A coordinate transformation design method for acoustic cloaks adapting to different wave propagation directions

Abstract

The present invention discloses a method for designing an acoustic cloak coordinate transformation that is adaptable to different wave propagation directions, comprising the following steps: S1, determining the direction of the incident sound wave; S2, splitting the cloak and constructing a multi-center local coordinate system; S3, for each split part, performing coordinate transformation in the multi-center local coordinate system to obtain the cloak design parameters; S4, equating the cloak design parameters to two layers of alternately arranged isotropic media. Compared with the prior art, the beneficial effect of the present invention is that: considering the incident sound wave conditions in different propagation directions, a corresponding structural splitting scheme is designed according to the direction of the incident sound wave, so that the designed cloak can have good control over the incident sound waves at different angles.

Description

Technical Field

[0001] The present invention relates to the technical field of acoustic cloaks, and in particular to a coordinate transformation design method for an acoustic cloak adapting to different wave propagation directions. Background Art

[0002] Acoustic metamaterials are artificially designed microstructures with subwavelength scales that can achieve acoustic properties that are difficult to achieve with ordinary acoustic materials, such as low-frequency band gaps in sound waves, negative refraction of sound, acoustic focusing, acoustic stealth, and directional transmission of sound. The combination of transformation acoustics theory and anisotropic acoustic metamaterials can accurately control the deformation of the sound field, thereby achieving acoustic stealth. Acoustic stealth means that sound waves will "bypass" the invisible object and move forward freely without scattering, thereby achieving the effect of stealth. The concept of acoustic stealth cloak based on transformation acoustics originated from the field of electromagnetism. Because sound waves and electromagnetic waves have the same wave form, the stealth strategy of electromagnetic waves has also been extended to the manipulation of sound waves. The core idea is to find spatial mapping and coordinate transformation according to the control requirements of sound waves, and thereby calculate the transformation medium, and finally realize the regulation of the sound field by the transformation medium.

[0003] In terms of acoustic cloak design, basic structures such as cylinders and spheres are hot topics in acoustic invisibility cloak research because of their strong symmetry. Figure 1 The figure shows the transformation principle of a two-dimensional cylindrical acoustic cloak. The transformation principle is to expand the origin O in the original space into a circle with a radius of a, and compress the entire circular area outward into a ring with an inner diameter a and an outer diameter b, which is essentially a mapping of the center point. Ellipses and prisms are common basic shapes with reduced symmetry. Studying them can provide ideas for designing stealth structures with complex shapes. Figure 2 The figure shows the coordinate transformation principle diagram of the elliptical acoustic cloak. In the figure, the major semi-axis of the outer boundary ellipse is a, the minor semi-axis is b, and the focal length is 2c. The transformation principle is to compress the inner boundary line segment of length 2c outward to form an elliptical ring, which is essentially a mapping of the line segment. Since the cylindrical cloak is highly symmetrical, the coordinate compression in all directions is exactly the same, so it has the same control effect on incident waves in all directions. However, when the symmetry of the stealth cloak structure is reduced, such as elliptical, prismatic or even arbitrary shapes, the stealth effect changes with the direction of the incident wave. Taking the elliptical cloak as an example, the sound field of its cloak is equivalent to the sound field of the sound wave incident on the horizontal rigid line segment. Therefore, it has a better stealth effect for sound waves propagating in the x direction, but a poorer stealth effect for sound waves propagating in the y direction. The simulation results are shown in Figure 3 and Figure 4As shown. In terms of coordinate transformation based on acoustic cloaks, existing research mainly focuses on coordinate transformation of acoustic cloaks of different arbitrary shapes, so as to achieve the control of sound waves by cloaks of arbitrary complex shapes. Or by adding an active control unit to the cloak, the sound waves can be controlled within a wide bandwidth. However, the stealth effect of this type of cloak is limited to the incident sound waves, and can only better control the sound waves in a certain direction or angle. A good stealth effect can be achieved in these single directions or angles, while the stealth effect is poor in other directions. Summary of the invention

[0004] In order to address the deficiencies in the prior art, the present invention provides a coordinate transformation design method for an acoustic cloak that is adaptable to different wave propagation directions. The incident sound waves in different propagation directions are taken into consideration, and a corresponding structural splitting scheme is designed according to the direction of the incident sound waves, so that the designed cloak can have good control over the incident sound waves at different angles.

[0005] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0006] A method for designing an acoustic cloak coordinate transformation that adapts to different wave propagation directions comprises the following steps:

[0007] S1. Determine the direction of the incident sound wave;

[0008] S2. Split the cloak and construct a multi-center local coordinate system

[0009] S3. For each split part, coordinate transformation is performed in a multi-center local coordinate system to obtain the cloak design parameters;

[0010] S4. The design parameters of the cloak are equivalent to two layers of alternately arranged isotropic media.

[0011] Furthermore, the cloak in S2 is split along the incident direction of the sound wave.

[0012] Furthermore, the coordinate transformation in S3 is an affine transformation based on the splitting direction.

[0013] Furthermore, in S3, the split part of each local coordinate system is equivalent to a cylindrical part with the local coordinate origin as a circle, and the coordinate transformation is performed according to the two-dimensional cylindrical coordinate transformation theory.

[0014] Furthermore, the equivalent medium theory is used in S4 to equate the cloak design parameters to two layers of alternatingly arranged isotropic media.

[0015] Furthermore, in S3, a circular area is compressed from the center outward to form a ring area through coordinate transformation, as follows:

[0016] For the two-dimensional case, the coordinate change from the virtual space (r, θ) to the physical space (r′, θ′) is as shown in formula (1):

[0017]

[0018] Where a and b are the inner and outer diameters of the cloak, respectively. That is, the cloak is an annular area surrounded by two concentric circles with radii a and b. The physical meaning of formula (1) is to compress a circular area from the center of the circle into an annular area. The Jacobian transformation matrix A of this coordinate transformation can be expressed as formula (2):

[0019]

[0020] Compared with the prior art, the beneficial effects of the present invention are:

[0021] The present invention comprehensively considers the incident conditions of sound waves in different propagation directions, and improves the limitation that the stealth effect of traditional acoustic cloak is only good in a single incident direction or angle but poor in other incident directions; the method has the advantages of simple design and wide applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Attached Figure 1 This is the principle diagram of the transformation of a two-dimensional cylindrical acoustic cloak;

[0023] Attached Figure 2 This is the schematic diagram of the coordinate transformation of the traditional elliptical acoustic cloak;

[0024] Attached Figure 3 This is the simulation effect diagram of the traditional oval cloak along the x-direction and y-direction of the sound wave;

[0025] Attached Figure 4 This is a simulation effect diagram of the rigid line segments of the traditional elliptical cloak along the x- and y-directions of the sound wave;

[0026] Attached Figure 5 It is a principle block diagram of the present invention;

[0027] Attached Figure 6 Schematic diagram of the design of the elliptical cloak structure adapted to the propagation of sound waves in the y direction according to Embodiment 1 of the present invention;

[0028] Attached Figure 7 This is a simulation effect diagram of Embodiment 1 of the present invention;

[0029] Attached Figure 8 Schematic diagram of the design of the elliptical cloak structure adapted to the propagation of sound waves in the y direction according to Embodiment 2 of the present invention;

[0030] Attached Fig. 9 This is a simulation effect diagram of Embodiment 2 of the present invention;

[0031] Attached Fig.10 It is a schematic diagram of the design of the elliptical cloak structure that is suitable for sound wave propagation in the x-direction according to Example 3 of the present invention. DETAILED DESCRIPTION

[0032] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the application equally.

[0033] like Figure 5 The invention discloses a method for designing an acoustic cloak coordinate transformation that can adapt to different wave propagation directions, comprising the following steps:

[0034] S1. Determine the direction of the incident sound wave;

[0035] S2. Split the cloak and construct a multi-center local coordinate system; preferably, the splitting direction of the cloak is the same as the incident direction of the sound wave. The splitting principle is to set the splitting direction along the incident direction of the sound wave. The coordinate transformation obtained is an affine transformation based on the splitting direction. The scattering of the incident sound wave along the splitting direction is minimal, and the designed cloak has the best control effect on the sound wave in this direction.

[0036] S3. For each split part, coordinate transformation is performed in a multi-center local coordinate system to obtain the cloak design parameters; coordinate transformation is performed according to the two-dimensional cylindrical coordinate transformation theory to obtain the cloak material design parameters; wherein, a circular area is compressed from the center to the outside to form a ring area through coordinate transformation, as follows:

[0037] For the two-dimensional case, the coordinate change from the virtual space (r, θ) to the physical space (r′, θ′) is as follows:

[0038]

[0039] Where a and b are the inner and outer diameters of the cloak, respectively. The physical meaning of formula (1) is to compress a circular area from the center of the circle into an annular area. The Jacobian transformation matrix A of this coordinate transformation can be expressed as formula (2):

[0040]

[0041] S4. The equivalent medium theory is used to equate the cloak design parameters to two layers of alternating isotropic media, which is convenient for material design.

[0042] Embodiment Example 1:

[0043] Combination Figure 6-Figure 7 This embodiment is described in detail, wherein Figure 3 and Figure 4 The simulation diagrams of the traditional acoustic cloak based on elliptical cylindrical coordinate transformation and the rigid line segment in different directions show that the acoustic field of the cloak is equivalent to the acoustic field of the horizontal rigid line segment when the sound wave is incident. The cloak designed by the traditional method has a good stealth effect for sound waves propagating in the x direction, but has a poor stealth effect for sound waves propagating in the y direction. Figure 6 The figure shows a schematic diagram of the design of an elliptical cloak structure that adapts to the propagation of sound waves in the y direction under the scheme of the present invention. In the figure, each layer of ellipse has the same focus, the focal length c is 0.87m, the outermost major semi-axis is 1.98m, the minor semi-axis is 1.78m, the inner major semi-axis is 1m, and the minor semi-axis is 0.5m. For the sound waves propagating in the y direction, the method is applied to split the elliptical structure along the vertical direction, and a central local coordinate system is constructed. The elliptical cylinder is divided every 5°. The design material parameters of each part of the split cloak are obtained by combining the coordinate transformation method and the equivalent medium theory. The elliptical cloak that adapts to the propagation of sound waves in the y direction can be designed by combining the parts. Repeat the above steps, and an elliptical acoustic cloak that adapts to sound waves incident in different directions can be obtained.

[0044] Figure 7 This is the simulation effect diagram of the elliptical cylindrical cloak obtained by applying the above steps. It can be seen in the figure that the sound wave bends along the cloak area. The designed scheme can achieve good control of the incident sound wave in the y direction. The cloak material parameters can be adjusted according to the direction of the incident wave, and the stealth effect is flexible and controllable.

[0045] Embodiment Example 2:

[0046] Combination Figure 8-Figure 9 This embodiment is described in detail. Figure 8 The schematic diagram of the design of the elliptical cloak structure adapted to the propagation of sound waves in the y direction under the scheme of the present invention is shown. For the sound waves incident in the y direction, the elliptical cloak structure is split along the y direction by the application method. Here, the elliptical cloak structure can be approximately composed of two semicircular structures and a rectangular structure. The semicircular part and the rectangular part are split into 30 parts along the y direction. For each split part, 30 central local coordinates are constructed, where O1 and O 30 The part with O1 as the center coordinate is the semi-cylindrical part, and the rest of the rectangular part is divided into small vertically distributed rectangular strips. The inner diameter of the approximate semi-cylindrical part is 1m, the outer diameter is 2m, the length of the middle rectangular part is 3m, and it is divided every 0.1m in the vertical direction. For the semi-cylindrical part, O1 and O 30The center coordinate is the center of the circle, and the material design parameters are obtained by applying the two-dimensional cylindrical coordinate transformation theory. For the vertically distributed small rectangular part, it is approximately equivalent to a part of a cylinder with an inner diameter of 1m and an outer diameter of 2m. The center of the circle is the central local coordinate of the corresponding part. The material design parameters are also obtained by applying the two-dimensional cylindrical coordinate transformation theory. Then, for the convenience of simulation design, the equivalent medium theory is applied to the above-obtained material parameters, which are equivalent to two alternating isotropic materials. A total of 20 layers are set. The various parts can be combined to design an elliptical cloak suitable for sound wave propagation in the y direction.

[0047] Fig. 9 This is the simulation effect diagram of the elliptical cylindrical cloak obtained by applying the above steps. It can be seen from the figure that the sound wave bends along the cloak area, and the incident sound wave along the y direction is well controlled. The cloak material parameters can be adjusted according to the direction of the incident wave, and the stealth effect is flexible and controllable.

[0048] Embodiment Example 3:

[0049] Combination Fig.10 This embodiment is described in detail. Fig.10 The figure shows a schematic diagram of the design of an elliptical cloak structure adapted to the propagation of sound waves in the x direction under the scheme of the present invention. For the sound waves incident in the x direction, the design scheme of the present patent is applied to split the elliptical cloak structure along the x direction. Here, the elliptical cloak structure can be approximately composed of two upper and lower semicircular structures and an arc structure in the middle. The semicircular part and the arc part are split into 40 parts along the x direction, and 40 central local coordinates are constructed for each split part, wherein the arc part is split into a plurality of horizontally distributed small rectangular strips, which are described in detail as follows: the central coordinates of the upper and lower semi-cylindrical parts are O1 and O2. 40 The inner diameter is 0.5m, the outer diameter is 2m, the length of the middle arc part is 4m, and it is divided every 0.1m in the horizontal direction. For the semi-cylindrical part, the center coordinates are O1 and O 40 The horizontally distributed small rectangular part is equivalent to a small part of the cylinder, and the center of the circle is the central local coordinate of the corresponding divided part. The material design parameters are also obtained by using the two-dimensional cylindrical coordinate transformation theory. Finally, the equivalent medium theory is used to equate the above-obtained material parameters to two isotropic materials arranged alternately, with a total of 20 layers, thereby designing an elliptical cloak suitable for sound wave propagation in the x direction.

Claims

1. A method for designing acoustic cloak coordinate transformation that adapts to different wave propagation directions, characterized in that: The following steps are involved: S1. Determine the direction of the incident sound wave; S2, split the cloak and construct a multi-center local coordinate system; S3. For each split part, coordinate transformation is performed in a multi-center local coordinate system to obtain the cloak design parameters; S4, the cloak design parameters are equivalent to two layers of alternately arranged isotropic media; Among them, the cloak in S2 is split along the incident direction of the sound wave; In S3, the split part of each local coordinate system is equivalent to a cylindrical part with the local coordinate origin as a circle, and the coordinate transformation is performed according to the two-dimensional cylindrical coordinate transformation theory. And through the coordinate transformation, a circular area is compressed from the center to the outside to form a ring area, as follows: For the two-dimensional case, from the virtual space ( r , θ ) to physical space( r ′, θ ′) is shown in formula (1): （1） in, a and b are the inner and outer diameters of the cloak, that is, the cloak is composed of a radius of a and b The physical meaning of formula (1) is to compress a circular area from the center of the circle into an annular area. The Jacobian transformation matrix A of this coordinate transformation can be expressed as formula (2) （2）。 2. The method for designing an acoustic cloak coordinate transformation that adapts to different wave propagation directions according to claim 1, characterized in that: The coordinate transformation in S3 is an affine transformation based on the splitting direction.

3. The method for designing an acoustic cloak coordinate transformation that adapts to different wave propagation directions according to claim 1, characterized in that: In S4, the equivalent medium theory is used to equate the cloak design parameters to two layers of alternately arranged isotropic media.

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