CN110287580B - Elastic wave converging device and application thereof - Google Patents

Abstract

The invention provides an elastic wave converging device and application thereof. The converging device has a hollow cylindrical shape; and, the convergence device is made of non-uniform transverse isotropic material, any cross section of the axial direction of the convergence device is composed of a plurality of microelements, each of the plurality of microelements is equivalent to uniform material, and the material parameters of each of the microelements meet the following requirements: (1) the equivalent densities of all the infinitesimals are equal: (2) the in-plane equivalent Poisson ratios of all the microelements are equal to each other and approach to 1; (3) the in-plane equivalent shear modulus of each micro element is in direct proportion to the square of the distance from the center point of the micro element to the circle center of the cross section; therefore, the elastic wave transmitted from the outer annular surface of the convergence device at any angle is transmitted along the inside of the convergence device and converged on the inner annular surface of the convergence device, so as to realize the absorption of the elastic wave. The convergence device can be applied to vibration reduction of buildings, isolation of subway vibration signals and buffer vibration reduction of vehicles.

Description

An elastic wave convergence device and use thereof

technical field

The present invention relates to the technical field of vibration reduction and energy absorption, in particular to an elastic wave convergence device and use thereof.

Background technique

The appearance of transportation has facilitated people's lives, but the accompanying vibration and noise problems have brought negative effects, such as the vibration when the subway passes by, the vibration of heavy trucks on the highway at night, and so on. Likewise, these vibrations can cause damage to equipment (especially precision instruments), and earthquakes can cause catastrophic damage to buildings and even critical reserves. Vibration caused by road unevenness to the vehicle can damage the items carried in the vehicle. When the aircraft lands, the impact of the landing gear on the ground, if there is no effective cushioning and vibration reduction, will also spread to the entire body, affecting the life of the body.

All of these vibration or shock problems are related to elastic waves. In the current elastic wave vibration damping technology, spring damping damper is one of the most common vibration damping methods. However, in the vibration-damping environment of low-frequency elastic waves, due to the large wavelength of low-frequency elastic waves, the elastic waves may be diffracted and the damping is very low, so that this type of shock absorber cannot exert its due vibration-damping effect. Especially in the field of subway vibration reduction, the main use of shield tunnels with steel spring floating plates and other vibration reduction measures. These vibration reduction measures have obvious effects on the attenuation of medium and high frequency vibration caused by the subway, but the attenuation effect on low frequency vibration is extremely limited.

The wave-wound method is a method of changing the path of elastic wave propagation by designing the distribution of material properties in space, so that it bypasses the components that need vibration isolation to achieve vibration reduction. By controlling the propagation path of the elastic wave, not only can the elastic wave bypass the object to be protected without causing serious disturbance, but also the elastic wave can be converged to collect and utilize the energy carried by it, that is, similar to In order to form an elastic wave black hole, the elastic wave black hole can capture various forms of propagating elastic waves within a certain range and converge the elastic waves to the center. However, how to control the propagation of elastic waves is a difficult inverse problem, because the composition of elastic waves is complex, including longitudinal waves, shear waves, and possibly various forms of coupled waves. The elasticity tensor is a fourth-order tensor (81 components), which makes it very difficult to infer the material parameters from the desired field variables.

SUMMARY OF THE INVENTION

In view of the above-mentioned problems, the present invention is proposed to provide an elastic wave converging device and uses thereof that overcome the above-mentioned problems or at least partially solve the above-mentioned problems.

According to an aspect of the embodiments of the present invention, an elastic wave convergence device is provided, the elastic wave convergence device has a hollow cylinder shape; and the elastic wave convergence device is made of a non-uniform transversely isotropic material, Any cross-section in the axial direction is composed of multiple micro-elements, and each micro-element in the multiple micro-elements is equivalent to a uniform material, then the material parameters of each micro-element satisfy the following conditions: (1) All The equivalent densities of the micro-elements are all equal: (2) the in-plane equivalent Poisson's ratios of all micro-elements are equal, and the in-plane equivalent Poisson's ratio approaches 1; (3) the in-plane equivalent Poisson's ratio of each micro-element is The equivalent shear mod The elastic waves introduced from the outer annular surface of the elastic wave converging device at any angle will be transmitted along the interior of the elastic wave converging device and converge to the inner annular surface of the elastic wave converging device, so as to realize the detection of the elastic wave. Absorption of elastic waves.

Optionally, the in-plane equivalent Poisson's ratio of each microelement is in the range of 0.9-1.

Optionally, an energy collecting device is provided at the central cavity of the elastic wave converging device for storing the energy of the elastic waves converging on the inner annular surface of the elastic wave converging device;

or,

An energy dissipating material is arranged at the central cavity of the elastic wave converging device, which is used to dissipate the energy of the elastic waves converging on the inner annular surface of the elastic wave converging device;

or,

The surface between the outer ring and the inner ring of the elastic wave convergence device forms a curved arc, so that the elastic waves introduced from the outer ring surface of the elastic wave convergence device converge to the elastic wave convergence device. The inner annular surface of the ring changes its own propagation direction at the same time, so as to guide the elastic wave to the bending direction.

Optionally, the micro-elements are hexagonal honeycomb units.

Optionally, the wall thickness and side length of the hexagonal honeycomb unit are determined by the following formulas:

Among them, ρ*, ν* and μ* are the equivalent density, in-plane equivalent Poisson’s ratio and in-plane equivalent shear modulus of the hexagonal honeycomb unit, respectively; ρ _s , ν _s and E _s are respectively are the density, Poisson's ratio and Young's modulus of the material constituting the hexagonal honeycomb unit; h and l are the outer lengths of the adjacent two sides of the hexagonal honeycomb unit respectively; h _b and _lb are respectively The inner side lengths of the hexagonal honeycomb unit corresponding to the outer side lengths h and l; t is the sum of the wall thicknesses of the two adjacent hexagonal honeycomb units; θ is the length of the hexagonal honeycomb unit. The angle between one of the two adjacent sides and the normal of the other.

Optionally, by disposing mass blocks on the inner walls of opposite sides of the hexagonal honeycomb unit, the quality change of the hexagonal honeycomb unit caused by different wall thicknesses can be compensated.

Optionally, the outer ring surface of the elastic wave converging device is further wrapped with a material for guiding waves, so that the outer contour of the elastic wave converging device is formed into a specified geometric shape.

According to another aspect of the embodiments of the present invention, a use of the above elastic wave converging device in building vibration reduction is also provided, including:

The elastic wave converging device is arranged around the building to absorb elastic waves.

According to yet another aspect of the embodiments of the present invention, a use of the above elastic wave convergence device in the isolation of subway vibration signals is also provided, including:

The elastic wave converging devices are arranged on both sides of the subway track to absorb the elastic waves generated by the operation of the subway.

According to yet another aspect of the embodiments of the present invention, a use of the above elastic wave convergence device as a buffer of a vehicle is also provided.

The elastic wave converging device proposed in the embodiment of the present invention, by designing the structure into a hollow cylinder shape and designing the material parameters, makes the elastic wave converging device made of non-uniform transversely isotropic material in any axial direction. Each micro-element in a cross section satisfies the following three conditions: the equivalent density of all micro-elements is equal, the in-plane equivalent Poisson's ratio of all micro-elements is equal and close to 1, the surface of each micro-element is equal The internal equivalent shear modulus is proportional to the square of the distance from the center point of the microelement to the center of the cross section. Such a design enables the elastic waves introduced from the outer annular surface of the elastic wave converging device at any angle to transmit along the interior of the elastic wave converging device and converge to the inner annular surface of the elastic wave converging device during use. That is, the elastic wave converging device forms an effect similar to an elastic wave black hole, captures the elastic waves propagating within the range of the outer annular surface thereof and converges the elastic waves to the center. The elastic wave converging device provided by the present invention has a significant absorption effect on elastic waves propagating in various forms, especially low-frequency elastic waves, and can be applied to applications such as building vibration reduction, subway vibration signal isolation, vehicle buffer vibration reduction, etc. .

The above description is only an overview of the technical solutions of the present invention, in order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the description, and in order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand , the following specific embodiments of the present invention are given.

The above and other objects, advantages and features of the present invention will be more apparent to those skilled in the art from the following detailed description of the specific embodiments of the present invention in conjunction with the accompanying drawings.

Description of drawings

Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are for the purpose of illustrating preferred embodiments only and are not to be considered limiting of the invention. Also, the same components are denoted by the same reference numerals throughout the drawings. In the attached image:

1 shows a schematic diagram of transforming a virtual space into a physical space by a transformation method in the prior art;

Figure 2 shows a schematic diagram of mapping a uniform virtual space into a black hole-like physical space by a transformation method;

FIG. 3 shows a schematic perspective view of an elastic wave converging device according to an embodiment of the present invention;

Fig. 4 shows a schematic diagram of any axial cross-section of the elastic wave converging device shown in Fig. 3;

5 shows a schematic diagram of an axial cross-section of an elastic wave converging device composed of a hexagonal honeycomb material according to an embodiment of the present invention;

Fig. 6 is a partial enlarged schematic view of the axial cross section of the elastic wave converging device composed of hexagonal honeycomb material shown in Fig. 5;

FIG. 7 shows a schematic diagram of converging elastic waves on the inner annular surface of the elastic wave converging device and directing them to a direction perpendicular to the plane where the incident direction of the elastic waves is located;

Figures 8a and 8b show the propagation effects of elastic waves incident from the left side of the control specimen and the test specimen in the control experiment, respectively;

Fig. 9 shows the acceleration decay diagram of the test specimen and the control specimen in the range of 10-1000 Hz in the control experiment;

FIG. 10 shows a schematic diagram of a simulation effect of an elastic wave converging device in vibration reduction of a building according to an embodiment of the present invention;

FIG. 11 shows a schematic diagram of the simulation effect of the elastic wave convergence device in the subway vibration reduction according to an embodiment of the present invention;

FIG. 12 shows a schematic diagram of an application scenario of the elastic wave convergence device as an aircraft landing gear buffer according to an embodiment of the present invention; and

FIG. 13 is a schematic diagram showing a simulation effect of an elastic wave converging device used as an aircraft landing gear buffer according to an embodiment of the present invention.

Detailed ways

Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure will be more thoroughly understood, and will fully convey the scope of the present disclosure to those skilled in the art.

The wave-wound method can change the path of elastic wave propagation by controlling the properties or structure of the material, so that it can bypass the components that need to be isolated to achieve vibration reduction. However, due to the complexity of elastic waves, controlling the propagation of elastic waves is a difficult inverse problem.

The transformation method that appeared in recent years provides a new solution to this design problem. The transformation method first appeared in the field of electromagnetic waves, and then the field of sound waves followed. This method first assumes an easy-to-understand virtual space in which materials are generally uniformly distributed and the boundary conditions are relatively simple, so it is easy to understand how waves propagate in it. Then, transform the virtual space, and the transformation form is related to the specific purpose to be realized. FIG. 1 shows a schematic diagram of transforming a virtual space into a physical space by a transformation method in the prior art, wherein (a) represents a uniform virtual space, and (b) represents a converted physical space. As shown in Figure 1, if you want the wave from the left to not pass through the object in the center, you can map the uniform virtual space into a physical space with a hole in the center. In this process, field variables (electric and magnetic fields for electromagnetic waves and displacement fields for elastic waves) need to be mapped with the grid. Specifically, the transformation method is to keep the measurable field variables u' and u's covariant components in the Lagrange embedded curve coordinate system unchanged before and after transformation, that is, u _i '=u _i , and the physical meaning is The vector u is warped along with the coordinate grid. The equation expressions before and after transformation are shown in formula (1):

Among them, G _i and g _i represent the curve coordinate base vectors before and after transformation, respectively. If the form of the governing equation describing the wave propagation remains unchanged after the mapping, the material parameters to be designed can be calculated through a one-to-one correspondence.

However, the governing equations of elastic waves do not satisfy this formal invariance. In order to solve the problem of how to design materials and control the propagation of elastic waves by transforming elastic waves, it is necessary to make the governing equations of elastic waves approximately satisfy invariance through processing. After theoretical research and derivation, the inventor proposed the approximate invariance theory of the elastic wave equation, that is, without strictly pursuing the theoretical form invariance, by introducing two conditions: first, conformal transformation; second, using the longitudinal wave velocity C For isotropic materials where _p is much larger than the shear wave velocity C _s , C _p >>C _s (equivalent to the equivalent Lamé first constant λ of the material is much larger than the equivalent Lamé second constant G, expressed as λ >> G), The redundant terms of the transformed equation are made as small as possible, so that the elastic wave equation approximately satisfies the form invariance and can be used. For the specific derivation process, please refer to application CN201810373244.2.

A black hole refers to a kind of celestial body and star body with considerable mass that exists in the universe according to the general theory of relativity. It is formed by the gravitational collapse of a star with sufficient mass after the nuclear fusion reaction fuel is exhausted. The supermassive mass of a black hole creates a gravitational field so strong that no amount of measurable matter and radiation, not even photons, can escape. It is called a black hole because it is similar to a black body that does not reflect light at all thermodynamically. Around the black hole is an undetectable event horizon, marking the tipping point of no return, and at the center of the black hole is a singularity with a density approaching infinity. The properties and structure of materials are designed based on the transformation method, and an elastic wave convergence device similar to the action mechanism of a black hole can be constructed. The elastic wave convergence device can capture and propagate in various forms within a certain range (corresponding to the event horizon). , and finally converge the elastic wave to the center (corresponding to the singularity).

The following is a detailed description of how to design through the transformation method, so that any form of elastic wave transmitted from any direction can converge to the center of the vibration damping material. Figure 2 shows a schematic diagram of mapping a homogeneous virtual space into a black hole-like physical space by a transformation method. Based on the transformation method mentioned above, it is assumed that there is a rectangular domain filled with homogeneous material in the virtual space, as shown in (a) of Fig. 2. In this rectangular domain, all elastic waves 1, 2, 3 that pass through the left boundary AA' will propagate to the right boundary BB'. The rectangular domain of the virtual space is mapped to the annular domain of the physical space by conformal transformation (as shown in (b) in Figure 2), then the left boundary AA' of the virtual space is mapped to the outer circle of the torus, and The right boundary BB' is mapped to the inner circle of the ring. In this process, the displacement field is also mapped into the physical space, that is, all elastic waves entering from the left boundary AA' are mapped to the elastic waves entering from the outer ring of the ring and propagate to the right boundary BB' The elastic wave of is mapped to the elastic wave that converges to the inner ring. In this way, in the mapped physical space, the goal of converging elastic waves from any direction in any form to the center is achieved. Therefore, this annular physical space can be called an elastic wave black hole. As for the material parameters required to realize the elastic wave black hole, it can be directly calculated based on the transformation method through the one-to-one correspondence between virtual space and physical space.

The derivation and calculation process of material parameters for realizing elastic wave black hole design will be described below.

In the aforementioned application CN201810373244.2, a non-uniform equilibrium equation of the general form shown in the following equation (2) is used, that is, the Galio of the LN equation (Lamé-Navier Equation) The Galerkin weighted residual scheme and the constitutive equation of the isotropic material shown in the following formula (3) are derived, and the two conditions required for the elastic wave equation to approximately satisfy the invariance are obtained: 1. In the virtual Use conformal transformation mapping between space and physical space; 2. Use isotropic materials whose longitudinal wave velocity is much larger than shear wave velocity (that is, the equivalent Lamé first constant λ of the material is much larger than the equivalent Lamé second constant G) .

D _ijkl =λδ _ij δ _kl +G(δ _ik δ _jl +δ _il δ _jk ) (3)

In equations (2) and (3), ε is the strain, u is the displacement, μ is the damping coefficient, f is the body force, and T is the surface force. The subscripts i, j, k, and l take the values 1 and 2.

Since the strict form conformal transformation holds only in two dimensions, for planar problems, transversely isotropic materials can be used to achieve the same effect as isotropic materials. For the plane problem, the constitutive equations of isotropic materials and the constitutive equations of transversely isotropic materials can be expressed as the following equations (4):

in,

In the above equations (4) and (5), μ is the in-plane shear modulus, v is the in-plane Poisson’s ratio, ε is the strain, and σ is the stress.

与λ对应，而面内剪切模量μ则与G对应。因此，为了实现弹性波方程变换方法的前提条件，对于横观各向同性材料，要求

即κ→1。在平面应力条件下，由κ＝(3-ν)/(1+ν)可推导出ν→1，即，面内泊松比趋近于1。面内泊松比的值越接近1，则弹性波方程越满足变换的不变性。进一步地，为了实现上述虚拟空间的矩形域向物理空间的圆环域的变换，选取保角变换z′＝e^z，其中，z＝x+iy，对应虚拟空间坐标；z′＝x′+iy′，对应物理空间的坐标。基于这个保角变换，得到虚拟空间和物理空间的材料参数的转换关系如下所示：Considering the transversely isotropic material under the condition of plane stress, then κ=(3-ν)/(1+ν). It has been deduced above that in order to make the elastic wave equation approximately satisfy the invariance, for isotropic materials, the required condition is λ>>G. For transversely isotropic materials, Lamé's first constant λ and Lamé's second constant G do not exist, but the quantities corresponding to λ and G can be found in the isotropic plane. The study found,

corresponds to λ, while the in-plane shear modulus μ corresponds to G. Therefore, in order to realize the prerequisites of the elastic wave equation transformation method, for transversely isotropic materials, it is required to

That is, κ→1. Under plane stress conditions, ν→1 can be deduced from κ=(3-ν)/(1+ν), that is, the in-plane Poisson’s ratio approaches 1. The closer the value of the in-plane Poisson's ratio is to 1, the more the elastic wave equation satisfies the transformation invariance. Further, in order to realize the transformation from the rectangular domain of the virtual space to the annular domain of the physical space, the conformal transformation z′=e ^z is selected, wherein z=x+iy, corresponding to the virtual space coordinate; z′=x′+ iy', the coordinates corresponding to the physical space. Based on this conformal transformation, the transformation relationship between material parameters in virtual space and physical space is obtained as follows:

Among them, ρ', ν' and μ' are the density, Poisson's ratio and shear modulus of the material at each point in the virtual space, respectively, and ρ, ν and μ are the density, Poisson's ratio and Shear modulus, R is the distance from the center of the circle at each point in the physical space, and Δ is the unit length introduced to ensure the correct dimension. It can be seen from formula (6) that the Poisson's ratio and density of the material at each point after the transformation are required to remain unchanged, while the shear modulus in the plane is proportional to the square of the distance between each point and the center of the circle. According to the proportional relationship in formula (6), the material parameters in the annular physical space are designed, and the in-plane Poisson's ratio ν of the material is made close to 1, then a similar black hole action principle can be constructed to absorb elastic waves elastic wave convergence device.

Based on the above technical concept, the embodiment of the present invention proposes an elastic wave converging device, which can capture and absorb elastic waves propagating in various forms by the action principle similar to that of a black hole. FIG. 3 shows a schematic perspective view of an elastic wave converging device according to an embodiment of the present invention. As shown in FIG. 3 , the elastic wave converging device has the shape of a hollow cylinder. The radius of the inner ring and the outer ring of the cylinder can be designed according to the actual application scenario requirements and vibration reduction requirements, and the design of the axial length of the cylinder is not limited. Also, the elastic wave converging device is made of a non-uniform transversely isotropic material. Any cross section in the axial direction of the elastic wave converging device is composed of a plurality of microelements. If each micro-element in multiple micro-elements is equivalent to a uniform material, the material parameters of each micro-element in any cross-section satisfy the following conditions: (1) The equivalent density of all micro-elements is equal: (2) All micro-elements have the same density. The in-plane equivalent Poisson’s ratios of the micro-elements are all equal, and the in-plane equivalent Poisson’s ratio approaches 1; (3) The in-plane equivalent shear modulus of each micro-element is the same as the center point of the micro-element The square of the distance from the center of the cross section is proportional. Reference herein to "in-plane" means "transversely isotropic in-plane". Through such a design, when in use, the elastic waves introduced from the outer annular surface of the elastic wave converging device at any angle will be transmitted along the interior of the elastic wave condensing device and converge to the inner annular surface of the elastic wave converging device, to absorb elastic waves. Preferably, the value of the in-plane equivalent Poisson’s ratio of each micro-element can be in the range of 0.9-1, so that the propagation direction of the elastic wave introduced into the elastic wave converging device can be better controlled, and the The elastic waves converge to the inner ring of the elastic wave converging device to achieve the effect of elastic wave absorption. FIG. 4 shows a schematic diagram of any cross section in the axial direction of the elastic wave converging device shown in FIG. 3 . FIG. 4 also schematically shows several micro-elements in the above-mentioned plurality of micro-elements by dashed lines, and these micro-elements are arranged centrally symmetrically around the center of the cross section. It should be noted that the number and shape of the micro-elements shown in FIG. 4 are only schematic.

In a preferred embodiment, the above-mentioned micro-elements may be hexagonal honeycomb units. The selection of materials composed of hexagonal honeycomb units can easily adjust the wall thickness and side length of the honeycomb units to achieve variable stiffness, so as to achieve in-plane Poisson's ratio trend within the range of transverse isotropy. Material parameters close to 1. And, as long as the basic configuration of the hexagon remains unchanged, the Poisson's ratio does not change. Preferably, the configuration of the honeycomb unit is a regular hexagon for easier design. 5 shows a schematic diagram of an axial cross-section of an elastic wave converging device composed of a hexagonal honeycomb material according to an embodiment of the present invention. As shown in FIG. 5 , in any cross section in the axial direction of the elastic wave converging device, a plurality of hexagonal honeycomb units are closely arranged symmetrically around the center of the cross section. In addition, in order to ensure the use effect and durability of the elastic wave converging device, the hexagonal honeycomb material can be made of a material with appropriate strength to ensure that the rigidity of the entire device meets the requirements for use. Preferably, the hexagonal honeycomb material may be made of aluminium.

FIG. 6 is a partial enlarged schematic view of an axial cross section of the elastic wave converging device made of hexagonal honeycomb material shown in FIG. 5 . The following describes how to determine the wall thickness and side length of the hexagonal honeycomb unit with reference to FIG. 6 .

As shown in Figure 6, h and l represent the outer side lengths of the adjacent two sides of the hexagonal honeycomb unit, respectively, h _b and _lb represent the inner side lengths of the hexagonal honeycomb unit corresponding to the outer side lengths h and l, respectively, t represents the sum of the wall thicknesses of two adjacent hexagonal honeycomb units, and θ represents the angle between one side of the adjacent two sides of the hexagonal honeycomb unit and the normal of the other side, then the following can be obtained: Analytical expression:

In particular, for a regular hexagon, there is l=h, l _b =h _b , θ=30°.

Among them, in equations (7)-(10), ρ*, ν* and μ* are the equivalent density, in-plane equivalent Poisson’s ratio and in-plane equivalent shear modulus of the hexagonal honeycomb unit, respectively, namely , the density, in-plane Poisson's ratio, and in-plane shear modulus derived from the equivalent of the hexagonal honeycomb unit as a uniform unit. The parameters with the subscript s are the original properties of the material constituting the hexagonal honeycomb unit. Specifically, ρ _s , ν _s and E _s are the density, Poisson’s ratio and Young’s of the material constituting the hexagonal honeycomb unit, respectively. modulus. The wall thickness and side length of each honeycomb unit of the specified hexagonal honeycomb material can be directly determined by performing corresponding calculations in combination with the above analytical expressions (7)-(10) and formula (6).

It can be known from the above analytical expressions (6)-(10) that the wall thickness of the hexagonal honeycomb unit will vary with the distance of the hexagonal honeycomb unit from the center of the circle. Specifically, the smaller the distance of the hexagonal honeycomb unit from the center of the circle, the smaller the wall thickness of the hexagonal honeycomb unit. Since the density of the honeycomb unit will change with the wall thickness of the honeycomb unit, it can be seen from equation (6) that in order to satisfy the invariance of the transformation of the elastic wave equation, the density of the material is required to remain unchanged, so the changed density needs to be corrected. .

In an optional embodiment, an equivalent way of the whole unit is used, that is, based on the average mass of each hexagonal honeycomb unit, by arranging mass blocks on the inner walls of opposite sides of the hexagonal honeycomb unit , to compensate for the quality change of the hexagonal honeycomb unit due to different wall thicknesses (specifically, to make up for the missing quality due to the reduced wall thickness), and try to ensure that the equivalent density of all hexagonal honeycomb units is equal or approximately equal . The cross-sectional shape of the mass block can be any shape, such as a circle, a triangle, etc., and a mass rod with a rectangular cross-section is preferably used. The material of the mass block can be the same or different from the material of the honeycomb unit, preferably a material with a lower density, such as nylon, so that the cross-sectional area of the mass block required to supplement the same amount of missing mass is larger, which is easier to process accurately . Taking the example shown in Figure 6, the cross-sectional dimension of the mass block is a*b, and the mass of the mass block should be equal to the mass lost by the hexagonal honeycomb unit due to the reduction of the wall thickness, so as to ensure the final hexagonal honeycomb unit. The equivalent mass does not change. The mass loss of the hexagonal honeycomb unit is calculated by formula (7), and then the cross-sectional size of the mass block can be determined according to the material density and axial length of the mass block. In practical applications, for convenience, the hexagonal honeycomb unit in the outermost circle of the elastic wave convergence device can be used as a reference to calculate the mass loss of other hexagonal honeycomb units due to the reduction of wall thickness. In addition, as shown in Figure 6, it can be seen from theoretical derivation that when the hexagonal honeycomb material is stressed, the most deformed part is concentrated at the root of the honeycomb wall (the position shown by the dashed box in Figure 6). The central additional mass of the opposite honeycomb inner sidewall does not have much effect on the equivalent stiffness of the material. At the same time, for the elastic wave in the low frequency band, the wavelength of the elastic wave is much larger than the size of the hexagonal honeycomb unit, and the honeycomb unit is not prone to local resonance. It will not affect the equivalent wave speed of the overall device.

Further, for the energy of the elastic waves converging to the inner ring of the elastic wave converging device, further processing can be performed, such as storing, consuming or steering, so as to better collect and utilize the energy.

In an optional implementation manner, an energy collecting device may be arranged at the central cavity of the elastic wave converging device (equivalent to the center of the black hole) for storing the energy of the elastic waves converging on the inner annular surface of the elastic wave converging device . The energy harvesting device can use piezoelectric materials (such as piezoelectric films) to store energy by converting the mechanical energy of the vibration of elastic waves into electrical energy.

In another optional embodiment, an energy dissipating material may be disposed at the central cavity of the elastic wave converging device for dissipating the energy of the elastic waves converging to the inner annular surface of the elastic wave converging device. For example, the energy of vibration of elastic waves can be absorbed by filling damping oil at the center cavity of the elastic wave converging device (equivalent to the center of a black hole).

In yet another optional embodiment, the elastic waves converged to the inner ring of the elastic wave converging device can also be directed to another dimension. By forming a curved radian on the surface between the outer ring and the inner ring of the elastic wave converging device, the elastic waves introduced from the surface of the outer ring of the elastic wave converging device are converged to the inner ring of the elastic wave converging device. The surface simultaneously changes its own propagation direction to guide the elastic wave in the direction of the curvature. Fig. 7 shows a schematic diagram of the dimension that converges elastic waves to the inner annular surface of the elastic wave converging device and is directed perpendicular to the incident direction of the elastic waves, wherein the gray scale on the right in Fig. 7 represents the gray scale and normalization The relationship of the normalized displacement amplitude, as the displacement increases, the gray value decreases, that is to say, the brighter the area in the figure, the higher the energy. As shown in Fig. 7, the hollow cylindrical elastic wave converging device and the surrounding uniform waveguide material form a rectangular area. By bending down the plane of the elastic wave converging device and the rectangular area, a curved arc is formed on the surface between the outer ring and the inner ring of the elastic wave converging device to form an arc surface. The elastic wave is introduced from the left boundary of the rectangular area, and after incident on the outer annular surface of the elastic wave converging device, it converges to the inner annular surface of the elastic wave converging device. is reflected, thereby changing the direction of propagation. Thus, the elastic wave converged to the inner ring of the elastic wave converging device is directed to a direction perpendicular to the plane of the rectangular area (ie, the plane where the incoming direction of the elastic wave is located). In this way, the propagation direction of the elastic wave can be aligned, so that it can be better utilized or consumed.

In addition, in an optional embodiment, a material for guiding waves can also be wrapped around the outer annular surface of the elastic wave converging device, so that the outer contour of the elastic wave converging device can be formed into a specified geometric shape, such as Rectangle, triangle, etc. to meet the needs of different application scenarios.

The following is a comparative experiment to determine the absorption effect of the elastic wave convergence device provided by the embodiment of the present invention on elastic waves. In the control experiment, the test specimen and the control specimen have the same square outline, and they form the same rectangular area along the plane along the incoming direction of the elastic wave. The test specimen is composed of the hollow cylindrical elastic wave converging device of the present invention and a uniform material wrapped around the outer annular surface of the elastic wave converging device. The control specimens are all made of the above-mentioned uniform materials, and have a cavity of the same size at the position corresponding to the central cavity of the elastic wave converging device. For the test specimen, elastic waves are introduced from the left boundary of the rectangular area, and then propagate to the right boundary of the rectangular area after passing through the elastic wave convergence device of the present invention (which can be regarded as a "black hole"), and the remaining energy is absorbed by the damping layer . For the control specimen, the elastic wave is introduced from the left boundary of the rectangular area, and then propagates to the right boundary of the rectangular area after passing through the correspondingly set cavity, and the remaining energy is also absorbed by the damping layer. In order to facilitate impedance matching with the boundary of the black hole, the surrounding uniform material directly adopts the material of the outermost layer of the black hole (ie, the elastic wave converging device of the present invention). In addition, in the experiment, along the incoming direction of the elastic wave to the specimen, accelerometers were installed at both ends of the test specimen and the control specimen to measure the attenuation of the acceleration signal after passing through the test specimen and the control specimen. , so as to detect the effect of the elastic wave converging device of the present invention absorbing elastic wave energy.

Figures 8a and 8b respectively show the propagation effects of elastic waves incident from the left side of the control specimen and the test specimen in the above control experiment, wherein the gray scale on the right side of the two figures represents the gray scale and the normalized The relationship between the displacement amplitude, as the displacement increases, the gray value decreases, that is to say, the brighter the area in the figure, the higher the energy. It can be seen from Fig. 8a that the control specimen composed of homogeneous materials has almost no effect on the propagation of elastic waves. After the elastic waves pass through the annular area marked in Fig. The energy is almost completely not attenuated. As can be seen from Figure 8b, after the elastic wave enters the marked annular region (ie, the elastic wave converging device of the present invention), the energy is concentrated to the center of the annular region (similar to the center of a black hole), and after the annular region , almost no displacement can be detected, and it can be considered that the energy of the elastic wave is almost completely absorbed by the elastic wave converging device, and the elastic wave converging device of the present invention has a remarkable absorption effect on elastic waves.

Figure 9 shows the acceleration attenuation diagram of the test specimen and the control specimen in the range of 10-1000 Hz, wherein the abscissa is the frequency f of the elastic wave (unit: Hz), and the ordinate is the acceleration attenuation value H (unit: dB) ). The calculation method of the acceleration decay value H is H=20log ₁₀ (a ₂ /a ₁ ), where a ₁ is the acceleration amplitude measured at the front end of the test specimen or control specimen without passing through the annular area, a ₂ is the acceleration amplitude after passing through the annular area measured at the rear end of the test specimen or control specimen. According to the comparative analysis in FIG. 9 , it can be seen that the elastic wave converging device of the present invention has a significant damping effect on low-frequency elastic waves in the frequency band range of 10-1000 Hz, especially 100-900 Hz.

The elastic wave converging device proposed by the present invention has a remarkable absorption effect on elastic waves propagating in various forms, especially low-frequency elastic waves, and can be applied to vibration reduction of buildings, subway vibration reduction, vehicles (such as airplanes, automobiles, etc.) Buffer vibration damping and other applications.

Example 1

This embodiment provides the application of the elastic wave converging device of the present invention in vibration reduction of buildings. The elastic wave converging device is arranged around the building to absorb the elastic wave, so as to realize the vibration reduction and protection of the building. Fig. 10 is a schematic diagram showing the simulation effect of the elastic wave converging device in building vibration reduction according to an embodiment of the present invention, wherein the gray scale on the right side in Fig. 10 represents the relationship between the gray scale and the normalized displacement amplitude , as the displacement increases, the gray value decreases, that is, the brighter the area in the figure, the higher the energy. In FIG. 10 , the ring part marked with solid lines is the elastic wave converging device of the present invention. It should be noted that, in FIG. 10 , only part of the elastic wave converging device is schematically marked with solid lines, but not marked. All elastic wave convergence devices.

As shown in Figure 10, the elastic wave convergence device of the present invention (may be called "elastic wave black hole") is placed around the building to be protected to surround the building, and the distance between the centers of two adjacent elastic wave black holes is 10m. Seismic waves are simulated as elastic waves at 10 Hz. When the elastic wave propagates to the elastic wave black hole, the elastic wave black hole converges to its center to realize the absorption of the elastic wave and protect the building. Generally speaking, the smaller the center size of an elastic wave black hole and the larger the distance between the centers of adjacent elastic wave black holes, the better the elastic wave absorption effect will be, and the more critical energy absorbing materials will be saved. In order to achieve the best absorption and vibration reduction effect, it is preferable that there is no gap between the outer annular surfaces of adjacent elastic wave black holes, so as to prevent elastic waves from passing through the gap and causing damage to the building. Since a large part of seismic waves will be converted into Rayleigh waves propagating along the surface, in practical application, the elastic wave converging device of the present invention is arranged around the building, and the axial height of the elastic wave converging device is the same as the foundation depth, that is, Can play an effective vibration damping effect. According to the simulation effect in FIG. 10 , in this way, the elastic wave converging device of the present invention can effectively absorb longitudinal waves of 10 Hz seismic waves and protect buildings, and the protected building area can be arbitrarily selected without any limitation.

Example 2

This embodiment provides the application of the elastic wave convergence device of the present invention in the isolation of subway vibration signals. The elastic wave convergence devices are arranged on both sides of the subway track to absorb the elastic waves generated by the operation of the subway, thereby isolating the vibration of the subway. FIG. 11 shows a schematic diagram of the simulation effect of the elastic wave converging device in the subway vibration reduction according to an embodiment of the present invention, wherein FIG. 11 uses the same gray scale as that of FIG. 10 . In FIG. 11 , the ring part marked with solid lines is the elastic wave converging device of the present invention. It should be noted that, in FIG. 11 , only part of the elastic wave converging device is schematically marked with solid lines, but not marked. All elastic wave convergence devices.

As shown in Figure 11, a sine wave displacement excitation with a frequency of 50 Hz along the x horizontal axis is applied at the vertical axis y=2m to simulate the vibration caused by the subway passing on the ground, and the vibration is mainly shear wave. The elastic wave converging device of the present invention (may be referred to as "elastic wave black hole") is placed on the ground on both sides of the sine wave displacement excitation center (ie, y=2m) 2m, and two adjacent elastic wave converging devices are placed on the ground. There are no gaps between the torus surfaces. When the vibration signal (mainly shear wave) propagates to the elastic wave black hole, it is converged by the elastic wave black hole to its center to realize the absorption of the vibration signal, thereby isolating the subway vibration. If the absorbing boundary condition at the center of the elastic wave black hole is replaced by an energy harvesting device, the vibrational energy can also be stored and utilized.

According to the simulation effect in FIG. 11 , it can be seen that the elastic wave converging device of the present invention also has a significant absorption effect on shear waves.

From the analysis of Fig. 10 and Fig. 11, it can be seen that the elastic wave convergence device of the present invention has a good absorption effect for the excitation of the general longitudinal wave and shear wave coupling.

Example 3

This embodiment provides the use of the elastic wave convergence device of the present invention as an aircraft landing gear buffer. As shown in FIG. 12 , the elastic wave converging device 10 of the present invention (may be referred to as an “elastic wave black hole”) is used as an aircraft landing gear buffer and is arranged between the left connecting rod 11 and the right connecting rod 12 of the aircraft landing gear . FIG. 13 is a schematic diagram illustrating a simulation effect of an elastic wave converging device as a landing gear buffer according to an embodiment of the present invention. In this simulation experiment, the first 1/4 cosine waveform with a frequency of 100 Hz was used to simulate the impact load of the landing gear bumper. As shown in Figure 13, the impact load is transmitted from the left connecting rod to the elastic wave black hole, and is concentrated to its center by the elastic wave black hole, and will not continue to be transmitted to the right connecting rod.

According to the simulation effect of FIG. 13 , when the elastic wave convergence device of the present invention is applied to the landing gear of an aircraft, it can effectively absorb the impact of the ground on the landing gear when the aircraft lands, thereby protecting the landing gear and the body.

According to any one of the foregoing optional embodiments or a combination of multiple optional embodiments, the embodiments of the present invention can achieve the following beneficial effects:

The elastic wave converging device proposed in the embodiment of the present invention, by designing the structure into a hollow cylinder shape and designing the material parameters, makes the elastic wave converging device made of non-uniform transversely isotropic material in any axial direction. Each micro-element in a cross section satisfies the following three conditions: the equivalent density of all micro-elements is equal, the in-plane equivalent Poisson's ratio of all micro-elements is equal and close to 1, the surface of each micro-element is equal The internal equivalent shear modulus is proportional to the square of the distance from the center point of the microelement to the center of the cross section. Such a design enables the elastic waves introduced from the outer annular surface of the elastic wave converging device at any angle to transmit along the interior of the elastic wave converging device and converge to the inner annular surface of the elastic wave converging device during use. That is, the elastic wave converging device forms an effect similar to an elastic wave black hole, captures the elastic waves propagating within the range of the outer annular surface thereof and converges the elastic waves to the center. The elastic wave converging device provided by the present invention has a significant absorption effect on elastic waves propagating in various forms, especially low-frequency elastic waves, and can be applied to applications such as building vibration reduction, subway vibration signal isolation, vehicle buffer vibration reduction, etc. .

In the description provided herein, numerous specific details are set forth. It will be understood, however, that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: Within the spirit and principle of the present invention, it is still possible to modify the technical solutions recorded in the foregoing embodiments, or to perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the corresponding technical solutions deviate protection scope of the present invention.

Claims (9)

1. An elastic wave converging device applied to low-frequency elastic waves, wherein the elastic wave converging device has the shape of a hollow cylinder; and the elastic wave converging device is made of a non-uniform transversely isotropic material , any cross-section in the axial direction is composed of a plurality of micro-elements, and each micro-element in the plurality of micro-elements is equivalent to a uniform material, then the material parameters of each micro-element satisfy the following conditions: (1) The equivalent densities of all micro-elements are equal: (2) the in-plane equivalent Poisson's ratios of all micro-elements are equal, and the in-plane equivalent Poisson's ratio approaches 1; (3) the surface of each micro-element The internal equivalent shear modulus is proportional to the square of the distance between the center point of the micro-element and the center of the cross section, where the in-plane refers to the transverse isotropic plane; The elastic waves introduced from the outer annular surface of the elastic wave converging device at any angle will be transmitted along the interior of the elastic wave converging device and converged to the inner annular surface of the elastic wave converging device, so as to realize the transmission of all the elastic waves. the absorption of elastic waves; An energy collecting device is arranged at the central cavity of the elastic wave converging device for storing the energy of the elastic waves converging on the inner annular surface of the elastic wave converging device; or, An energy dissipating material is arranged at the central cavity of the elastic wave converging device, which is used to dissipate the energy of the elastic waves converging on the inner annular surface of the elastic wave converging device; or, The surface between the outer ring and the inner ring of the elastic wave convergence device forms a curved arc, so that the elastic waves introduced from the outer ring surface of the elastic wave convergence device converge to the elastic wave convergence device. The inner annular surface of the ring changes its own propagation direction at the same time, so as to guide the elastic wave to the bending direction. 2 . The elastic wave converging device applied to low-frequency elastic waves according to claim 1 , wherein the in-plane equivalent Poisson’s ratio of each micro-element is in the range of 0.9-1. 3 . 3 . The elastic wave converging device applied to low-frequency elastic waves according to claim 1 or 2 , wherein the micro-elements are hexagonal honeycomb cells. 4 . 4. The elastic wave converging device applied to low-frequency elastic waves according to claim 3, wherein the wall thickness and side length of the hexagonal honeycomb unit are determined by the following formulas:

Among them, ρ*, ν* and μ* are the equivalent density, in-plane equivalent Poisson’s ratio and in-plane equivalent shear modulus of the hexagonal honeycomb unit, respectively; ρ _s , ν _s and E _s are respectively are the density, Poisson's ratio and Young's modulus of the material constituting the hexagonal honeycomb unit; h and l are the outer lengths of the adjacent two sides of the hexagonal honeycomb unit respectively; h _b and _lb are respectively The inner side lengths of the hexagonal honeycomb unit corresponding to the outer side lengths h and l; t is the sum of the wall thicknesses of the two adjacent hexagonal honeycomb units; θ is the length of the hexagonal honeycomb unit. The angle between one of the two adjacent sides and the normal of the other. 5. The elastic wave converging device applied to low-frequency elastic waves according to claim 4, characterized in that, by arranging mass blocks on the inner walls of opposite sides of the hexagonal honeycomb unit, the hexagonal honeycomb unit due to different wall thicknesses is compensated for. Variation in the mass of the angular honeycomb cells. 6. The elastic wave converging device applied to low-frequency elastic waves according to claim 1 or 2, characterized in that, the outer ring surface of the elastic wave converging device is further wrapped with a material for guiding waves, so that the The outer contour of the elastic wave converging device is formed into a specified geometric shape. 7. The use of the elastic wave converging device applied to low-frequency elastic waves in building vibration reduction according to any one of claims 1-6, wherein the elastic wave converging device is arranged around the building , to absorb elastic waves. 8. The use of the elastic wave converging device applied to low-frequency elastic waves in the isolation of subway vibration signals according to any one of claims 1-6, wherein the elastic wave is arranged on both sides of the subway track. Wave converging device to absorb elastic waves generated by subway operation. 9. Use of the elastic wave converging device applied to low-frequency elastic waves according to any one of claims 1-6 as a buffer for a vehicle.

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