Metamaterial rod that outputs only stretch waves and applications thereof
By designing the cell structure and external friction of metamaterial rods, the function of flipping compression waves into tensile waves and filtering out tensile waves was realized, solving the problem that the mechanical wave properties are difficult to change in the existing technology, and providing a powerful mechanical signal control platform.
Patent Information
- Application Number
- CN202310877799.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-07-17
- Publication Date
- 2026-02-06
- Estimated Expiration
- 2043-07-17
AI Technical Summary
Existing technologies cannot alter the fundamental properties of mechanical waves during propagation, making it impossible to output waveforms with only a single property.
Design a metamaterial rod that uses an even number of symmetrically arranged guide rods and linearly arranged cells to achieve the flipping and filtering function of elastic waves by utilizing external friction and stiffness softening effect, so that it outputs only tensile waves.
Metamaterial rods can invert compression waves into tension waves and filter out tension waves from mixed-loaded waves, maintaining waveform and amplitude, and providing a powerful platform for mechanical signal manipulation.
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Figure CN117189808B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present scheme belongs to the technical field of structural mechanics, and particularly relates to a metamaterial rod outputting only tensile waves and application thereof. BACKGROUND
[0002] Metamaterials have properties that traditional materials cannot achieve, providing powerful tools for manipulating physical signals. Such as wave perfect absorption, invisibility cloaks, superlenses and holographic imaging in electromagnetics, optics, acoustics, thermodynamics and magnetism. In addition, metamaterials have opened the door to abnormal mechanical behavior, not only realizing negative Poisson's ratio, negative compressibility in static state, tensile-torsional coupling effect and mechanical cloaks, but also making one-way propagation, stable propagation and vibration attenuation of mechanical waves possible. Among them, metamaterials with stiffness softening effect can convert compression pulses into leading sparse waves and oscillatory waves, so that stress waves can be attenuated without relying on plasticity and damping, and have received extensive attention in recent years. However, for the basic properties of mechanical waves, i.e. compression and tension, it is still difficult to change during propagation, so it is impossible to realize the output of only a single attribute wave for inputting arbitrary waveforms. SUMMARY
[0003] The present scheme aims to overcome at least one of the defects in the prior art and provide a metamaterial rod outputting only tensile waves.
[0004] In order to solve the above technical problems, the following technical scheme is adopted:
[0005] In a first aspect, a metamaterial rod outputting only tensile waves includes an even number of guide rods arranged symmetrically and a plurality of cells linearly arranged on the guide rods. Each cell includes a first connecting plate, a second connecting plate, a first inclined rod, a second inclined rod, a third inclined rod, a fourth inclined rod and a spring. The first connecting plate and the second connecting plate are parallel to each other. The first end of the first inclined rod and the first end of the second inclined rod are pivotally connected to one side of the first connecting plate facing the second connecting plate. The first end of the third inclined rod and the first end of the fourth inclined rod are pivotally connected to one side of the second connecting plate facing the first connecting plate. The second end of the first inclined rod, the second end of the third inclined rod and the first end of the spring are pivotally connected. The second end of the second inclined rod, the second end of the fourth inclined rod and the second end of the spring are pivotally connected. In adjacent two cells, the second connecting plate of the former cell and the first connecting plate of the latter cell are shared or connected as one. The first connecting plate and the second connecting plate are provided with an even number of through holes for the guide rods to pass through. In the elastic wave input direction, the stiffness of the first cell is smaller than that of the other cells.
[0006] The present scheme proposes a special nonlinear metamaterial rod with customizable stiffness softening effect. By using external friction, the momentum conservation of the system is broken, and through in-depth analysis of the elastic wave propagation mechanism, a non-uniform distribution of metamaterial rods is designed. The non-uniform arrangement of the unit cells achieves the unusual function of only outputting tensile waves. Whether an impact, sudden stretching, or alternating stretching and compression loads are applied to one end of the rod, only tensile signals are output at the other end of the rod. This means that this material rod can completely reverse the compression stress wave into a tensile wave and can filter out the tensile wave from the mixed stretching and compression load wave. The transmission of the tensile wave also exhibits the characteristics of a solitary wave, maintaining the original wave shape and amplitude during propagation. It is worth noting that the peculiar reversal and filtering function of the elastic wave of the metamaterial rod exhibits unidirectionality (non-reciprocity), and similar non-reciprocity has shown strong application prospects in the fields of acoustics, optics, and mechanics. More importantly, we have found the key cell that controls these unique functions - the first cell, like a key gene switch on a biological DNA chain, can turn on or off these functions by adjusting the performance of this key cell, which opens up a powerful design platform for mechanical signal manipulation.
[0007] The first cell with smaller stiffness is the switch to realize the elastic wave reversal and filtering function. If the first cell is replaced by a cell with the same stiffness as other cells, the elastic wave reversal and filtering function cannot be realized. The cell not only can produce a large elastic deformation, but also has a strong stiffness softening effect, which is derived from the geometric configuration of the cell and mainly affected by the longitudinal angle θ (the angle between the first, second, third, or fourth inclined rod and the length direction of the metamaterial rod). The larger the θ, the weaker the stiffness softening effect of the cell, so its stiffness softening effect can be customized by changing the longitudinal angle θ. In addition, the stiffness and number of springs are also factors that affect the stiffness of the cell. Therefore, the stiffness of the cell can be customized by adjusting one or more of the spring stiffness, the number of springs, and the size of the longitudinal angle. To make the stiffness of the first cell smaller than that of the other cells, the spring stiffness of the first cell can be made smaller than that of the other cells, the number of springs of the first cell can be made smaller than that of the other cells, or the longitudinal angle of the first cell can be made larger than that of the other cells.
[0008] The efficiency of output momentum after the conversion of elastic wave reflects the inversion ability of the metamaterial rod to the elastic wave, and research shows that the momentum conversion efficiency increases with the increase of k2 / k1 and decreases with the increase of θ2 / θ1, wherein k1 is the spring stiffness coefficient of the first cell, k2 is the spring stiffness coefficient of the other cells, θ1 is the longitudinal angle of the first cell, and θ2 is the longitudinal angle of the other cells. When k2 / k1 is between 3-4.5 and θ2 / θ1 is between 25°-35°, the momentum conversion efficiency can reach more than 0.5. Therefore, the spring stiffness coefficient k1 of the first cell and the spring stiffness coefficient k2 of the other cells preferably satisfy: 3≤k2 / k1≤4.5, and the longitudinal angle θ1 of the first cell and the longitudinal angle θ2 of the other cells preferably satisfy: 25 / 35≤θ2 / θ1≤35 / 35.
[0009] The metamaterial rod needs a certain number of cells for stress wave inversion or screening. The smaller the critical number of cells, the stronger the inversion and screening function. Theoretical results show that when the input amplitude of the pulse is constant, the critical number of cells increases with the increase of the spring stiffness coefficient k1 of the first cell and decreases with the increase of the sliding friction coefficient μ. This is because a larger k1 means that the strain of the first cell is small, so more energy is transmitted to the second cell, which increases the number of cells required for the compression wave to decay to zero. As discussed earlier, when k1 approaches k2, the stress wave conversion and screening function is lost. Increasing the sliding friction coefficient μ will make the compression wave decay to zero faster. By selecting appropriate values of k1 and μ, only 7 cells are needed to achieve stress wave conversion and screening. Therefore, by designing the values of k1 and μ, the effective critical number of cells of the metamaterial rod can be customized.
[0010] The guide rod can apply external friction (sliding friction) to the metamaterial rod, and the size of the sliding friction coefficient μ can be controlled by adjusting the surface roughness of the rod, and the stability of the metamaterial rod to longitudinal wave propagation can be ensured. The guide rod, the through hole of the first connecting plate and the second connecting plate are provided with a sliding bearing, which can further improve the stability of the metamaterial rod to longitudinal wave propagation.
[0011] The first connecting plate and the second connecting plate are provided with a mass block to adjust the mass of the first connecting plate and the second connecting plate. The mass block can be a nut. The two ends of the first inclined rod, the second inclined rod, the third inclined rod and the fourth inclined rod are pivoted by a pivot shaft, and a rolling bearing is arranged between the pivot shaft and the first inclined rod, the second inclined rod, the third inclined rod and the fourth inclined rod to reduce the resistance when the inclined rod starts. The spring is a tension-compression spring, and the two ends of the spring are pivoted to the first inclined rod, the second inclined rod, the third inclined rod and the fourth inclined rod through a connecting block.
[0012] In the second aspect, the application of the metamaterial rod in the field of impact mitigation can completely convert the impact compression pulse into a stretching pulse, so that the end of the rod does not feel the impact.
[0013] Thirdly, the tensile wave propagating in the metamaterial rod will exhibit the characteristics of soliton, keeping the original waveform and amplitude during the propagation, which paves the way for long-distance transmission of mechanical signals. Similarly, optical soliton has shown bright prospects in the field of communication.
[0014] Compared with the prior art, the present application has the following beneficial effects: the metamaterial rod uses external friction and non-uniform distribution of the cell with stiffness softening effect to realize the conversion of compression wave into tensile wave, and can filter the tensile wave from the mixed tensile and compression wave, so that only the tensile wave is output. This special function opens up a powerful designable platform for mechanical signal control, and also opens up unprecedented opportunities for robot actuators, impact resistance, new material design, energy collection and utilization. BRIEF DESCRIPTION OF DRAWINGS
[0015] The drawings are only used for illustrative description, and should not be understood as a limitation on the present application; in order to better illustrate the present application, some components in the drawings may be omitted, enlarged or reduced, and do not represent the actual product size; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.
[0016] Figure 1 is a schematic diagram of the metamaterial rod, special performance and mechanical explanation. Among them, A is a schematic diagram of the metamaterial rod outputting only tensile wave function, in which red represents compression wave and blue represents tensile wave; B is a schematic diagram of propagation mechanism, in which red straight line represents compression wave and blue straight line represents tensile wave, the arrow direction represents the wave propagation direction, ρ a and ρ b respectively represent the initial density of the cell, c a and c b respectively represent the wave speed of the wave propagating in a and b; C is a schematic diagram of the composition of the metamaterial rod; D is the force-strain curve of the two kinds of cells (the first single cell is marked as a, and the other single cells are marked as b), the solid line represents the experimental result, the dotted line represents the theoretical result, and the shadow represents the standard deviation of three experiments; E is the stiffness-strain curve of the two kinds of cells.
[0017] Figure 2 is a schematic diagram of the assembly of the single cell.
[0018] Figure 3 is a schematic diagram of the static experiment of the single cell.
[0019] Figure 4 is the equivalent stiffness curve of the cell under different parameters. Among them, A is the equivalent stiffness curve of the single cell under four different spring stiffnesses; B is the equivalent stiffness curve of the single cell under four different angles.
[0020] Figure 5Figure 1 is a schematic diagram of the loading device. Wherein, A is the initial velocity plate impact loading; B is the exciter loading.
[0021] Figure 6 Figure 2 is a schematic diagram of the dynamic experiment. Wherein, A is a schematic diagram of the dynamic experiment in which the oscilloscope is used to measure the force-time curve and the high-speed camera is used to measure the motion-time curve of each cell; B is a schematic diagram of the PVDF piezoelectric film pasting.
[0022] Figure 7 Figure 3 is the dynamic response of the metamaterial rod. Wherein, A is the experimental snapshot of the metamaterial rod at t = -0.03 s, t = 0.1 s, t = 0.2 s, t = 0.25 s and t = 0.37 s, wherein the red (blue) band arrow straight line represents the axial compression (tension) displacement of the plate, and the length represents the size of the displacement; B is the cell strain history corresponding to the experimental snapshot, wherein t = 0.1 s, t = 0.2 s, t = 0.25 s respectively upward translation of 0.6, 0.4, 0.2 strain; C is the force-time curve at the 3rd, 8th, 13th and 17th plate; D is the cell strain contour map obtained by applying a compression pulse to the metamaterial rod, wherein the tensile strain is positive and the compressive strain is negative; E is the force-time curve at the 1st, 3rd, 8th and 17th plate obtained by applying a compression pulse, wherein the force-time curve measured at the 1st plate is the input force-time curve, and the force-time curve measured at the 17th plate is the output force-time curve; F is the cell strain contour map obtained by applying a tensile-compression mixed pulse to the metamaterial rod; G is the force-time curve at the 1st, 3rd, 8th and 17th plate obtained by applying a tensile-compression mixed pulse, wherein the output curve is translated in the two-dimensional graph to compare the frequency change of the input and output curves; H is the strain history of the cell at several time points obtained by applying a tensile pulse to the metamaterial rod; I is the force-time curve at the 1st, 3rd, 8th and 17th plate obtained by applying a tensile pulse.
[0023] Figure 8 Figure 4 is the switching cell function of the metamaterial rod and the proof of non-reciprocity. Wherein, A is the experimental forward input schematic diagram and the experimental results of the compression pulse and the mixed waveform of the forward input, wherein the red spring represents the small stiffness spring in the experiment, the gray spring represents the large stiffness spring in the experiment, and the negative (positive) value in the curve represents the pressure (tension); B is the experimental result of the forward input after replacing the switching cell; C is the experimental result of the reverse input.
[0024] Figure 9 Figure 5 is the influencing factors of the conversion screening function. Wherein, A is the contour map of the critical number of cells required for the metamaterial rod to complete the flipping function, and the contour lines of each main position are marked on the graph; B is the contour map of the critical number of cells required for the metamaterial rod to complete the screening function; C is the contour map of the momentum conversion efficiency η.
[0025] Explanation of reference signs: guide rod 100, first connecting plate 211, second connecting plate 212, first inclined rod 221, second inclined rod 222, third inclined rod 223, fourth inclined rod 224, spring 230. DETAILED DESCRIPTION
[0026] In order to make the skilled in the art better understand the present scheme, the present scheme will be further described in detail below in combination with specific embodiments.
[0027] The present scheme proposes a kind of metamaterial rod, realize only the unusual function of outputting tensile wave, whether the impact, sudden stretching, or stretching, compression alternating repeated load is applied to its one end, only tensile signal is output in the other end of rod, such as Figure 1 (A).This means that this material rod can completely turn compression stress wave into tensile wave, and can filter out tensile wave from the wave of mixed stretching and compression.The metamaterial rod has two kinds of cells, each kind of cell is composed of four hinged inclined rods, two tension-compression springs and two connecting plates (the number of springs can also be configured as one or more, symmetrically or uniformly arranged on the pivot shaft of inclined rod or any point on the inclined rod parallel to the connecting plate) in the embodiment. One kind of cell has smaller stiffness, and the other kind of cell has larger stiffness. The cell with smaller stiffness is used as the first cell, and all other cells starting from the second cell use the cell with larger stiffness to arrange periodically in one dimension, and then two stainless steel guide rods are symmetrically passed through the connecting plates at both ends of each cell, thereby forming a metamaterial rod, such as Figure 1 (C).
[0028] I. Preparation and assembly of metamaterial rod
[0029] HY-303 glue is used to bond the spring and the connecting block, the rolling bearing and the inclined rod, and the sliding bearing and the connecting plate, and then M2 screw is used to connect the inclined rod with the connecting plate and the connecting block of spring, thereby assembling a cell, as shown in Figure 2 The nut on the connecting plate acts as a mass block and can be used to adjust the mass of the plate. The connecting plate and the connecting block are 3D printed with 9400 resin material, and the spring is customized with spring steel. The specifications of the springs of the two kinds of cells are 0.6*10*18 (11 turns) and 0.5*7*18 (12 turns) respectively, and the spring stiffnesses are 0.28 N / mm and 0.9 N / mm respectively. The sliding bearing has a specification of LMUT13, and the rolling bearing has a specification of MF52ZZ. The masses of the parts are shown in Table 1. The values of the parameters in the experiment are determined based on extensive theoretical calculations, in which the length of the inclined rod is 20 mm, and the angle θ with the longitudinal direction is 32°.
[0030] Table 1 Masses of components in unit cell
[0031]
[0032] The cell with smaller stiffness is taken as the first cell, and all other cells starting from the second cell are arranged periodically in one dimension with the cell with larger stiffness, and then two stainless steel guide rods are symmetrically passed through the connecting plates at both ends of each cell to form a metamaterial rod, such as Figure 1 (C), and the ends of the guide rods are fixed by supports.
[0033] II. Static experimental method
[0034] In order to prove the elastic deformation ability and stiffness softening effect of the cell, a three-point bending test machine with a range of 500N was used to measure the force-displacement curve and stiffness-strain curve of the cell. The upper plate and the lower plate of the cell were fixed with the indenter of the test machine and the clamp fixed on the workbench through the pins, respectively, and the upper plate moved up and down with the indenter, as shown in Figure 3 The cell was subjected to compression or tensile loading at a speed of 5mm / min, and the force-displacement curve and stiffness-strain curve of the cell were obtained. Three experiments were conducted for each cell to verify the repeatability. As shown in Figure 1 (D, E), the cell composed of articulated linkages and springs not only can produce large elastic deformation, but also has strong stiffness softening effect, and the stiffness has decreased to 0 when the strain reaches 0.3. The stiffness softening effect of the cell is mainly affected by the longitudinal angle θ, and the larger the angle θ, the weaker the stiffness softening effect of the cell (see Figure 4 ), so the stiffness softening effect can be customized by changing the longitudinal angle θ.
[0035] III. Dynamic experiment
[0036] In order to prove the flipping function of the metamaterial rod, a spring launching device was used to impact the left end of the metamaterial rod with a plate at a certain initial speed, and the right end of the metamaterial rod was fixed on the support. The spring in the spring launching device has a diameter of 10cm, a length of 15cm, and a stiffness of 1N / mm. The two ends of the spring were fixed with the 3D printed plate by glue, and one end was fixed to the support by a bolt. The spring launching device was compressed by the impact plate, and after release, the impact plate could be launched along the longitudinal direction at an initial speed, and the initial speed of the impact plate could be controlled by the compression strain of the spring. A magnet was pasted on the impact plate and the first plate of the metamaterial rod, respectively, so that after the impact plate collided with the first plate, they became a whole and moved together due to the magnetic force, as shown in Figure 5 (A).
[0037] Red dots were painted on the side of the plate with a mark pen, and then a high-speed camera with model Nova S9 was used to shoot the dynamic response of the metamaterial rod, and then the DIC (digital image correlation) digital image correlation technology was used to analyze the motion of each cell in the metamaterial rod. The dynamic experiment measurement schematic diagram is shown in Figure 6(A). The rod deformation process and the resulting cell strain history were recorded by a high-speed camera Figure 7 (A, B).
[0038] Polyvinylidene fluoride) PVDF sensors were used to measure the force-time curves at some positions of the metamaterial rod. Specifically, the 3rd, 8th, 13th and 17th (the last one) plates were pasted with two thin plates in the middle to facilitate the pasting of PVDF sensors to measure the corresponding force-time curves, as shown in Figure 6 The sum of the masses of the two thin plates was equal to the mass of the other plates. The PVDF sensor was LDT1028K, which was connected in turn with a charge amplifier of model KD5008C and a TDS2014C oscilloscope. The voltage-time curve measured by the oscilloscope could be used to deduce the corresponding force-time curve. Finally, by embedding piezoelectric films between the cells, the force-time curves of the 3rd, 8th, 13th and 17th (the last one) plates were measured, as shown in Figure 7 (C).
[0039] From Figure 7 (A), it can be found that at t = 0.1 s, the first cell first produces a very obvious compressive strain, but at t = 0.2 s, the first cell changes from a state of significant compression to a state of tension, while the subsequent cells only have a small compressive strain, indicating that most of the compression wave is converted into a tensile wave, which can also be observed from the force-time curve of the third plate in Figure 7 (C), Figure 7 (C) can be seen, Figure 7 (C), the 17th plate (the output end) outputs a pure tensile stress.
[0040] In order to more intuitively feel the flipping function of the metamaterial rod to elastic waves, a JZQ-50 exciter was used to apply a compression pulse to the metamaterial rod. The excitation head was fixed to the 3D printed rod, and the excitation force was applied to the metamaterial rod through the rod, as shown in 7(B). A thin block was added between the rod and the first plate, which could fall down when the exciter output a sinusoidal excitation force, so that the metamaterial rod was only subjected to a compression pulse for one period (when subjected to a tensile force, the thin block fell down, and the metamaterial rod was no longer affected by the exciter). During the process of the exciter applying a compression pulse to the metamaterial rod, the response of the metamaterial rod was as shown in Figure 7 (D, E). Figure 7It can be found in (D) that the compressive wave is almost disappeared after the 15th cell, only tensile wave is left, and only tensile stress is detected at the output end Figure 7 (E), which realizes the conversion of input compressive wave to output tensile wave.
[0041] To prove the filtering function of the metamaterial rod, we stick the exciter head and the first plate together with glue, set the output of the exciter to be a sinusoidal excitation force, and apply a 10-cycle tensile-compressive mixed sinusoidal stress wave to the first plate of the metamaterial rod by the JZQ-50 exciter. The input and output waveforms are shown in Figure 7 (F). It can be clearly observed that after the mixed stress wave is applied to the metamaterial rod, the compressive wave has disappeared around the 15th cell, and only the periodic tensile wave is detected at the output end, and the frequency of the output force basically corresponds to that of the input force Figure 7 (G). This proves the filtering function of the metamaterial rod. This function is realized due to the nature of the stiffness softening effect of the metamaterial rod, which makes the amplitude of the compressive stress wave received by the second cell significantly smaller than that of the tensile stress wave, as shown in Figure 7 (G). Under the action of the nonlinear dispersion of the cell to the compressive wave and the external friction, the compressive wave will disappear. In comparison, due to the solitary propagation characteristic of the tensile wave of the metamaterial rod (see the next paragraph), the tensile wave with a larger amplitude is retained (if the amplitude of the input mixed wave is relatively large, the compressive wave will be converted into a tensile wave, superimposed with the input tensile wave, and the output tensile wave is enhanced).
[0042] We found that the metamaterial rod not only has the functions of conversion and filtering, but also enables the tensile wave to have the characteristics of tensile solitary wave. We replace the first cell of the metamaterial rod with the same cell as the following cells, and then use a rope to apply a tensile pulse to the metamaterial rod. Specifically, we tie a rope on the magnet, make the magnet attract the magnet on the first plate of the metamaterial rod, and quickly pull the rope along the axial direction. The magnet will quickly separate from the first plate, and the first plate will be subjected to a tensile pulse. The tensile pulse will form a tensile solitary wave within a certain number of cells, and then stably propagate in the rod, as shown in Figure 7 (H, I). When the spring and the mass of the inclined rod as well as the friction are all taken as 0, it is theoretically derived that the tensile wave is a solitary wave solution of the KDV equation during propagation (see Figure 8 (H) green curve). This is caused by the mutual balance of the stiffness softening effect and the dispersion effect of the metamaterial rod. The spring and the mass of the inclined rod represent the lateral inertia effect of the metamaterial rod, which, like the friction, causes the tensile solitary wave to have a certain attenuation during propagation.
[0043] It should be emphasized that the first weak cell is the switch for realizing the functions of elastic wave conversion and filtering. If the first cell is replaced with the same cell as the other cells, the functions of elastic wave conversion and filtering cannot be realized, as shown inFigure 8 (B) shows. As mentioned before, if the first two cells are the same, the efficiency of the conversion from compression wave to extensional wave is not high, and the converted extensional wave will be quickly dissipated by friction, leaving only the compression wave at the output end. Similarly, when the input is a mixed wave, the compression wave energy transmitted to the second cell is large, and it will be output together with the extensional wave at the output end, as shown in Figure 8 (B). It can be further concluded that the metamaterial rod has non-reciprocity for the propagation of compression and mixed waves, i.e. when the wave is input in the opposite direction, the metamaterial rod does not have the inversion and filtering functions of elastic waves, as shown in Figure 9 (C).
[0044] In addition to the first switch cell, the friction of the guide rail on the rod also plays a key role in the conversion of stress waves, so that it will not be like many studies that can only convert compression waves into a leading sparse wave followed by an oscillating compression wave. Without external friction, according to the momentum theorem, the internal force will not change the system momentum, and the total momentum output will be equal to the compression momentum input after a long time of accumulation. The guide rail plays a key role in the impulse of the metamaterial rod in the form of friction, making the output momentum become tensile momentum. Fortunately, most of the time, materials and structures need to be supported rather than suspended in the air, and the friction between the support is inevitable, providing natural conditions for this unique phenomenon.
[0045] In order to have a deeper understanding of these influencing factors of inversion and filtering functions, we analyzed the theoretical results under different parameters. The metamaterial rod needs a certain number of cells for the propagation of waves to complete the inversion or filtering of stress waves, and the smaller the critical number of cells, the stronger the inversion and filtering functions. The theoretical results show that when the input amplitude of the pulse is constant, the critical number of cells increases with the increase of the spring stiffness coefficient k1 of the first cell, and decreases with the increase of the sliding friction coefficient μ, as shown in Figure 9 (A, B). This is because a larger k1 means that the strain of the first cell is small, so the energy transmitted to the second cell is larger, which increases the number of cells required for the compression wave to decay to zero. As discussed earlier, when k1 approaches k2, the stress wave conversion and filtering functions are lost. An increase in the sliding friction coefficient μ will make the compression wave decay to zero faster. From Figure 9 (A, B), it can be found that when k1 and μ take appropriate values, only 7 cells are needed to achieve the conversion and filtering of stress waves. Therefore, by designing the values of k1 and μ, the effective critical number of cells of the metamaterial rod can be customized.
[0046] It is worth noting that the inversion ability of the metamaterial rod for stress waves not only lies in the critical number of cells, but also lies in the efficiency of the output momentum after the completion of the elastic wave conversion. Here, the momentum conversion efficiency η = -p out / pin where p out represents the momentum output at the critical cell, p in represents the momentum input to the system. By Figure 4 (C) it can be found that the value of η increases with the increase of k2 / k1 and decreases with the increase of θ2 / θ1, because k2 / k1, θ2 / θ1 will change the stiffness of the first two cells (see Figure 9 ), the greater the difference between the two cell stiffnesses, the higher the conversion efficiency will be. When k2 / k1 is between 3 and 4.5, θ2 / θ1 takes 25 / 35 to 35 / 35, the momentum conversion efficiency can reach more than 0.5, as shown by the red dashed box in (C). Therefore, the momentum conversion efficiency of the metamaterial rod can also be controlled by changing the geometric parameters k1, k2, θ1, θ2 of the first two cells.
[0047] We show that the metamaterial rod with customizable stiffness softening effect can achieve unprecedented functionality of only outputting tensile waves, so that whether the compression wave, tensile wave, or mixed wave of tensile and compression waves propagates through the metamaterial rod, only tensile wave is output. The metamaterial rod can completely convert the impact compression pulse into a tensile pulse, so that the end of the rod does not feel the impact. The mechanism of the reverse and screening functions and the design of the metamaterial structure have important significance in the field of reusable impact mitigation. In addition, the structure can move as a whole in the loading direction under impact, which can be used to design impact-driven reverse motion soft robots. The only output tensile wave function of the metamaterial rod provides a more powerful logic manipulation platform for mechanical wave manipulation.
[0048] Obviously, the above-described embodiments of the present scheme are merely examples for clearly illustrating the present scheme, and are not intended to limit the implementation of the present scheme. For those skilled in the art, on the basis of the above description, other different forms of changes or variations can also be made. Here, it is not necessary and impossible to exhaust all the implementation manners. Any modification, equivalent replacement and improvement made within the spirit and principles of the present scheme shall be included in the protection scope of the claims of the present scheme.
Claims
1. A metamaterial rod characterized by, The metamaterial rod only outputs tensile waves, and includes an even number of guide rods arranged symmetrically and a plurality of cells arranged linearly on the guide rods; Each cell includes a first connecting plate, a second connecting plate, a first inclined rod, a second inclined rod, a third inclined rod, a fourth inclined rod and a spring, the first connecting plate and the second connecting plate are parallel to each other, the first end of the first inclined rod and the first end of the second inclined rod are pivotally connected to one side of the first connecting plate facing the second connecting plate, the first end of the third inclined rod and the first end of the fourth inclined rod are pivotally connected to one side of the second connecting plate facing the first connecting plate, the second end of the first inclined rod, the second end of the third inclined rod and the first end of the spring are pivotally connected, and the second end of the second inclined rod, the second end of the fourth inclined rod and the second end of the spring are pivotally connected; in adjacent two cells, the second connecting plate of the former cell and the first connecting plate of the latter cell are shared or connected as one body; the first connecting plate and the second connecting plate are provided with an even number of through holes for the guide rods to pass through; In the elastic wave input direction, the stiffness of the first cell is smaller than that of the other cells.
2. The metamaterial rod of claim 1, wherein, The spring stiffness of the first cell is smaller than that of the other cells; and / or the number of springs of the first cell is smaller than that of the other cells; and / or the longitudinal angle of the first cell is larger than that of the other cells, the longitudinal angle being the angle between the first inclined rod, the second inclined rod, the third inclined rod or the fourth inclined rod and the length direction of the metamaterial rod.
3. The metamaterial rod of claim 2, wherein, The spring stiffness coefficient k1 of the first cell and the spring stiffness coefficient k2 of the other cells satisfy: 3≤k2 / k1≤4.5; and / or the longitudinal angle θ1 of the first cell and the longitudinal angle θ2 of the other cells satisfy: 25 / 35≤θ2 / θ1<35 / 35.
4. The metamaterial rod of any of claims 1-3, wherein, The number of cells exceeds the effective critical cell number of the metamaterial rod, and the effective critical cell number depends on the spring stiffness coefficient k1 of the first cell and the sliding friction coefficient μ of the metamaterial rod.
5. The metamaterial rod of any of claims 1-3, wherein, The guide rod and the through holes of the first connecting plate and the second connecting plate are provided with sliding bearings.
6. The metamaterial rod of any of claims 1-3, wherein, The first connecting plate and the second connecting plate are provided with mass blocks.
7. The metamaterial rod of any of claims 1-3, wherein, The two ends of the first inclined rod, the second inclined rod, the third inclined rod and the fourth inclined rod are pivotally connected through pivot shafts, and the pivot shafts are provided with rolling bearings between the first inclined rod, the second inclined rod, the third inclined rod and the fourth inclined rod.
8. The metamaterial rod of any of claims 1-3, wherein, The spring is a tension-compression spring.
9. The metamaterial rod of any of claims 1-3, wherein, The two ends of the spring are pivotally connected to the first inclined rod, the second inclined rod, the third inclined rod and the fourth inclined rod through connecting blocks.
10. The application of the metamaterial rod according to any one of claims 1-9 in the field of shock mitigation.