Method for elastic wave rainbow trapping by varying the position of the connecting arms and metamaterials

Abstract

The application discloses a structure design method and a metamaterial for realizing elastic wave rainbow trapping by changing the position of connecting arms, and comprises the following steps: 1) constructing a unit structure composed of two geometric monomers connected by connecting arms, and arranging the unit structure in cycles to form a phononic crystal metamaterial structure; and 2) adjusting the position and / or quantity of the connecting arms between the two geometric monomers to make the unit structure generate a new band gap, and meanwhile, the frequency corresponding to the point with a group velocity of 0 can be changed, and the rainbow trapping effect is realized based on the adjusted unit structure. The application changes the position of the connecting arms to realize the positioning transmission of the elastic wave by using the characteristic that the group velocity is 0, provides a new scheme for the regulation of the elastic wave, and the structure design has certain universality, the structure shape can be replaced on the basis, engineering application is facilitated, and the regulation of the elastic wave has more choices.

Description

Technical Field

[0001] This invention relates to the structural design of elastic wave metamaterials and provides a relatively universal method. Specifically, it relates to a method and metamaterial for achieving rainbow capture of elastic waves by changing the position of the connecting arm. This method generates a new bandgap in the structure by changing the position of the connecting arm, and at the same time, it controls the frequency corresponding to the point where the group velocity is 0, thereby achieving adjustable positioning and transmission of elastic waves and causing the elastic waves to exhibit rainbow capture phenomenon. Background Technology

[0002] Phononic crystal metamaterials have attracted widespread attention due to their advantage of being able to control the propagation paths of elastic waves / acoustic waves through structural design. The rainbow trapping phenomenon originates from the field of optics; different wavelengths of light have different refractive indices in materials, causing different colors of light to be separated at different angles, forming a rainbow. Research on rainbow trapping behavior in the acoustic / elastic wave field is relatively limited. Rainbow trapping is generally achieved using two methods: utilizing bandgap characteristics and achieving a group velocity of zero. Bandgap characteristics involve changing structural parameters to create differences in the bandgap range of different structures. Utilizing these bandgap differences allows elastic / acoustic waves to propagate to a specific interface and stop propagating further, achieving targeted transmission within a certain frequency range. Conversely, when the group velocity is zero, the wave remains at the interface, ceasing further propagation, resulting in an energy concentration and amplification effect.

[0003] Both methods can generate rainbow capture phenomena for the localized transmission of elastic / acoustic waves, but they also have certain differences. Utilizing bandgap characteristics to generate localized transmission is relatively easier to design, but this type of wave reflects at the interface. When only one wave packet is given, all the energy is reflected at the interface and does not remain. Utilizing the zero group velocity characteristic, the wave also reflects at the interface, but unlike acoustic waves, a large portion of the energy remains at the boundary, resulting in energy accumulation. This type of rainbow capture phenomenon is more beneficial for energy trapping design in engineering and has broader application prospects. Unlike acoustic waves, elastic waves are vector waves. Due to the coupling between different wave modes, designing the dispersion curve and adjusting the structure are more complex and difficult. Achieving both zero group velocity and decoupling between in-plane modes to generate a new bandgap in a one-dimensional phononic crystal presents a significant challenge. Summary of the Invention

[0004] The purpose of this invention is to provide a method and metamaterial for achieving rainbow capture of elastic waves by varying the position of the connecting arms in an elastic wave phononic crystal metamaterial. This is a novel method for achieving rainbow capture by adjusting the position of the connecting arms. The dispersion relation curve corresponding to this configuration has certain special characteristics. This scheme can successfully adjust the band gap and the frequency corresponding to the group velocity of 0 by changing the position of the connecting arms, thereby achieving the localization and transmission of elastic waves. Furthermore, this configuration has a certain degree of universality; changing the geometry of the connecting arms in the structure can also achieve the rainbow capture phenomenon and achieve the same purpose.

[0005] The technical solution adopted by this invention to solve the technical problem is as follows:

[0006] Methods for capturing elastic wave rainbows by changing the position of the connecting arm include the following:

[0007] 1) Construct a phononic crystal metamaterial structure consisting of a unit structure composed of two geometrically connected units with connecting arms, arranged periodically.

[0008] 2) By adjusting the position and / or number of connecting arms between two geometric units, a new band gap is generated in the unit structure, and the frequency corresponding to the point where the group velocity is 0 can be changed. The rainbow capture effect is achieved based on the adjusted unit structure.

[0009] In the above technical solution, the phononic crystal metamaterial structure is further composed of a unit structure arranged periodically in a one-dimensional direction.

[0010] Furthermore, the unit structure is a symmetrical structure formed by connecting two identical geometric units with connecting arms. Before adjustment, the geometric units with connecting arms are symmetrical structures. Each geometric unit has two types of connecting arms: the first type is used to connect with another geometric unit, and the second type is used to connect with other unit structures. During adjustment, the position and / or number of the first type of connecting arms are changed to disrupt the structural symmetry of the geometric unit.

[0011] Furthermore, all connecting arms in the unit structure are the same size and shape.

[0012] Furthermore, the unit structures obtained through different adjustment methods are superimposed to form several interfaces. The positioning and transmission of different frequencies at each interface are achieved by having a group velocity of 0, which results in the rainbow capture phenomenon, while energy is concentrated and amplified.

[0013] The beneficial effects of this invention are as follows:

[0014] 1. This invention provides a novel method for constructing structures with zero group velocities and generating new band gaps.

[0015] 2. In this invention, the method of changing the position of the connecting arm is used to achieve elasticity control, which increases the dimension of elastic wave propagation control and makes the control more diversified.

[0016] 3. In addition to the features mentioned above, the most crucial advantage of this invention lies in its universality. By changing the shape of the geometric unit connected by the connecting arm, different configurations can be designed to achieve the same effect and purpose. Essentially, it only requires changing the relative positions of the left and right connecting arms within the same geometric configuration. For example, if the geometric unit is a square, one connecting arm can be designed on the left, while two connecting arms are designed on the right, with inconsistent relative positions of the left and right connecting arms. This allows for better applicability to different scenarios in engineering applications. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the unit structure and structural parameters of the initial phonon crystal constructed in this invention.

[0019] Figure 2 This is a schematic diagram of the metamaterial structure formed by the periodic arrangement of phonon crystals according to the present invention.

[0020] Figure 3 These are the dispersion relationship curves corresponding to the four unit structures when the position of the connecting arm changes in this invention.

[0021] Figure 4 This is a schematic diagram of a structure consisting of four types of unit structures and having three interfaces.

[0022] Figure 5 Figures from COMSOL Multiphysics finite element simulations of elastic wave propagation at different frequencies.

[0023] Figure 6 Phononic crystal structure unit designed by changing the number of the first type of connecting arms.

[0024] Figure 7 The dispersion curve of the structure after adjusting the position of the connecting arm and the simulation diagram of the rainbow capture phenomenon achieved.

[0025] Figure 8 The diagrams of two unit structures are designed by changing the geometry of the second type of connecting arm and the number of the first type of connecting arms. Detailed Implementation

[0026] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0027] The method for capturing elastic wave rainbows by changing the position of the connecting arm according to the present invention includes the following:

[0028] 1) Construct an initial phonon crystal structure unit with tunable connecting arms;

[0029] 2) By adjusting the position of the connecting arms of the constructed structural unit, the symmetry of the unit structure is changed to a certain extent, thereby changing the shape of the dispersion relation curve, regulating the propagation of elastic waves, and realizing positioning transmission.

[0030] The initial phonon crystal structure unit is designed as a symmetrical structure formed by connecting two identical geometric units with connecting arms. The main shape of the geometric unit can be any axisymmetric figure such as a square, rectangle, or isosceles triangle. Each geometric unit is designed with two types of connecting arms: the first type is used to connect with another geometric unit, and the second type is used to connect with other unit structures. All connecting arms are the same in size and shape and can be rectangular connecting arms. Before adjustment, the geometric unit with connecting arms is a symmetrical structure. During adjustment, changing the position of the connecting arms changes the symmetry of the unit structure to a certain extent. This "position" can be achieved by directly changing the position of the first type of connecting arms or by increasing the number of the first type of connecting arms. At this time, it is equivalent to the overall position of the first type of connecting arms changing relative to before adjustment. Through this adjustment, the structural symmetry of the geometric unit can be destroyed, thereby changing the symmetry of the unit structure to a certain extent.

[0031] This invention presents a phonon crystal structure unit made of steel plate, consisting of two squares connected by rectangular connecting arms of a certain width. The unit cells are arranged regularly and periodically along the horizontal direction, thus forming a phonon crystal structure. By adjusting the position of the connecting arms, the third dispersion curve (focusing only on in-plane modes) can be effectively controlled, creating a band gap between it and the second dispersion curve. Furthermore, due to the structural design, the second dispersion curve exhibits a pattern of first increasing and then decreasing, altering its monotonicity, resulting in negative group velocities and points where the group velocity is zero. Specifically:

[0032] like Figure 1As shown, the elastic wave metamaterial constructed in this example is composed of a 5mm thick steel plate arranged periodically in unit cells. In engineering practice, it is constructed by cutting and processing. Its initial structural unit is a symmetrical structure composed of two identical squares connected by a rectangular connecting arm of width w. There is a rectangular connecting arm in the middle of each of the two sides of the square.

[0033] The lattice size of this structural unit is a= , where l is Figure 1 The square connected by rectangular connecting arms has a side length of w and a length of h. In this example, in the original structure, w = 1 mm and l = 10 mm. The initial position of the rectangular connecting arms is located at the midpoint of the left and right sides of the square. Figure 1 The right side shows the dispersion curve of this structural unit. It can be seen that the second and third dispersion curves intersect from bottom to top. By adjusting the position of the rectangular connecting arm between the two squares, the dispersion curve of the structure and the frequency corresponding to the point where the group velocity is 0 can be changed.

[0034] The positions of the connecting arms between the two squares in the initial unit structure are adjusted so that they are not on the same horizontal plane as the connecting arms on the left side of the first square and the right side of the second square. Then, the modified structural units are periodically arranged along the horizontal direction to form a phononic crystal structure. For example... Figure 2 As shown, the metamaterial structure is obtained by periodically arranging structural units along the horizontal direction. In the initial unit structure, the side length of the square is l, and the middle connecting arm is initially located at the middle position of the square's side, denoted as point 0. Its position is adjusted so that it is located in the upper half of the rectangle. , , , Even if the two connecting arms of a single square are in different horizontal positions, thus disrupting its structural symmetry, it also disrupts the overall horizontal symmetry of the entire unit structure to some extent.

[0035] like Figure 3 As shown, changing the position of the connecting arm between the two squares significantly alters the dispersion curve. Figure 1 There is frequency overlap between the second and third dispersion curves. At this point, different wavelengths at the same frequency correspond to different modes. Even if there is a point where the group velocity is 0, the corresponding frequency exhibits dual modes, preventing the wave from becoming stationary. After the position is adjusted, such as... Figure 3As shown, a new band gap is generated between the second and third dispersion curves, at which point there is no frequency overlap, preparing the necessary conditions for the localized transmission of elastic waves. Further changing the position of the rectangular connecting arm can adjust the frequency of the elastic wave corresponding to a group velocity of 0. When different structures are combined, the elastic wave with a group velocity of 0 will remain at different interfaces, achieving localized transmission and producing a rainbow capture effect. Therefore, by changing the position of the connecting arm, the form of the dispersion curve can be changed, thus creating the desired band gap and the point of group velocity 0. By superimposing the four structures together, three interfaces are formed, and localized transmission at different frequencies at the three interfaces is achieved with a group velocity of 0. Figure 4 This is a schematic diagram of a metamaterial structure constructed by stacking structures with different rectangular arm widths. For example... Figure 5 As shown, waves of different frequencies remain at different locations, achieving positioning and transmission, resulting in rainbow capture, and simultaneously exhibiting the effect of energy concentration and amplification.

[0036] As mentioned earlier, the method of changing the position of the connecting arm can include two aspects. Firstly, changing the position of the connecting arm itself creates a band gap between the second and third dispersion curves. At this point, the elastic wave located between the two frequency bands cannot propagate within the structure. The second dispersion curve contains a point where the group velocity is 0. By adjusting the position of the connecting arm, the frequency corresponding to the point where the group velocity is 0 can be controlled, allowing elastic waves of different frequencies to remain at different positions, thus achieving adjustable positioning and transmission of the elastic wave. Secondly, this structural design only requires that the connecting arms on the left and right sides of the square are not at the same horizontal position, thus disrupting the symmetry about the horizontal direction. This allows for the construction of a series of configurations that can achieve the rainbow capture effect. Adjustments can be made to the shape and size according to engineering needs; for example, the number of connecting arms between the two squares can be directly adjusted. Figure 6 As shown. Adjusting the position of the first connecting arm between the squares can control the frequency corresponding to the point where the group velocity is 0, such as... Figure 7 The figure shows the dispersion curves for each configuration after changing the position of one of the connecting arms, as well as the simulation diagram of the rainbow capture phenomenon achieved.

[0037] The method of this invention is a universal method; by changing the geometry of the connecting arms in the structure, the rainbow capture phenomenon can be achieved, thus achieving the same purpose. For example... Figure 8 This invention presents two structural designs: one involving altering the geometry of the connecting arms, and the other involving changing the number of connecting arms. These metamaterials can be fabricated using machine tools through cutting. This type of metamaterial is easy to process and its geometry can be designed according to specific scenarios, facilitating engineering applications. This invention also provides a new solution for the positioning and control of elastic waves, designing a universally applicable structure.

[0038] The embodiments described above are merely some preferred embodiments of the present invention, and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A structural design method for capturing elastic wave rainbows by varying the position of the connecting arm, characterized in that, Including the following: 1) Construct a phononic crystal metamaterial structure consisting of a unit structure composed of two geometrically connected units with connecting arms, arranged periodically. 2) By adjusting the position and / or number of connecting arms between two geometric units, a new band gap is generated in the unit structure, and the frequency corresponding to the point where the group velocity is 0 can be changed. The rainbow capture effect is achieved based on the adjusted unit structure. The unit structure is a symmetrical structure formed by connecting two identical geometric units with connecting arms. Each geometric unit has two types of connecting arms: the first type is used to connect with another geometric unit, and the second type is used to connect with other unit structures. Before adjustment, the geometric units with connecting arms are symmetrical structures. During adjustment, the position and / or number of the first type of connecting arms are changed to disrupt the structural symmetry of the geometric units. All connecting arms in the unit structure are the same size and shape.

2. The structural design method for capturing elastic wave rainbows by changing the position of the connecting arm according to claim 1, characterized in that, 1) The one-dimensional phononic crystal metamaterial structure is formed by periodically arranging unit structures in one-dimensional direction.

3. The structural design method for capturing elastic wave rainbows by changing the position of the connecting arm according to claim 1, characterized in that, The unit structures obtained through different adjustment methods are superimposed to form several interfaces. The positioning and transmission of different frequencies at each interface are achieved by the group velocity being 0, which results in the rainbow capture phenomenon, while energy is concentrated and amplified.

4. A metamaterial capable of capturing elastic wave rainbows, characterized in that, It is designed using the method described in any one of claims 1-3.

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