CN110231675A - A kind of waveguide concealed device and its design method applied to ripples - Google Patents
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Abstract
本发明公开了一种应用于水波的波导隐身装置及其设计方法，包括本体，所述本体为两个左右并排布置的类等腰梯形结构。或，所述本体为多个连续并排布置的一端为高度渐变的斜坡段的类直角梯形结构。或，所述本体由多个圆柱体阵列排布而成的桩柱结构。经过设计后，类梯形等腰结构、类直角梯形结构或阵列桩柱结构在具有特定的波长和频率的平面波入射时，能够在波导中部大幅度消减波幅，从而实现隐身效果。The invention discloses a waveguide cloaking device applied to water waves and a design method thereof, which includes a body, and the body is two isosceles trapezoidal structures arranged side by side. Or, the body is a plurality of right-angled trapezoidal structures arranged continuously side by side with slope sections with gradually changing heights at one end. Or, the body is a pile structure formed by a plurality of cylindrical arrays. After design, the quasi-trapezoidal isosceles structure, quasi-right-angled trapezoidal structure or array pile structure can greatly reduce the wave amplitude in the middle of the waveguide when a plane wave with a specific wavelength and frequency is incident, thereby achieving a stealth effect.
Description
技术领域technical field
本发明涉及波浪理论和工程技术领域，尤其涉及一种应用于水波的波导隐身装置及其设 计方法。The invention relates to the field of wave theory and engineering technology, in particular to a waveguide cloaking device applied to water waves and a design method thereof.
背景技术Background technique
平面波在遇到固体结构时，总是会发生反射，造成在固体结构周边的波场发生错乱，不 再保持平面波的特征。波浪在传播过程中对水中的结构施加作用力，水面的浮体结构会随着 波浪晃动，而且平面波的波幅很难被降低。在以往的理论研究和实践中，一直没有有效的办 法来消减波浪的波幅。When a plane wave encounters a solid structure, it will always be reflected, causing the wave field around the solid structure to be disordered and no longer maintain the characteristics of a plane wave. The wave exerts force on the structure in the water during the propagation process, and the floating body structure on the water surface will shake with the wave, and the amplitude of the plane wave is difficult to be reduced. In previous theoretical research and practice, there has been no effective way to reduce the wave amplitude.
发明内容Contents of the invention
本发明的目的是针对现有技术的不足，提供一种具有消波效果的波浪调控装置及设计方 法，解决了波场调控的技术难题。The purpose of the present invention is to address the deficiencies of the prior art, to provide a wave control device and design method with wave-absorbing effect, which solves the technical problem of wave field control.
本发明解决技术问题所采用的技术方案如下：一种应用于水波的波导隐身装置，包括本 体，所述本体为两个左右并排布置的类等腰梯形结构。The technical solution adopted by the present invention to solve the technical problem is as follows: a waveguide cloaking device applied to water waves, including a body, and the body is two isosceles trapezoidal structures arranged side by side.
进一步的，所述类等腰梯形结构主要由水平段平板和对称连接在水平段平板两端的两段斜 坡段曲面板构成，本体在波导中沿水波传播方向布置，类等腰梯形结构的总长度为L，每个 斜坡段曲面板的长度为L1，水平段平板的长度为L2；Further, the quasi-isosceles trapezoidal structure is mainly composed of a flat plate in the horizontal section and two sections of slope section curved panels symmetrically connected to both ends of the flat plate in the horizontal section. The main body is arranged in the waveguide along the direction of water wave propagation. is L, the length of each curved panel in the slope section is L 1 , and the length of the flat panel in the horizontal section is L 2 ;
当本体浸没于水中时，本体下底面处的水深为h，将水传播方向作为x轴，x轴位于本体 的对称面上，本体沿x轴方向的高度分布记为d(x)，则本体上表面处的水深分布便为h(x)＝h-d(x)；在确定不同水深处的折射率分布n(x)后，根据折射率计算公式：When the body is submerged in water, the water depth at the bottom of the body is h, the direction of water propagation is taken as the x-axis, and the x-axis is located on the symmetry plane of the body, and the height distribution of the body along the x-axis direction is recorded as d(x), then the body The water depth distribution at the upper surface is h(x)=h-d(x); after determining the refractive index distribution n(x) at different water depths, according to the refractive index calculation formula:
求得本体高度分布函数 Find the body height distribution function
不同区域处的折射率分布曲线n(x)需要满足以下两个条件：The refractive index distribution curve n(x) at different regions needs to meet the following two conditions:
1)当时，由于该区域为本体的水平段平板部分，即该区域中水深为常量，则 此时该区域内任意点处的折射率也为常量，假设为N1，则此时该区域的折射率表示成： n(x)＝N1；1) when When , since this area is the flat plate part of the horizontal section of the body, that is, the water depth in this area is constant, then the refractive index at any point in this area is also constant at this time, assuming it is N 1 , then the refractive index of this area at this time Expressed as: n(x)=N 1 ;
2)当时，由于该区域为本体的斜坡段曲面板部分，该区域中水深与折射率沿 x方向变化，则此时该区域的折射率表示成：n2(x)＝f(x)；2) when When , since this area is the curved plate part of the slope section of the body, the water depth and refractive index in this area change along the x direction, then the refractive index of this area at this time is expressed as: n 2 (x)=f(x);
当斜坡段区域水深最小时，折射率而当水深最大时，折射率为代入 计算后可得f(x)表达式；When the water depth in the slope section area is the smallest, the refractive index And when the water depth is maximum, the refractive index After substituting into the calculation, the f(x) expression can be obtained;
当f(x)＝kx+b时，求得 When f(x)=kx+b, get
当f(x)＝ax2+bx时，求得 When f(x)＝ax 2 +bx, get
当时，求得 when when, get
本发明的第二目的是提供一种应用于水波的波导隐身装置的设计方法，包括如下步骤：The second object of the present invention is to provide a design method of a waveguide cloaking device applied to water waves, comprising the following steps:
(1)取一由斜坡段曲面板和水平段平板组成类等腰梯形结构作为本体，总长度记为L；(1) Take a quasi-isosceles trapezoidal structure composed of a slope section curved panel and a horizontal section flat panel as the body, and record the total length as L;
(2)将本体在波导中沿水波传播方向并排布置，记斜坡段曲面板在沿水波传播方向上的 投影长度为L1，水平段平板在沿水波传播方向上的长度为L2；(2) Arrange the bodies side by side in the waveguide along the direction of water wave propagation, record the projected length of the curved plate in the slope section along the direction of water wave propagation as L1, and the length of the flat plate in the horizontal section along the direction of water wave propagation as L2 ;
(3)当本体浸没于水中时，本体下底面处的水深为h，本体沿x轴方向的高度分布记为 d(x)，则本体上底面处的水深分布便为h(x)＝h-d(x)；(3) When the body is submerged in water, the water depth at the lower bottom of the body is h, and the height distribution of the body along the x-axis direction is recorded as d(x), then the water depth distribution at the upper bottom of the body is h(x)=h-d (x);
(4)在确定不同水深处的折射率分布n(x)后，可根据折射率计算公式：(4) After determining the refractive index distribution n(x) at different water depths, the refractive index can be calculated according to the formula:
求得本体高度分布函数 Find the body height distribution function
(5)不同区域处的折射率分布曲线n(x)需要满足以下两个条件：(5) The refractive index distribution curve n(x) at different regions needs to meet the following two conditions:
1)当时，由于该区域为本体的水平段平板部分，即该区域中水深为常量，则 此时该区域内任意点处的折射率也为常量，假设为N1，则此时该区域的折射率可以表示成： n(x)＝N1 1) when When , since this area is the flat plate part of the horizontal section of the body, that is, the water depth in this area is constant, then the refractive index at any point in this area is also constant at this time, assuming it is N 1 , then the refractive index of this area at this time Can be expressed as: n(x)=N 1
2)当时，由于该区域为本体的斜坡段曲面板部分，该区域中水深与折射率沿 x方向变化，则此时该区域的折射率可以表示成：n2(x)＝f(x)2) when When , since this region is the curved plate part of the slope section of the body, the water depth and refractive index in this region change along the x direction, then the refractive index of this region can be expressed as: n 2 (x)=f(x)
当f(x)＝kx+b；其中，k、b为系数，当斜坡段区域水深最小时，折射率n(x1)＝N1；而当 水深最大时，折射率为n(x2)＝1，代入计算后可得： When f(x)=k x +b; among them, k and b are coefficients, when the water depth of the slope section area is the smallest, the refractive index n(x 1 )=N 1 ; and when the water depth is the largest, the refractive index is n(x 2 )=1, after substituting into the calculation, we can get:
当(x)＝ax2+bx时，其中，a、b为系数，当斜坡段区域水深最小时，折射率n(x1)＝N1；而 当水深最大时，折射率为n(x2)＝1，代入计算后可得：当时，其中，k、b为系数，当斜坡段区域水深最小时，折射率n(x1)＝N1；而 当水深最大时，折射率为n(x2)＝1，代入计算后可得 When (x)=ax 2 +bx, where a and b are coefficients, when the water depth in the slope section area is the smallest, the refractive index n(x 1 )=N 1 ; and when the water depth is the largest, the refractive index is n(x 2 )=1, after substituting into the calculation, we can get: when , where k and b are coefficients, when the water depth of the slope section area is the smallest, the refractive index n(x 1 )=N1; and when the water depth is the largest, the refractive index is n(x2)=1, which can be obtained after substituting into the calculation
本发明的第三目的是提供一种应用于水波的波导隐身装置，包括本体，所述本体为多个连 续并排布置的一端为高度渐变的斜坡段的类直角梯形结构。The third object of the present invention is to provide a waveguide cloaking device applied to water waves, which includes a body, and the body is a plurality of right-angled trapezoidal structures arranged continuously side by side with a gradient section at one end.
进一步的，所述类直角梯形结构主要由水平段平板和连接在水平段平板一端的一段斜坡段 曲面板构成，本体在波导中沿水波传播方向布置，类直角梯形结构的总长度为L，斜坡段曲 面板的长度为L1，水平段平板的长度为L2；Further, the quasi-right-angled trapezoidal structure is mainly composed of a flat plate in the horizontal section and a curved section of a slope section connected to one end of the flat plate in the horizontal section. The body is arranged in the waveguide along the direction of water wave propagation. The length of the segmental curved plate is L 1 , and the length of the horizontal segmental plate is L 2 ;
当本体浸没于水中时，本体下底面处的水深为h，将水波传播方向作为x轴，x轴原点位 于本体的中心点上，本体沿x轴方向的高度分布记为d(x)，则本体上表面处的水深分布便为When the body is submerged in water, the water depth at the bottom of the body is h, the propagation direction of the water wave is taken as the x-axis, the origin of the x-axis is located at the center of the body, and the height distribution of the body along the x-axis direction is recorded as d(x), then The water depth distribution at the upper surface of the body is
h(x)＝h-d(x)；h(x)=h-d(x);
在确定不同水深处的折射率分布n(x)后，根据折射率计算公式：After determining the refractive index distribution n(x) at different water depths, according to the refractive index calculation formula:
求得本体高度分布函数 Find the body height distribution function
不同区域处的折射率分布曲线n(x)需要满足以下两个条件：The refractive index distribution curve n(x) at different regions needs to meet the following two conditions:
1)当0＜x＜L1时，由于该区域为本体的斜坡段曲面板部分，该区域中水深与折射率沿 x方向变化，则此时该区域的折射率表示成：n2(x)＝f(x)；1) When 0<x<L 1 , since this area is the curved plate part of the slope section of the body, the water depth and refractive index in this area change along the x direction, then the refractive index of this area at this time is expressed as: n 2 (x ) = f(x);
2)当L1＜x＜L时，由于该区域为本体的水平段平板部分，即该区域中水深为常量，则 此时该区域内任意点处的折射率也为常量，假设为N1，则此时该区域的折射率表示成：n2(x)＝N1；2) When L 1 <x<L, since this area is the flat part of the horizontal section of the body, that is, the water depth in this area is constant, then the refractive index at any point in this area is also constant at this time, assuming N 1 , then the refractive index of this region is expressed as: n 2 (x)=N 1 ;
当斜坡段区域水深最小时，折射率n(L)＝N1；而当水深最大时，折射率为n(0)＝1；代入 计算后可得f(x)表达式；When the water depth in the slope area is the smallest, the refractive index n(L)=N 1 ; and when the water depth is the largest, the refractive index is n(0)=1; after substituting it into the calculation, the expression f(x) can be obtained;
当f(x)＝kx+b时，求得 When f(x)=kx+b, get
当时，求得 when when, get
本发明的第四目的是提供一种应用于水波的波导隐身装置的设计方法，包括如下步骤：The fourth object of the present invention is to provide a design method of a waveguide cloaking device applied to water waves, comprising the following steps:
(1)取一由斜坡段曲面板和水平段平板组成类直角梯形结构作为本体，总长度记为L；(1) Take a right-angled trapezoidal structure composed of a slope section curved panel and a horizontal section flat plate as the body, and record the total length as L;
(2)将本体在波导中沿水波传播方向布置，记斜坡段曲面板在沿水波传播方向上的投影 长度为L1，水平段平板在沿水波传播方向上的长度为L2；(2) Arrange the main body in the waveguide along the direction of water wave propagation, record the projected length of the curved plate on the slope section along the direction of water wave propagation as L1, and the length of the flat plate on the horizontal section along the direction of water wave propagation as L2 ;
(3)当本体浸没于水中时，本体下底面处的水深为h，本体沿x轴方向的高度分布记为 d(x)，则本体上底面处的水深分布便为h(x)＝h-d(x)；(3) When the body is submerged in water, the water depth at the lower bottom of the body is h, and the height distribution of the body along the x-axis direction is recorded as d(x), then the water depth distribution at the upper bottom of the body is h(x)=h-d (x);
(4)在确定不同水深处的折射率分布n(x)后，可根据折射率计算公式求得本体高度分布函数 (4) After determining the refractive index distribution n(x) at different water depths, the refractive index can be calculated according to the formula Find the body height distribution function
(5)不同区域处的折射率分布曲线n(x)需要满足以下两个条件：(5) The refractive index distribution curve n(x) at different regions needs to meet the following two conditions:
1)当0＜x＜L1时，由于该区域为本体的斜坡段曲面板部分，即该区域中水深为变量， 该区域中水深与折射率沿x方向变化，则此时该区域的折射率可以表示成：n2(x)＝f(x)；1) When 0<x<L 1 , since this area is the slope section of the main body, that is, the water depth in this area is a variable, and the water depth and refractive index in this area change along the x direction, then the refraction of this area at this time The rate can be expressed as: n 2 (x)=f(x);
2)当L1＜x＜L时，由于该区域为本体的水平段平板部分，即该区域中水深为常量，则 此时该区域内任意点处的折射率也为常量，假设为N1，则此时该区域的折射率可以表示成： n(x)＝N1；2) When L 1 <x<L, since this area is the flat part of the horizontal section of the body, that is, the water depth in this area is constant, then the refractive index at any point in this area is also constant at this time, assuming N 1 , then the refractive index of this region can be expressed as: n(x)=N 1 ;
当f(x)＝kx+b；其中，k、b为系数，当斜坡段区域水深最小时，折射率n(x1)＝N1；而当水 深最大时，折射率为n(x2)＝1，代入计算后可得 When f(x)=kx+b; among them, k and b are coefficients, when the water depth of the slope section area is the smallest, the refractive index n(x 1 )=N 1 ; and when the water depth is the largest, the refractive index is n(x 2 )=1, after substituting into the calculation, we can get
当时，其中，k、b为系数，当斜坡段区域水深最小时，折射率n(x1)＝N1；而 当水深最大时，折射率为n(x2)＝1，代入计算后可得 when , where k and b are coefficients, when the water depth of the slope section area is the smallest, the refractive index n(x 1 )=N 1 ; and when the water depth is the largest, the refractive index is n(x2)=1, which can be obtained after substituting into the calculation
本发明的第五目的是提供一种应用于水波的波导隐身装置，包括本体，所述本体由多个圆 柱体或棱柱体阵列排布而成的桩柱结构。The fifth object of the present invention is to provide a waveguide cloaking device applied to water waves, which includes a body, and the body is a pile structure formed by a plurality of cylinders or prism arrays.
进一步的，所述本体主要由多个直径不同、阵列间距相同的圆柱体构成，记共排成p排， 每排q个，总长度为L，其中，本体的中间一段由多个直径相同且间距相同的圆柱体构成， 长度为L1。Further, the body is mainly composed of a plurality of cylinders with different diameters and the same array spacing, which are arranged in p rows, q in each row, and the total length is L, wherein the middle section of the body is composed of a plurality of cylinders with the same diameter and Consists of equally spaced cylinders with length L 1 .
本发明的第六目的是提供一种应用于水波的波导隐身装置的设计方法，包括如下步骤：The sixth object of the present invention is to provide a design method of a waveguide cloaking device applied to water waves, comprising the following steps:
(1)取多个直径不同、阵列间距相同的圆柱体组成本体，排成p排、每排q个，本体总长度L，其中，本体的中间一段由多个直径相同且间距相同的圆柱体构成，长度为L1；(1) Take a plurality of cylinders with different diameters and the same array spacing to form the body, arrange them in p rows, q in each row, and the total length of the body is L. Among them, the middle section of the body consists of multiple cylinders with the same diameter and the same spacing constitute, the length is L 1 ;
(2)本体在水槽中沿水波传播方向布置，水波传播方向作为x轴，水深方向作为y轴， 当本体浸没于水中时，本体下底面处的水深为h，本体高度为d，本体沿x轴方向的折射率分 布记为n(x)，n(x)满足以下两个条件：(2) The body is arranged in the water tank along the direction of water wave propagation. The direction of water wave propagation is taken as the x-axis, and the direction of water depth is taken as the y-axis. When the body is immersed in water, the water depth at the bottom of the body is h, the height of the body is d, and the body is along x The refractive index distribution in the axial direction is recorded as n(x), and n(x) satisfies the following two conditions:
1)当时，由于该区域由直径相同的圆柱体构成，则此时该区域内任意点处的 折射率为常量，假设为N1，则此时该区域的折射率可以表示成：n(x)＝N1 1) when , since the region is composed of cylinders with the same diameter, the refractive index at any point in the region is constant at this time, assuming N 1 , then the refractive index of the region can be expressed as: n(x)= N 1
2)当时，由于该区域由直径不同、间距相同的圆柱体构成，则此时该区域的 折射率可以表示成：2) when , since this region is composed of cylinders with different diameters and the same spacing, the refractive index of this region can be expressed as:
n2(x)＝f(x)＝kx2+bn 2 (x)=f(x)=kx 2 +b
其中，k、b为系数，此处定义有效折射率为其中Q为布洛赫波矢，K为波数；Among them, k and b are coefficients, and the effective refractive index is defined here Where Q is the Bloch wave vector, K is the wave number;
当x＝0时，折射率当时，折射率为代入计算后可得：When x=0, the refractive index when , the refractive index After substituting into the calculation, we can get:
由此可以算出满足折射率变化的圆柱体的直径。From this, the diameter of the cylinder that satisfies the change in the refractive index can be calculated.
相对于现有技术，本发明的有益效果如下：(1)经过设计后，类梯形等腰结构、类直角 梯形缓坡结构或阵列桩柱结构在具有特定的波长和频率的平面波入射时，能够实现几乎无反 射波；(2)本体的周边仍保持平面波，本体上部的平面波波幅有所放大，本体中间区域的波 幅显著降低，在本体中间区域消波明显；(3)提出了实现这种功能的设计方法，而且该方法 具有一定的可拓展性和灵活性，可以设计出多种满足要求的结构参数、水深参数和折射率参 数。Compared with the prior art, the beneficial effects of the present invention are as follows: (1) After the design, the quasi-trapezoidal isosceles structure, the quasi-right-angled trapezoidal gentle slope structure or the array pile structure can realize There is almost no reflected wave; (2) the periphery of the body still maintains a plane wave, the amplitude of the plane wave on the upper part of the body is enlarged, the amplitude of the wave in the middle area of the body is significantly reduced, and the wave elimination is obvious in the middle area of the body; (3) a method for realizing this function is proposed Design method, and this method has a certain degree of scalability and flexibility, and can design a variety of structural parameters, water depth parameters and refractive index parameters that meet the requirements.
附图说明Description of drawings
图1为本发明的类梯形缓坡结构波浪调控装置的俯视图；Fig. 1 is the top view of the trapezoidal gentle slope structure wave control device of the present invention;
图2为本发明的类梯形缓坡结构波浪调控装置的半剖图；Fig. 2 is a half-sectional view of the trapezoidal gentle slope structure wave regulating device of the present invention;
图3为本发明的圆柱阵列结构波浪调控装置的俯视图；Fig. 3 is the top view of the cylindrical array structure wave control device of the present invention;
图4为本发明的圆柱阵列结构波浪调控装置的半剖图；Fig. 4 is a half-sectional view of the cylindrical array structure wave regulating device of the present invention;
图5为本发明的类直角梯形缓坡结构波浪调控装置的俯视图；Fig. 5 is a top view of the wave control device with a right-angled trapezoidal gentle slope structure of the present invention;
图6为本发明的类直角梯形缓坡结构波浪调控装置的半剖图。Fig. 6 is a half-sectional view of the wave control device with a similar right-angled trapezoidal gentle slope structure of the present invention.
图中，1为斜坡段曲面板，2为水平段平板。In the figure, 1 is the curved panel of the slope section, and 2 is the flat panel of the horizontal section.
具体实施方式Detailed ways
下面结合实施例和附图对本发明做进一步的详细说明。本实施例以本发明技术方案为前提 进行实施，给出了详细的实施方式和具体的操作过程，但本发明的保护范围不限于下述的实 施例。The present invention will be further described in detail below in conjunction with the embodiments and the accompanying drawings. The present embodiment implements on the premise of the technical solution of the present invention, and provides detailed implementation and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.
实施例1：Example 1:
(1)取一由斜坡段曲面板1和水平段平板2组成类等腰梯形缓坡结构作为本体，在类梯 形缓坡结构两端设置长度为1.78m，宽度为0.15m的斜坡段，斜坡段的侧面为高度渐变曲面； 中间水平段区域设置长度为2.44m，高度为0.133m，宽度为0.15m的水平段，本体总长度为 6m，将本体在波导中沿水波传播方向并排布置；俯视图如图1所示，剖视图如图2所示；(1) Take an isosceles trapezoidal gentle slope structure composed of a slope section curved panel 1 and a horizontal section flat plate 2 as the body, and set a slope section with a length of 1.78m and a width of 0.15m at both ends of the similar trapezoidal gentle slope structure. The side is a height-gradient curved surface; the middle horizontal section area is set to a horizontal section with a length of 2.44m, a height of 0.133m, and a width of 0.15m. The total length of the body is 6m. The body is arranged side by side in the waveguide along the direction of water wave propagation; the top view is shown in the figure 1, the cross-sectional view is shown in Figure 2;
(2)将类梯形缓坡结构的本体浸没于水中时，本体下底面处的水深为h，h＝0.15m；本体 沿x轴方向的高度分布记为d(x)，则本体上底面处的水深分布便为h(x)＝h-d(x)；(2) When the body of the similar trapezoidal gentle slope structure is immersed in water, the water depth at the bottom of the body is h, h=0.15m; the height distribution of the body along the x-axis direction is recorded as d(x), then the water depth at the bottom of the body The water depth distribution is then h(x)=h-d(x);
(3)在确定不同水深处的折射率分布n(x)后，可根据折射率计算公式(3) After determining the refractive index distribution n(x) at different water depths, the refractive index can be calculated according to the formula
求得本体高度分布函数其中h＝0.15。Find the body height distribution function where h=0.15.
(4)不同区域处的折射率分布曲线n(x)需要满足以下两个条件：(4) The refractive index distribution curve n(x) at different regions needs to meet the following two conditions:
第一条件：当-1.22m＜x＜1.22m时，由于该区域为本体的水平段平板部分，即该区域中 水深为常量，则此时该区域内任意点处的折射率也为常量N1＝2.97，则此时该区域的折射率可 以表示成：The first condition: when -1.22m<x<1.22m, since this area is the flat part of the horizontal section of the body, that is, the water depth in this area is constant, then the refractive index at any point in this area is also a constant N 1 = 2.97, then the refractive index of this area can be expressed as:
n(x)＝2.97，-1.22m＜x＜1.22mn(x)=2.97, -1.22m<x<1.22m
第二条件：当-3m＜x＜-1.22m或1.22m＜x＜3m时，由于该区域为本体的斜坡段曲面板部 分，该区域中水深与折射率沿x方向变化，则此时该区域的折射率可以表示成：The second condition: when -3m<x<-1.22m or 1.22m<x<3m, since this area is the curved plate part of the slope section of the body, the water depth and refractive index in this area change along the x direction, then the The refractive index of the region can be expressed as:
n2(x)＝kx+b，-3m＜x＜-1.22m或1.22m＜x＜3m；n 2 (x)=kx+b, -3m<x<-1.22m or 1.22m<x<3m;
其中，k、b为系数，当斜坡段区域水深最小时，折射率n(x1)＝2.97；而当水深最大时，折射 率为n(x2)＝1；代入计算后可得n2(x)＝-4.4x+14.2；Among them, k and b are coefficients. When the water depth in the slope section is the smallest, the refractive index n(x 1 )=2.97; and when the water depth is the largest, the refractive index is n(x 2 )=1; after substituting it into the calculation, we can get n 2 (x)=-4.4x+14.2;
由此可以得到缓坡段高度曲线函数： From this, the height curve function of the gentle slope section can be obtained:
实施例2：Example 2:
(1)取多个直径不同、阵列间距为0.5m的圆柱体组成隐身装置本体，排成13排，每排3 个，本体总长度L为6m，其中，本体的中间一段由多个直径相同且间距相同的圆柱体构成， 长度为L1为2m，，如图3和图4所示；(1) Take a plurality of cylinders with different diameters and an array spacing of 0.5m to form the main body of the cloaking device, arrange them in 13 rows, with 3 cylinders in each row, and the total length L of the main body is 6m. And the cylinders with the same spacing are formed, and the length L is 2m, as shown in Figure 3 and Figure 4;
(2)本体在水槽中沿水波传播方向布置，令水波传播方向作为x轴，水深方向作为y轴， 当本体浸没于水中时，本体下底面处的水深为0.5m，本体高度为0.7m，本体沿x轴方向等间 距分布，本体沿x轴方向的折射率分布记为n(x)，n(x)在x方向上满足公式：(2) The body is arranged in the water tank along the direction of water wave propagation. Let the direction of water wave propagation be the x-axis and the water depth direction as the y-axis. When the body is immersed in water, the water depth at the bottom of the body is 0.5m, and the height of the body is 0.7m. The body is equally spaced along the x-axis direction, and the refractive index distribution of the body along the x-axis direction is recorded as n(x), and n(x) satisfies the formula in the x direction:
1)当-1＜x＜1时，由于该区域由直径相同的圆柱体构成，则此时该区域内任意点处的 折射率为常量，假设为N1，则此时该区域的折射率可以表示成：n2(x)＝N1＝1.51) When -1<x<1, since the region is composed of cylinders with the same diameter, the refractive index at any point in the region is constant at this time, assuming N 1 , then the refractive index of the region at this time It can be expressed as: n2(x)=N 1 =1.5
2)当1＜|x|＜3时，由于该区域由直径不同、间距相同的圆柱体构成，则此时该区域的 折射率可以表示成：2) When 1<|x|<3, since this region is composed of cylinders with different diameters and the same spacing, the refractive index of this region can be expressed as:
n2(x)＝f(x)＝kx2+bn 2 (x)=f(x)=kx2+b
其中，k、b为系数，此处定义有效折射率为其中Q为布洛赫波矢，K为波数。当x＝0时，折射率ne0＝1.5；而当x＝±3时，折射率为ne1＝1；Among them, k and b are coefficients, and the effective refractive index is defined here Where Q is the Bloch wave vector and K is the wave number. When x=0, the refractive index n e0 =1.5; and when x=±3, the refractive index n e1 =1;
代入计算后可得After substituting into the calculation, it can be obtained
n2(x)＝-0.139x2+1.5；n 2 (x)=-0.139x 2 +1.5;
由此可以算出满足折射率变化的不同桩柱的直径。From this, the diameters of different piles satisfying the variation of the refractive index can be calculated.
需要说明的是，当本体由多个棱柱体阵列排布而成的桩柱结构，棱柱体可以为三棱柱、 四棱柱或多边形棱柱，由多个棱柱体阵列排布而成的桩柱结构的设计方法和圆柱体的类似， 区别在于布洛赫波矢Q的计算结果不同，本领域技术人员知晓如何计算，这里不再赘述。It should be noted that when the body is a pile structure formed by a plurality of prism arrays, the prism can be a triangular prism, a quadrangular prism or a polygonal prism, and the pile structure formed by a plurality of prism arrays The design method is similar to that of a cylinder, except that the calculation result of the Bloch wave vector Q is different. Those skilled in the art know how to calculate it, and will not repeat it here.
实施例3：Example 3:
(1)取五个由斜坡段曲面板和水平段平板组成类直角梯形结构连续并排布置作为本体； 在类直角梯形缓坡结构一端设置长度为1.78m，宽度为0.15m的斜坡段，斜坡段的侧面为高 度渐变曲面；中间水平段区域设置长度为4.22m，高度为0.133m，宽度为0.15m的水平段， 本体总长度为6m，将本体在波导中沿水波传播方向并排布置；俯视图如图5所示，剖视图如 图6所示；(1) Take five quasi-right-angled trapezoidal structures composed of slope section curved panels and horizontal section flat panels and arrange them side by side continuously as the main body; set a slope section with a length of 1.78m and a width of 0.15m at one end of the quasi-right-angle trapezoidal gentle slope structure. The side is a height-gradient curved surface; the middle horizontal section area is set to a horizontal section with a length of 4.22m, a height of 0.133m, and a width of 0.15m. The total length of the body is 6m. The body is arranged side by side in the waveguide along the direction of water wave propagation; the top view is shown in the figure 5, the cross-sectional view is shown in Figure 6;
(2)将类直角梯形结构的本体浸没于水中时，本体下底面处的水深为h，h＝0.15m；本体 沿x轴方向的高度分布记为d(x)，则本体上底面处的水深分布便为h(x)＝h-d(x)；(2) When the body of the quasi-right-angled trapezoidal structure is immersed in water, the water depth at the bottom of the body is h, where h=0.15m; the height distribution of the body along the x-axis direction is denoted as d(x), and the The water depth distribution is then h(x)=h-d(x);
(3)在确定不同水深处的折射率分布n(x)后，可根据折射率计算公式(3) After determining the refractive index distribution n(x) at different water depths, the refractive index can be calculated according to the formula
求得本体高度分布函数其中h＝0.15m。Find the body height distribution function where h=0.15m.
(4)不同区域处的折射率分布曲线n(x)需要满足以下两个条件：(4) The refractive index distribution curve n(x) at different regions needs to meet the following two conditions:
第一条件：当0m＜x＜1.78m时，由于该区域为本体的斜坡段曲面板部分，该区域中水深 与折射率沿x方向变化，则此时该区域的折射率可以表示成：The first condition: when 0m<x<1.78m, since this area is the curved plate part of the slope section of the body, the water depth and refractive index in this area change along the x direction, then the refractive index of this area at this time can be expressed as:
n2(x)＝kx+b，0m＜c＜1.78m，其中，k、b为系数；n 2 (x)=kx+b, 0m<c<1.78m, where k and b are coefficients;
第二条件：当1.78m＜x＜6m时，由于该区域为本体的水平段平板部分，即该区域中水深 为常量，则此时该区域内任意点处的折射率也为常量N1＝2.97，则此时该区域的折射率可以表 示成：The second condition: when 1.78m<x<6m, since this area is the flat part of the horizontal section of the body, that is, the water depth in this area is constant, then the refractive index at any point in this area is also constant N 1 = 2.97, then the refractive index of this region can be expressed as:
n(x)＝2.97，1.78m＜x＜6mn(x)=2.97, 1.78m<x<6m
当斜坡段区域水深最小时，折射率n(x1)＝2.97；而当水深最大时，折射率为n（x2)＝1；代入计 算后可得n2(x)＝4.4x+1；When the water depth in the slope area is the smallest, the refractive index n(x 1 )=2.97; and when the water depth is the largest, the refractive index is n(x 2 )=1; after substituting into the calculation, n 2 (x)=4.4x+1 ;
由此可以得到缓坡段高度曲线函数： From this, the height curve function of the gentle slope section can be obtained:
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