column.
In this embodiment, the obtained plate has a thickness of 6mm, a plurality of different element models are generated, the structure of the element model generated in the finite element software is shown in fig. 2, and in order to accurately calculate the phase change of the transmitted wave of the element model
And a transmission coefficient, wherein a perfect matching layer in the wave propagation direction and a periodic condition perpendicular to the wave propagation direction are set in the finite element software.
Respectively applying exciting forces with different frequencies to the generated unit models, and respectively calculating the phase change of the transmitted wave of each unit model under the exciting forces with different frequencies
And a transmission coefficient until a basic cell model is found, the basic cell model satisfying the following conditions: basic unit model at a certain frequency
Is pi or-pi, and the transmission coefficient of the basic cell model at the frequency is not less than 0.4, then the frequency is the operating frequency, and in the basic cell model obtained in this embodiment, the diameter of the bottom surface of the pillar is 3.6mm, the height of the pillar is 6.6mm, and the operating frequency is 59.17 kHz.
After the working frequency is determined, an exciting force with the frequency of 59.17kHz is applied to the basic unit model, the diameter of the bottom surface of the column in the basic unit model is kept unchanged, the height of the column in the basic unit model is continuously increased or decreased, and the phase change of the transmitted wave of the unit model is calculated
And the transmission coefficient to obtain the phase change of the transmitted wave
In the range of [ - π, π]With respect to the variation function of the height of the pillars.
Phase change of transmitted wave in the present embodiment
FIG. 3 shows the relationship between the change in height of the cylinder and the corresponding phase change of the transmitted wave at different heights
Different from that, the product is finally obtained]The phase of the transmitted wave in the inner part is changed by the corresponding column height range. By changing the height of the column, the unit model can transmit [0, 2 pi ] of lamb wave while maintaining a large transmission coefficient]Phase global coverage, as shown in fig. 3. If the cylinders with different heights are arranged in a row to form the super-structured surface, the transmission wave front regulation of any shape can be realized by designing the phase distribution along the super-structured surface.
Calculating the transmitted wave phase variation of the cell model
And the transmission coefficient is specifically: applying an excitation force in the outer direction of the plane plate on one side of the column body in the unit model in a slightly long distance, arranging a detection point at any point in a slightly long distance position on the other side of the column body in the unit model, and transmitting wave phase change
Transmission coefficient T ═ w1/w0L where w1For out-of-plane displacement measured at the detection point, w0The out-of-plane displacement measured at the detection point without columns in the unit model.
After the exciting force is applied, the generated transmitted wave is transmitted in the flat plate with free upper and lower boundaries, the displacement when a column is present and the displacement when no column is present are measured at the detection point, and the phase change of the transmitted wave is calculated
And a transmission coefficient.
Then, the required wavefront shape is obtained, in this embodiment, the focusing ultrastructure surface is designed, a continuous phase distribution design along the arrangement direction (x direction) of the cylinders is performed according to the wavefront shape, then, the continuous phase distribution is subjected to a discrete operation according to the unit width to obtain a discrete phase distribution, as shown in fig. 4, each discrete point in the discrete phase distribution corresponds to one cylinder, the phase of the discrete point is taken as the phase of the center point of the cylinder,according to the phase change of the transmitted wave obtained in the step S3
Determining the height of each column body according to a graph of the change relation with the height of the column body, wherein the unit width is the distance between the central points of two adjacent column bodies and is slightly larger than the diameter of the bottom surface of the column body, and the diameter of the bottom surface of the column body is 4.8 mm; all the geometric parameters of the lamb wave regulation equipment are completely determined.
The lamb wave focusing effect of the designed lamb wave regulation and control equipment is verified in simulation and experiment, and is shown in fig. 5. The elastic wave energy can form a focal spot in a design area, and the device has a good plane wave focusing effect and achieves the initial design purpose.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (8)
1. The lamb wave regulation and control equipment is characterized by comprising a flat plate and a super-structure surface arranged above the flat plate, wherein the super-structure surface is connected with the flat plate and consists of a row of columns with the same bottom surface diameter and arranged at equal intervals, and the height of each column is adapted to the shape of the wave front of the needed lamb wave.
2. A lamb wave conditioning apparatus according to claim 1, wherein the posts are formed integrally with the plate and are of the same material.
3. A lamb wave conditioning apparatus according to claim 2, wherein the cylinder is integrally formed with the plate by 3D printing.
4. A method of designing a lamb wave modulation device, for designing a lamb wave modulation device according to any one of claims 1 to 3, comprising the steps of:
s1: obtaining the thickness of a flat plate, and generating a plurality of unit models with different geometric parameters, wherein each unit model comprises the flat plate and a single cylinder arranged above the flat plate, and the geometric parameters comprise the bottom surface diameter of the cylinder and the height of the cylinder;
s2: respectively applying exciting forces with different frequencies to each unit model, and calculating the phase change of the transmitted wave of each unit model at each frequency
And a transmission coefficient, obtaining a basic unit model, wherein the basic unit model satisfies the following conditions: phase change of transmitted wave of basic unit model at certain frequency
Is pi or-pi, and the transmission coefficient of the basic unit model at the frequency is not less than the preset transmission coefficient threshold, and the frequency is recorded as the working frequency of the basic unit model;
s3: applying an exciting force with the frequency equal to the working frequency to the basic unit model, keeping the diameter of the bottom surface of the column in the basic unit model unchanged, continuously changing the height of the column in the basic unit model and calculating the phase change of the transmitted wave of the basic unit model
And transmission coefficient until the phase change of the transmitted wave is obtained
In the range of [ - π, π]A variation function of the cylinder height internally with respect to the basic cell model;
s4: acquiring a required wave front shape, acquiring continuous phase distribution of an ultra-structured surface on a flat plate according to the wave front shape, performing discrete operation on the continuous phase distribution according to the unit width to obtain discrete phase distribution, wherein each discrete point in the discrete phase distribution corresponds to a cylinder, the height of each cylinder is determined according to the phase of each discrete point, and the unit width is the distance between the central points of two adjacent cylinders and is greater than the diameter of the bottom surface of the cylinder;
s5: and manufacturing lamb wave regulating and controlling equipment based on the discrete phase distribution obtained in the step S4 and the height of each column.
5. The method of claim 4, wherein the element model is generated in finite element software and the transmitted wave phase variation of the element model is calculated
And a transmission coefficient.
6. The method of claim 5, wherein the cell model generated in step S1 further includes a perfect matching layer and a periodic condition perpendicular to the propagation direction of the wave.
7. The method according to claim 4, wherein the phase change of the transmitted wave of the unit model is calculated
And the process of transmission coefficient is as follows:
applying an excitation force in the outer direction of the plane plate on one side of the cylinder in the unit model, arranging a detection point on the other side of the cylinder in the unit model, and transmitting wave phase change
Transmission coefficient T ═ w1/w0L where w1For out-of-plane displacement measured at the detection point, w0Detecting points when there is no column in the unit modelThe measured out-of-plane displacement.
8. The design method of a lamb wave modulation device according to claim 4, wherein the preset threshold value of the transmission coefficient is 0.4.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2010029762A1 (en) * | 2008-09-12 | 2010-03-18 | 国立大学法人山梨大学 | Lamb wave-type elastic wave element |
| WO2019201178A1 (en) * | 2018-04-17 | 2019-10-24 | 江苏必得科技股份有限公司 | Train component crack damage detection method and system based on lamb wave imaging |
| CN112115639A (en) * | 2020-09-03 | 2020-12-22 | 南京理工大学 | Electromagnetic superstructure surface construction method under unit near-coupling condition based on deep learning |
-
2021
- 2021-03-31 CN CN202110350582.6A patent/CN113111551A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2010029762A1 (en) * | 2008-09-12 | 2010-03-18 | 国立大学法人山梨大学 | Lamb wave-type elastic wave element |
| WO2019201178A1 (en) * | 2018-04-17 | 2019-10-24 | 江苏必得科技股份有限公司 | Train component crack damage detection method and system based on lamb wave imaging |
| CN112115639A (en) * | 2020-09-03 | 2020-12-22 | 南京理工大学 | Electromagnetic superstructure surface construction method under unit near-coupling condition based on deep learning |
Non-Patent Citations (3)
| Title |
|---|
| YABIN JIN, WAN WANG, ABDELKRIM KHELIF, BAHRAM DJAFARI-ROUHANI: "Elastic Metasurfaces for Deep and Robust Subwavelength Focusing and Imaging", 《PHYSICAL REVIEW APPLIED》 * |
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