阅读说明：本技术 一种非周期机械拓扑绝缘体单胞模型的设计方法 (Design method of non-periodic mechanical topological insulator unit cell model ) 是由 游世辉 张圣东 于 2021-06-28 设计创作，主要内容包括：一种非周期机械拓扑绝缘体单胞模型的设计方法,包括以下步骤：构建周期机械拓扑绝缘体单胞模型；采用随机坐标公式对两个散射体的位置进行非周期化,以在基体内形成非周期传播通道；构建周期机械拓扑绝缘体单胞模型不同形态的周期通道板超胞和非周期机械拓扑绝缘体单胞模型不同形态的非周期通道板超胞,并在周期通道板超胞和非周期通道板超胞的左端分别输入谐振激励生成对应的总位移响应图进行对比分析,以确定弹性波或机械波在非周期传播通道内均匀传播。本发明通过采用随机方法对基体内的散射体进行非周期化,以在基体内形成非周期传播通道,使弹性波或机械波得以均匀的在非周期传播通道内传播,从而避免在非周期传播通道内发生响应过大的现象。(A design method of a non-periodic mechanical topological insulator unit cell model comprises the following steps: constructing a periodic mechanical topological insulator unit cell model; the positions of the two scatterers are subjected to non-periodicity by adopting a random coordinate formula so as to form a non-periodic propagation channel in the matrix; and respectively inputting resonance excitation at the left ends of the periodic channel plate supercell and the non-periodic channel plate supercell to generate corresponding total displacement response graphs for comparative analysis so as to determine that the elastic waves or the mechanical waves are uniformly transmitted in the non-periodic transmission channel. The invention adopts a random method to carry out non-periodicity on the scatterers in the matrix so as to form a non-periodic propagation channel in the matrix, so that elastic waves or mechanical waves can be uniformly propagated in the non-periodic propagation channel, and the phenomenon of overlarge response in the non-periodic propagation channel is avoided.)

1. A design method of a non-periodic mechanical topological insulator unit cell model is characterized by comprising the following steps:

s10, constructing a periodic mechanical topological insulator unit cell model by taking the magnetorheological elastomer as a matrix and taking pure iron as a scatterer in the matrix;

step S11, the positions of the two scatterers are non-periodically processed by adopting a random coordinate formula to form a non-periodic propagation channel in the matrix, namely the periodic mechanical topological insulator unit cell model is converted into a non-periodic mechanical topological insulator unit cell model, wherein the random coordinate formula is as follows:

wherein x is₁₀、y₁₀Is the original circle center coordinate, x, of the first one of the scatterers₁、y₁The coordinates of the center of a circle, rho, of the first scatterer after random variation₁＝0.1～0.2L，θ₁＝2π，rand₁Is a random uniform distribution function between 0 and 1, L is the distance between the original center coordinates of the first scatterer and the second scatterer, x₂₀、y₂₀Is the original circle center coordinate, x, of the second one of the scatterers₂、y₂The centre coordinates, rho, of the second scatterer after random variation₂＝0.1～0.2L，θ₂＝2π，rand₂A random uniform distribution function between 0 and 1;

step S12, constructing periodic channel plate supercells of different forms of a periodic mechanical topological insulator single cell model and non-periodic channel plate supercells of different forms of a non-periodic mechanical topological insulator single cell model, and respectively inputting resonance excitation at the left ends of the periodic channel plate supercells and the non-periodic channel plate supercells to generate corresponding total displacement response graphs for comparative analysis so as to determine that elastic waves or mechanical waves are uniformly transmitted in a non-periodic transmission channel.

2. The method of designing an aperiodic mechanical topological insulator unit cell model as recited in claim 1, wherein after step S12, the method further comprises:

step S121, converting the total displacement response graph of the supercell of the non-periodic channel plate in different forms into a total displacement contour map;

step S122, in the total displacement contour map, calculating the distance of the point where the same total displacement value is located at the upper and lower interfaces of the aperiodic propagation channels with different forms to obtain the channel width of the aperiodic propagation channels with different forms in the propagation process of the elastic wave or the mechanical wave, and calculating the average value and the mean square error of the channel width to determine that the response of the elastic wave or the mechanical wave is uniform at each position in the aperiodic propagation channels with different forms.

3. The method of claim 1, wherein in step S10, the substrate is 30% MR elastomer, the elastic modulus is 5.36MPa, the Poisson' S ratio is 0.47, and the density is 3211kg/m³。

4. The method of claim 1, wherein in step S11, L is 0.6dm, the radius of the first scatterer is 0.1-0.2 mm, and the radius of the second scatterer is 0.05-0.1 mm.

5. The method of claim 4, wherein in step S12, the periodic channel plate supercell and the aperiodic channel plate supercell respectively have a linear shape, a zigzag shape and an inverted S shape.

Technical Field

The invention relates to the technical field of mechanical topological insulators, in particular to a design method of a non-periodic mechanical topological insulator unit cell model.

Background

The mechanical topological insulator has the characteristics which are not possessed by the conventional mechanical metamaterial, such as the robustness of nondestructive transmission and conduction of elastic waves or mechanical waves. Among them, the periodic mechanical topological insulator has gained much attention because of its superior performance. However, it has been found that periodic mechanical topological insulators tend to respond very much at excitation, and although elastic waves can be limited to propagate only in the edge state channels of topological protection, for practical applications, situations of excessive response should be avoided.

Disclosure of Invention

Based on the above, the present invention aims to provide a design method of a non-periodic mechanical topological insulator unit cell model, which constructs a non-periodic propagation channel by non-periodically configuring a periodic topological insulator, so that elastic waves or mechanical waves can be uniformly propagated in the non-periodic propagation channel.

A design method of a non-periodic mechanical topological insulator unit cell model comprises the following steps:

s10, constructing a periodic mechanical topological insulator unit cell model by taking the magnetorheological elastomer as a matrix and taking pure iron as a scatterer in the matrix;

step S11, the positions of the two scatterers are non-periodically processed by adopting a random coordinate formula to form a non-periodic propagation channel in the matrix, namely the periodic mechanical topological insulator unit cell model is converted into a non-periodic mechanical topological insulator unit cell model, wherein the random coordinate formula is as follows:

wherein x is₁₀、y₁₀Is the original circle center coordinate, x, of the first one of the scatterers₁、y₁The coordinates of the center of a circle, rho, of the first scatterer after random variation₁＝0.1～0.2L，θ₁＝2π，rand₁Is a random uniform distribution function between 0 and 1, L is the distance between the original center coordinates of the first scatterer and the second scatterer, x₂₀、y₂₀Is the original circle center coordinate, x, of the second one of the scatterers₂、y₂For the second scatterer to randomizeChanged center coordinates, ρ₂＝0.1～0.2L，θ₂＝2π，rand₂A random uniform distribution function between 0 and 1;

step S12, constructing periodic channel plate supercells of different forms of a periodic mechanical topological insulator single cell model and non-periodic channel plate supercells of different forms of a non-periodic mechanical topological insulator single cell model, and respectively inputting resonance excitation at the left ends of the periodic channel plate supercells and the non-periodic channel plate supercells to generate corresponding total displacement response graphs for comparative analysis so as to determine that elastic waves or mechanical waves are uniformly transmitted in a non-periodic transmission channel.

Compared with the prior art, the scattering body in the substrate is subjected to non-periodicity by adopting a random method to form a non-periodic propagation channel in the substrate, so that the elastic wave or the mechanical wave can be uniformly propagated in the non-periodic propagation channel, and the phenomenon of overlarge response in the non-periodic propagation channel is avoided.

Further, after step S12, the design method further includes:

step S121, converting the total displacement response graph of the supercell of the non-periodic channel plate in different forms into a total displacement contour map;

step S122, in the total displacement contour map, calculating the distance of the point where the same total displacement value is located at the upper and lower interfaces of the aperiodic propagation channels with different forms to obtain the channel width of the aperiodic propagation channels with different forms in the propagation process of the elastic wave or the mechanical wave, and calculating the average value and the mean square error of the channel width to determine that the response of the elastic wave or the mechanical wave is uniform at each position in the aperiodic propagation channels with different forms. .

Further, in step S10, the matrix is 30% magnetorheological elastomer, the elastic modulus is 5.36MPa, the Poisson ratio is 0.47, and the density is 3211kg/m³。

Further, in step S11, L is 0.6dm, the radius of the first scatterer is 0.1 to 0.2mm, and the radius of the second scatterer is 0.05 to 0.1 mm.

Further, in step S12, the shapes of the periodic channel plate supercell and the non-periodic channel plate supercell include a linear shape, a zigzag shape, and an inverted S shape, respectively.

Drawings

FIG. 1 is a flow chart of a design method of a non-periodic mechanical topological insulator unit cell model according to the present invention;

FIG. 2(a) is a schematic structural diagram of a mechanical topological insulator in accordance with the present invention;

FIG. 2(b) is a schematic structural diagram of the periodic mechanical topological insulator unit cell model of the present invention;

FIG. 3(a1) is a wave propagation response diagram of the periodic mechanical topological insulator unit cell model in the linear state at the 20 th order frequency;

FIG. 3(a2) is a wave propagation response diagram of the aperiodic mechanical topological insulator unit cell model at the 20 th order frequency in the linear state;

FIG. 3(b1) is a wave propagation response diagram of the periodic mechanical topological insulator unit cell model at the 15 th order frequency in the zigzag state in the present invention;

FIG. 3(b2) is a wave propagation response diagram of the aperiodic mechanical topological insulator unit cell model at the 28 th order frequency in the zigzag state in the present invention;

FIG. 3(c1) is a wave propagation response diagram of the periodic mechanical topological insulator unit cell model in the inverted S form at the 15 th order frequency;

FIG. 3(c2) is a wave propagation response diagram of the aperiodic mechanical topological insulator unit cell model at 34 th order frequency in the inverted S shape;

FIG. 4(a) is a contour diagram of the total displacement of the aperiodic mechanical topological insulator unit cell model at the 20 th order frequency in the linear state in accordance with the present invention;

FIG. 4(b) is a total displacement contour plot of the aperiodic mechanical topological insulator unit cell model at 28 th order frequency in the zigzag state in accordance with the present invention;

FIG. 4(c) is a contour diagram of the total displacement at 34 th order frequency in the inverted S shape of the aperiodic mechanical topological insulator unit cell model in accordance with the present invention.

The following detailed description will further illustrate the invention in conjunction with the above-described figures.

Detailed Description

To facilitate an understanding of the invention, the invention will now be described more fully with reference to the accompanying drawings. Several embodiments of the invention are presented in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

It will be understood that when an element is referred to as being "secured to" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. The terms "vertical," "horizontal," "left," "right," and the like as used herein are for illustrative purposes only.

Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

Referring to fig. 1 to fig. 3, a method for designing an aperiodic mechanical topological insulator unit cell model according to an embodiment of the present invention includes the following steps:

s10, constructing a periodic mechanical topological insulator unit cell model by taking the magnetorheological elastomer as a matrix and taking pure iron as a scatterer in the matrix;

step S11, the positions of the two scatterers are non-periodically processed by adopting a random coordinate formula to form a non-periodic propagation channel in the matrix, namely the periodic mechanical topological insulator unit cell model is converted into a non-periodic mechanical topological insulator unit cell model, wherein the random coordinate formula is as follows:

wherein x is₁₀、y₁₀Is the original circle center coordinate, x, of the first one of the scatterers₁、y₁The coordinates of the center of a circle, rho, of the first scatterer after random variation₁＝0.1～0.2L，θ₁＝2π，rand₁Is a random uniform distribution function between 0 and 1, L is the distance between the original center coordinates of the first scatterer and the second scatterer, x₂₀、y₂₀Is the original circle center coordinate, x, of the second one of the scatterers₂、y₂The centre coordinates, rho, of the second scatterer after random variation₂＝0.1～0.2L，θ₂＝2π，rand₂A random uniform distribution function between 0 and 1;

step S12, constructing periodic channel plate supercells of different forms of a periodic mechanical topological insulator single cell model and non-periodic channel plate supercells of different forms of a non-periodic mechanical topological insulator single cell model, and respectively inputting resonance excitation at the left ends of the periodic channel plate supercells and the non-periodic channel plate supercells to generate corresponding total displacement response graphs for comparative analysis so as to determine that elastic waves or mechanical waves are uniformly transmitted in a non-periodic transmission channel.

Referring to fig. 2 and 3, it should be noted that the filling ratio is the total area of the scatterers divided by the area of the substrate. Specifically, as shown in fig. 2, the filling ratio is equal to the area of two circles divided by the area of the base (excluding the area of two circles). Because the elastic modulus of the magnetorheological elastomer matrix is small, a complete parallelogram matrix is difficult to obtain a complete band gap, and therefore, circular domains generated at four corners are excavated through difference set operation, so that the filling rate of the scatterer is improved. However, since the filling ratio of the scatterers cannot be increased without limit, in order to increase the range of random distribution of the scatterers, the radius of the first scatterer is 0.1 to 0.2mm, the radius of the second scatterer is 0.05 to 0.1mm, and the value of L is 0.6 dm.

Specifically, the two corners on the long diagonal have two identical first sectors, the two corners on the short diagonal have two identical second sectors, and the area of the second sectors is twice that of the first sectors.

Further, after step S12, the design method further includes:

step S121, converting the total displacement response graph of the supercell of the non-periodic channel plate in different forms into a total displacement contour map;

step S122, in the total displacement contour map, calculating the distance of the point where the same total displacement value is located at the upper and lower interfaces of the aperiodic propagation channels with different forms to obtain the channel width of the aperiodic propagation channels with different forms in the propagation process of the elastic wave or the mechanical wave, and calculating the average value and the mean square error of the channel width to determine that the response of the elastic wave or the mechanical wave is uniform at each position in the aperiodic propagation channels with different forms.

Example 1

In this example, the material parameters of the base and scatterer are shown in table 1.

TABLE 1 Material parameter Table of aperiodic mechanical topological insulator unit cell model

On the basis of a periodic mechanical topological insulator unit cell model, through performing non-periodicity on scatterers in a channel, elastic waves are uniformly transmitted in the whole channel, and therefore three forms, namely a linear form, a Z-shaped form and an inverted S form, are constructed for periodic channel plate supercell and non-periodic channel plate supercell.

In the modeling process, after the randomly distributed coordinates are obtained by the method, the randomly distributed coordinates are replaced by the coordinates of the scatterers in various morphological channels, wherein rho₁＝ρ₂0.2L, 0.6dm, the radius of the first scatterer is 0.15mm and the radius of the second scatterer is 0.075 mm.

Specifically, (x)₁₀,y₁₀) (0, 0) in mm. When rand₁Values of 0.81, 0.91, 0.13, 0.91, 0.63, 0.09, 0.27, 0.54, 0.95, 0.96, 0.15, 0.97, 0.95, 0.48, 0.80, 0.14, 0.42, 0.91, 0.79, 0.95 correspond to (x)₁,y₁) The coordinates of (a) are: (-6.07,4.08),(11.14,7.74),(3.94, -6.72),(10.50, -11.02),(-4.24,9.03),(0.32,0.42),(-0.33,2.57),(-7.23, -7.38),(-6.57, -11.36),(5.60, -11.78),(-1.89,6.85),(11.58, -10.68),(-1.97, -9.71),(8.53,7.60),(8.85,7.34),(3.05,0.07),(-2.89, -2.13),(-4.70,9.69),(10.23, -5.48),(11.48,11.59).

(x₂₀,y₂₀) (21.213 ) in mm when rand₂Values of 0.75, 0.25, 0.50, 0.69, 0.89, 0.95, 0.54, 0.13, 0.14, 0.25, 0.84, 0.25, 0.81, 0.24, 0.92, 0.34, 0.19, 0.25, 0.61, 0.47 correspond to (x)₂,y₂) The coordinates of (a) are: (14.94,30.16),(24.87,13.97),(13.44,29.58),(11.51,19.39),(31.05,31.00),(18.58,14.18),(21.63,30.46),(21.37,15.58),(16.17,14.81),(14.34,13.66),(31.02,24.59),(28.31,24.99),(10.53,32.00),(22.57,17.34),(31.80,30.67),(26.76,14.01),(14.69,19.50),(13.84,21.03),(30.88,25.78),(16.61,24.32).

And generating a model through Comsol with Matlab joint simulation, and importing the model into Comsol Multiphysics. And (3) setting resonance excitation with the amplitude of 10mm at the left end of the channel plate, calculating by using a solid mechanics module in Comsol Multiphysics, setting the sweep frequency range to be 460-500 Hz, and performing frequency domain analysis.

Referring to fig. 3(a1) -3 (c2), specifically, the total displacement in the board is used as a calculation parameter to calculate the corresponding periodic and aperiodic propagation response maps respectively.

From the wave propagation characteristic response graphs of fig. 3(a1), fig. 3(b1) and fig. 3(c1), it can be concluded that the total displacement response graphs of the periodic mechanical topological insulator supercells all have responses in the channels, and the responses outside the channels are zero, which indicates that the edge state propagation of the elastic wave topological protection is realized at this time. If an external load is connected to the input end, elastic waves can be guided to a proper position through the mode, thereby protecting equipment or machinery to be isolated. However, it should be noted that the response at the input end of the resonant load is large and exceeds the range of the channel, and as can be seen from the wave propagation characteristic response diagram, the response value at the input end is much higher than other positions of the channel, and fatigue failure is easy to occur.

As can be seen from the wave propagation characteristic response graphs in fig. 3(a2), fig. 3(b2) and fig. 3(c2), the aperiodic mechanical topological insulator supercell is a state in which the elastic wave propagates relatively uniformly in the channel, and the response of the excitation end is not much higher than that of other parts in the channel plate, which indicates that after the scatterers in the channel are aperiodic, the edge state of the topological protection is not destroyed, but the propagation effect of the elastic wave can be improved.

Example 2

Referring to fig. 4(a) -4 (c), in order to obtain the wave propagation characteristics of the aperiodic mechanical topological insulator supercell, it is necessary to count the morphological characteristics during the propagation process. In particular, where p₁＝ρ₂The radius of the first scatterer is 0.15mm, the radius of the second scatterer is 0.075mm, the post-processing function of Comsol Multiphysics is utilized to convert the total displacement response diagram in fig. 3(a2) -3 (c2) under the parameters into a corresponding total displacement contour diagram in fig. 4(a) -4 (c), the distance of points where the same total displacement value exists at the upper and lower interfaces of the channel is calculated to obtain the channel width in the wave propagation process, and the average value and the variance are calculated, and the calculation result is shown in table 2.

TABLE 2 three aperiodic propagation channel geometries

Channel configuration	Channel mean	Mean square error of channel
			Straight line shape	36.2mm	0.74
Z-shaped	43.3mm	0.73
			Inverted S shape	37.1mm	0.89

As can be seen from table 2, the average value of the straight channels is the smallest, while the average value of the zigzag and inverted S channels is larger, because the zigzag and inverted S channels affect the propagation of other segments of the zigzag and inverted S channels when the direction changes. From the view of the mean square error, the mean square error values of the three types of channels are small, which shows that the response of each position of the elastic wave or the mechanical wave is uniform when the elastic wave or the mechanical wave propagates in the three topologically protected edge state channels. And the mean square error values of the three channels are relatively close to each other, because the three types of topological insulators have the same non-periodic mode and randomly and uniformly point the positions of small circular scatterers in the channels within the range of 0.1L.

In summary, in the present invention, the scattering body in the substrate is aperiodic by using a random method to form an aperiodic propagation channel in the substrate, so that the elastic wave or the mechanical wave can be uniformly propagated in the aperiodic propagation channel, thereby avoiding the phenomenon of too large response in the aperiodic propagation channel.

The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.