A gradient-coupled-based elastic wave strong localization plate beam structure

Abstract

The application relates to the technical field of elastic wave metamaterials, in particular to an elastic wave strong localization plate beam structure based on gradient coupling. The structure comprises multiple resonance units, a stacking structure and a truncated defect structure; the resonance units are sequentially arranged along a first direction to form scale coupling chains, and the coupling stiffness between adjacent resonance units monotonously changes along the direction according to a geometric scale law; the stacking structure is formed by stacking multiple scale coupling chains along a second direction; the truncated defect structure is located at the right end of the middle layer of the stacking structure, and a local vacancy is formed by removing a resonance unit or a connecting plate at the end of the middle layer, which is used for inducing an enhanced localized state. The gradient coupling mechanism is adopted, the wave function space redistribution effect generated by the geometric scale law is utilized, the elastic wave energy shows stronger localization characteristics at the defect, and the localization degree is significantly better than that of a traditional SSH model. Through the synergistic effect of the gradient coupling and the dislocation-induced defect state, efficient localization enhancement of the elastic wave energy is realized, and the application is suitable for the fields of vibration energy collection, high-sensitivity sensing and elastic wave signal processing.

Description

Technical Field

[0001] This invention relates to the field of elastic wave metamaterials, and in particular to an elastic wave strongly localized plate-beam structure based on gradient coupling. Background Technology

[0002] Traditional elastic wave localization techniques primarily rely on periodic phonon crystals or resonant cavity arrays to confine elastic waves to specific regions by introducing defect states or boundary states. However, these methods typically require precise design of multi-period unit structures, resulting in large device sizes, complex manufacturing processes, and often fixed localization frequencies, making it difficult to flexibly adapt to different operating frequency bands. In recent years, the development of topological elastic waves has provided new ideas for localization, such as achieving topological boundary states through alternating coupling strengths based on the Su-Schrieffer-Heeger (SSH) model, but its local energy concentration is limited. Most existing elastic wave localization devices still rely on complex superatomic configurations or strictly periodic arrangements, making it difficult to simultaneously achieve structural simplicity with high robustness and high energy concentration. Therefore, there is an urgent need to develop a novel control device that is simple in structure, easy to fabricate, and capable of achieving enhanced localization of elastic waves. Summary of the Invention

[0003] The purpose of this invention is to address the problems existing in the background technology and the shortcomings of traditional elastic wave localization devices. It proposes a gradient-coupled, strongly localized plate-beam structure for elastic waves, which efficiently confines elastic wave energy to a specific substrate, improving local energy concentration and anti-interference capability, thus achieving enhanced localized capture of elastic waves. Because the designed device uses a simple plate-beam combination configuration, it avoids complex periodic metamaterial or multi-layer stacking processes, and features a compact structure, low manufacturing cost, significant localization effect, and strong robustness. It can be widely used in vibration energy harvesting, high-sensitivity sensing, and elastic wave logic devices.

[0004] The device first constructs a one-dimensional scaled coupling chain, in which the coupling stiffness between adjacent resonant units changes monotonically according to a geometric scaling law, replacing the alternating coupling mode of the SSH model. The SC chain achieves a 44.6% increase in localized energy density compared to SSH. Furthermore, the SC chain is stacked in a vertical array of seven layers, with a plate truncated at the rightmost end of the fourth layer. Utilizing the defect mode induced by the truncation boundary, the localized energy density of the defect state in the stacked structure is increased by 33.9% compared to the similarly stacked SSH structure. Due to the simplicity of the designed SC chain structure, the ease of fabrication of the stacked and truncated configurations, and the significantly higher localized energy concentration compared to existing SSH-based localized states, this device can be widely applied in fields such as vibration energy harvesting, high-sensitivity sensing, and elastic wave signal processing.

[0005] According to the technical solution of the present invention, a first aspect of the present invention provides a strongly localized elastic wave plate-beam structure based on gradient coupling, comprising a plurality of resonance units, a stacked structure and a truncated defect structure; A plurality of resonance units are sequentially arranged along a first direction to form a scaling coupling chain, and the coupling stiffness between adjacent resonance units changes monotonically along the direction according to a geometric scaling law; the scaling coupling chain comprises resonance units formed of square aluminum plates and a spring-like proton structure formed of elastic beams connecting each aluminum plate.

[0006] The stacked structure is formed by stacking a plurality of scaling coupling chains in parallel along a second direction; The truncated defect structure is located at the rightmost end of the middle layer of the stacked structure, and forms a local vacancy by removing a resonance unit or a connecting plate at the end of the middle layer, which is used to induce and generate an enhanced localized state.

[0007] Preferably, the number of stacked layers of the stacked structure is an odd number of layers.

[0008] Preferably, the geometric scaling law is a geometric sequence, and the decreasing formula of coupling strength is: , wherein is the coupling strength of each beam, is the reference coupling strength, s is a scaling coefficient, and s satisfies 0<s<1 or s>1.

[0009] Preferably, the common ratio of the geometric scaling law is 0.34, and the reference coupling strength is 130.

[0010] Preferably, the scaling coupling chain comprises five resonance units, the connection strength between adjacent units decreases from left to right in sequence with a common ratio of 0.34, and the specific values of each coupling strength are: 130; 44.2; 15.02; 5.11; the magnitude of the coupling strength is achieved by setting the geometric parameters of each beam; The geometric parameters of each beam, including the width w of the beam, the length l and the position height h relative to the center line of the plate, jointly control the magnitude of the coupling strength.

[0011] Preferably, in the stacked structure, the scaling coupling chains are parallel to each other and the interlayer coupling strength is weaker than the coupling strength in the x direction, that is, the interlayer coupling is weak coupling.

[0012] Preferably, in a seven-layer stacked structure, the truncated defect structure is located at the rightmost end of the fourth layer, so that the number of resonance units in the fourth layer is one less than that of the other six layers, forming a stepped truncated surface.

[0013] Preferably, the resonance unit is an aluminum alloy straight beam structure, the substrate is made of aluminum alloy, and the overall device excites elastic waves through an exciter.

[0014] Preferably, in the stacked structure, the energy concentration of the enhanced local state induced by the truncated defect is more than 1.4 times that of the defect local state in the SSH model with the same parameters.

[0015] The second aspect of the present invention provides an application of an elastic wave enhancement localization structure based on scale coupling chain stacking and defect-induced elastic wave enhancement. Using the above-mentioned elastic wave enhancement localization structure, the exciter is arranged at the leftmost end of the middle layer to excite broadband elastic waves. Through the wave function spatial redistribution effect generated by geometric scaling law gradient coupling and the strong defect mode induced by local truncation in the multi-layer stack, the elastic wave energy is highly confined to the vicinity of the truncation region, thereby realizing the enhanced capture and detection of elastic wave signals. It is applicable to the fields of vibration energy harvesting, high-sensitivity sensing and elastic wave signal processing.

[0016] Compared with the prior art, the present invention has the following beneficial technical effects: 1. This invention utilizes the SC chain to replace the alternating coupling of the SSH model through geometric scaling law coupling, which improves the boundary local state energy density by 44.6% compared to SSH; dislocation defects are introduced into the stacked structure to localize the energy, thereby realizing the enhanced localization of elastic waves in the two-dimensional structure, and the defect state energy density is improved by 33.9% compared to the SSH model with the same parameters.

[0017] 2. This invention utilizes SC chains and only requires adjusting the connection stiffness between adjacent units (such as changing the width, thickness, or position of the connecting bridge), without the need for complex periodic superatoms or multi-layered staggered configurations; the stacked structure is a simple 7-layer parallel arrangement, and truncation only requires removing a plate at the end of the fourth layer, resulting in low overall processing cost and good consistency.

[0018] 3. Starting from the SC chain, this invention can be easily extended to stacking in the y direction, and the cut-off position, number of layers, and cut-off shape can all be adjusted as needed, providing a multi-degree-of-freedom optimization space for different application scenarios.

[0019] 4. The local mechanism based on gradient coupling and truncation defects is insensitive to process errors and local disturbances, and can still maintain a stable local enhancement effect in strong scattering or non-uniform environments. Attached Figure Description

[0020] Figure 1 This is a top view of the chain-like structure of the elastic wave localization plate-beam structure of the present invention; Figure 2 This is a schematic diagram of the geometric parameters of the connecting beam of the present invention; Figure 3 Numerical calculations were performed on the boundary state wave function probability density distribution of the chain structure of the elastic wave localized plate beam structure of this invention and the traditional SSH chain structure. Figure 4The present invention provides a COMSOL simulation of the energy localization phenomenon in the chain-like structure of the elastic wave localized plate-beam structure. Figure 5 This is the frequency response diagram of the chain structure of the elastic wave localized plate-beam structure of the present invention; Figure 6 This is a top view of the stacked defect structure of the elastic wave localized plate-beam structure of the present invention; Figure 7 Numerical calculation of the boundary state wave function probability density distribution of the stacked defect structure of the elastic wave localized plate beam structure of the present invention and the traditional SSH stacked defect structure. Figure 8 This invention provides a COMSOL simulation of the energy localization phenomenon in the stacked defect structure of the elastic wave localized plate-beam structure. Figure 9 This is a frequency response diagram of the stacked defect structure of the elastic wave localized plate-beam structure of the present invention.

[0021] Reference numerals: 1. Defect region; 2. Localized energy region. Detailed Implementation

[0022] Example 1 like Figure 1 As shown, the present invention proposes an elastic wave strongly localized plate-beam structure based on gradient coupling, which includes multiple resonant units, a stacked structure, and a truncated defect structure. Several resonant units are arranged sequentially along the first direction to form a scaling coupling chain, and the coupling stiffness between adjacent resonant units varies monotonically along this direction according to the geometric scaling law. The stacked structure consists of multiple scale coupling chains stacked parallel to each other along the second direction; The truncated defect structure is located at the rightmost end of the middle layer of the stacked structure. A local void is formed by removing a resonant unit or connecting plate at the end of the middle layer, which is used to induce the generation of enhanced local states.

[0023] To facilitate understanding of the solution in this application, a specific case will be used for detailed explanation below: The plate-beam structure specifically includes a resonant substrate and connecting beams with different coupling strengths.

[0024] The SC chain structure consists of multiple resonant units arranged sequentially along the x-direction, with the coupling stiffness between adjacent resonant units varying monotonically along the x-direction according to a geometric scaling law. In this embodiment, the SC chain is composed of a square aluminum alloy plate (80 mm long, 80 mm wide, and 3 mm thick) and connecting beams whose coupling strength varies according to a gradient law. Figure 1 As shown, there are 5 elements from left to right. The coupling strength parameters of the connecting beams are as follows: 130; 44.2; 15.02; 5.11. It exhibits a monotonically decreasing distribution.

[0025] Numerical calculations using a tight-binding model were performed to calculate the boundary state wave function probability density of the SC model, and the result was compared with that of a conventional SSH chain with the same baseline coupling strength and scaling factor. Figure 3 As shown, the boundary local state energy density of the SC chain is 44.6% higher than that of the SSH chain. Figure 4 and Figure 5 This demonstrates the energy localization phenomenon of the SC chain, showing that the energy is completely confined to a specific substrate. This embodiment verifies the significant enhancement effect of a one-dimensional plate-beam structure under the scaling coupling mechanism on localized energy.

[0026] Example 2 like Figure 6 As shown, based on the SC chain structure of Example 1, seven identical SC chains are stacked parallel to each other along the y-direction to form a stacked structure. The structural parameters of each SC chain layer are completely consistent with those of Example 1, with a layer spacing of 75 mm and weak coupling between layers. In addition, a truncated defect is set at the rightmost end of the fourth layer (i.e., the middle layer) of the two-dimensional stacked structure: the last resonant unit and its connecting beam of the fourth layer are removed, so that the number of units in the fourth layer becomes 4 (one less than the other four layers), forming a stepped truncated section. The remaining four layers retain 5 complete units, and the size of the truncated gap is consistent with the removed unit (length 80 mm, width 80 mm). Among them, 1 is the defect region, and 2 is the energy localization region.

[0027] Numerical calculations using the tight-binding model were performed to determine the probability density of the defect state wavefunction in the SC stack defect state model, and the result was compared with that of the SSH stack defect state model using the same baseline coupling strength and scaling factor. Figure 7 As shown, the energy density of the defect local states in the SC stacked defect structure is 33.9% higher than that in the SSH model. Figure 8 and Figure 9 This demonstrates the energy localization phenomenon of the SC defect state structure, showing that the energy is completely confined to the substrate at the defect location. This embodiment verifies the significant enhancement effect of the defect state plate-beam structure under the scaling coupling mechanism on localized energy.

[0028] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A plate-beam structure with strong localization of elastic waves based on gradient coupling, characterized in that, It includes multiple resonant units, stacked structures, and truncated defect structures; Several resonant units are arranged sequentially along the first direction to form a scaling coupling chain, and the coupling stiffness between adjacent resonant units varies monotonically along this direction according to the geometric scaling law. The stacked structure consists of multiple scale coupling chains stacked parallel to each other along the second direction; The truncated defect structure is located at the rightmost end of the middle layer of the stacked structure. A local void is formed by removing a resonant unit or connecting plate at the end of the middle layer, which is used to induce the generation of enhanced local states.

2. The elastic wave strongly localized plate-beam structure based on gradient coupling according to claim 1, characterized in that, Number of stacking layers in a stacked structure The number of layers is odd.

3. The elastic wave strongly localized plate-beam structure based on gradient coupling according to claim 1, characterized in that, The geometric scaling law follows a geometric sequence, and the formula for decreasing coupling strength is: , where is the coupling strength of each beam, is the reference coupling strength, s is the scaling coefficient, and s satisfies 0<s<1 or s>1.

4. The elastic wave strongly localized plate-beam structure based on gradient coupling according to claim 1, characterized in that, The common ratio of the geometric scaling law is 0.34, and the reference coupling strength is... It is 130.

5. The elastic wave strongly localized plate-beam structure based on gradient coupling according to claim 1, characterized in that, The scaling coupling chain contains five resonant units. The connection strength between adjacent units decreases from left to right by a common ratio of 0.

34. The specific coupling strengths are: 130; 44.2; 15.02; 5.

11. The magnitude of the coupling strength is achieved by setting the geometric parameters of each beam. The geometric parameters of each beam, including its width w, length l, and height h relative to the centerline of the plate, collectively control the magnitude of the coupling strength.

6. The elastic wave strongly localized plate-beam structure based on gradient coupling according to claim 1, characterized in that, In a stacked structure, the scaling coupling chains are parallel to each other and the interlayer coupling strength is weaker than the coupling strength in the x-direction.

7. The elastic wave strongly localized plate-beam structure based on gradient coupling according to claim 1, characterized in that, In the seven-layer stacked structure, the truncated defect structure is located at the rightmost end of the fourth layer, which makes the number of resonant units in the fourth layer one less than the other six layers, forming a stepped truncated surface.

8. The elastic wave strongly localized plate-beam structure based on gradient coupling according to claim 1, characterized in that, The resonant unit is an aluminum alloy straight beam structure, the substrate is made of aluminum alloy, and the whole device excites elastic waves through an exciter.

9. The elastic wave strongly localized plate-beam structure based on gradient coupling according to claim 1, characterized in that, In the stacked structure, the energy concentration of the enhanced local states induced by the truncation defect is more than 1.4 times that of the defect local states in the SSH model with the same parameters.

10. An application of a localized elastic wave enhancement structure based on scale-coupled chain stacking and defect-induced elastic waves, characterized in that, Using the elastic wave enhancement localization structure described in any one of claims 1-9, the exciter is arranged at the leftmost end of the middle layer to excite broadband elastic waves. Through the wave function spatial redistribution effect generated by the geometric scaling law gradient coupling and the strong defect mode induced by local truncation in the multi-layer stack, the elastic wave energy is highly confined to the vicinity of the truncation region, thereby realizing the enhanced capture and detection of elastic wave signals. It is applicable to the fields of vibration energy harvesting, high-sensitivity sensing and elastic wave signal processing.

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