Piezoelectric metamaterial plate system combining high-order resonance circuit and structural defect

Abstract

The invention discloses a piezoelectric metamaterial plate system combining a high-order resonance circuit and structural defects, which is characterized in that the piezoelectric metamaterial plate system comprises a piezoelectric metamaterial plate, the piezoelectric metamaterial plate comprises a piezoelectric metamaterial substrate, a piezoelectric plate array is arranged on the surface of the piezoelectric metamaterial substrate, and the piezoelectric plate array is composed of a plurality of first piezoelectric plates; the geometric center of the piezoelectric metamaterial plate is provided with a defect structure, the defect structure comprises four cavities, a cross-shaped cantilever plate is arranged among the four cavities, four cantilevers of the cross-shaped cantilever plate are respectively provided with a second piezoelectric plate, and the central position of the cross-shaped cantilever plate is provided with a mass block; the defect structure is connected with a multi-mode parallel resonance circuit, the multi-mode parallel resonance circuit comprises a plurality of parallel branches, and each parallel branch comprises a current circulation branch and a resonance branch which are connected in series. According to the method, a plurality of defect modes can be generated, the frequency of the defect modes can be flexibly controlled, and the localization effect of the defect modes can be enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of energy saving and energy recovery, and in particular to a piezoelectric metamaterial plate system combining high-order resonant circuit and structural defects. BACKGROUND

[0002] Defect state is a special mode of metamaterials. By introducing material or geometric defects into the periodic structural units of metamaterials, defect states can be generated within the band gap, so that waves of specific frequencies propagate in the structural defect area and are suppressed in the area outside the structural defect, thereby achieving energy localization enhancement. However, the existing technology has significant limitations in generating defect modes. First, the number of defect modes is limited. Traditional methods usually adjust defect modes through single structural defects or simple first-order circuits, and can only generate a single defect state, which is difficult to meet the application requirements of multiple frequency bands. Second, the frequency adjustment range of the existing technology is limited, and it is difficult to achieve flexible control within a wide frequency band.

[0003] In existing research, some technologies achieve energy localization and vibration energy amplification by introducing structural defects into phononic crystals, but the number of defect modes is usually one. Another study constructs double structural defects and uses defect state splitting mechanism to generate two defect modes, thereby improving energy collection efficiency, but the frequency range is still very limited, which is difficult to adapt to diversified needs.

[0004] Piezoelectric metamaterials are a new type of intelligent structure, and due to their unique electromechanical coupling characteristics, they have important application potential in vibration suppression, energy harvesting and elastic waveguide fields. By modifying the circuit parameters of the local units connected to the piezoelectric metamaterial, defect states and energy concentration effects can also be generated using the defect state construction mechanism. However, the single resonance characteristics of traditional first-order circuits also limit the number of defect modes and the tuning ability, reducing the flexibility and efficiency of piezoelectric metamaterials in practical applications. SUMMARY

[0005] In order to solve the problems of limited number of defect modes and narrow frequency adjustable range in existing defect mode technology, the present application proposes a piezoelectric metamaterial plate system combining high-order resonant circuit and structural defects, which aims to solve the above problems through the synergistic effect of multi-modal parallel resonant circuit and structural defects.

[0006] The present application discloses a piezoelectric metamaterial plate system combining high-order resonant circuit and structural defects, which comprises a piezoelectric metamaterial plate, the piezoelectric metamaterial plate comprises a piezoelectric metamaterial substrate, the surface of the piezoelectric metamaterial substrate is provided with a piezoelectric sheet array, the piezoelectric sheet array is composed of a plurality of first piezoelectric sheets, and each first piezoelectric sheet is connected with a multi-modal parallel resonant circuit; The geometric center of the piezoelectric metamaterial plate is provided with a defect structure, the defect structure includes four cavities, a cross-shaped cantilever plate is arranged between the four cavities, a second piezoelectric sheet is arranged on each of the four cantilevers of the cross-shaped cantilever plate, and a mass block is arranged at the center position of the cross-shaped cantilever plate. The multi-modal parallel resonant circuit includes a plurality of parallel branches, and each parallel branch includes a current flow branch and a resonant branch in series.

[0007] Preferably, the gap between the first piezoelectric sheets is filled with an epoxy insulating layer to prevent short circuiting between adjacent first piezoelectric sheets.

[0008] Preferably, the piezoelectric metamaterial substrate and the mass block material are aluminum alloys.

[0009] Preferably, the first piezoelectric sheets and the second piezoelectric sheets are PZT-5H piezoelectric sheets.

[0010] Preferably, the electrode connection mode of the piezoelectric sheet array is as follows: Positive connection: the upper surface electrodes of all first piezoelectric sheets are connected to a common positive bus; Negative connection: the lower surface electrodes of all first piezoelectric sheets are connected to a common negative bus.

[0011] Preferably, each second piezoelectric sheet is connected in series with a resistor for energy harvesting.

[0012] Preferably, the current flow branch includes a first inductor and a capacitor in series, wherein n represents the number of branches, and N represents the number of target bandgaps.

[0013] Preferably, the resonant branch includes a second inductor and a resistor in series.

[0014] Preferably, the piezoelectric sheet array is equivalent to a voltage source and an equivalent capacitor in series.

[0015] Preferably, the bandgaps are generated by adjusting the parameters of the first inductor and the parameters of the second inductor in the multi-modal parallel resonant circuit, including the following steps: When the first inductor in the branch is tuned to , the current flow branch works at the electrical resonance frequency , and the current flow branch is approximately short-circuited;​ Second inductance Equivalent capacitance to form an electrical resonance, the electrical resonance frequency being , and a band gap is generated at the electrical resonance frequency .

[0016] The beneficial effects of the present application are: 1. Multiple defect modes: Compared with traditional single defect modes, the present application can generate multiple defect modes in a wide frequency band, improving application flexibility.

[0017] 2. Frequency adjustability: By adjusting the circuit and structure parameters, the defect mode frequency can be flexibly controlled to meet different needs.

[0018] 3. Frequency independent tuning: Unlike the mutual coupling of resonances in traditional high-order circuits, the present application can independently tune multiple band gaps, allowing precise control of defect mode frequencies in a wide frequency band, enhancing system flexibility.

[0019] 4. Energy enhancement: The vibration amplitude of the defect mode is significantly enhanced, effectively improving energy harvesting efficiency.

[0020] 5. Wide frequency band performance: The present application exhibits excellent band gap characteristics in multiple frequency ranges, suitable for complex scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a schematic diagram of a piezoelectric metamaterial plate and defect structure of an embodiment of the present application; Figure 2 is a schematic diagram of a multi-modal parallel resonance circuit of an embodiment of the present application.

[0022] The reference signs are as follows: 1-piezoelectric metamaterial substrate, 2-first piezoelectric sheet, 3-cavity, 4-cross-shaped cantilever plate, 5-mass, 6-second piezoelectric sheet. DETAILED DESCRIPTION

[0023] To make the purpose, technical solutions and advantages of the present application clearer, the following refers to the drawings and examples to further describe the present application in detail.

[0024] The present application discloses a piezoelectric metamaterial plate system combining high-order resonance circuits and structural defects, including a piezoelectric metamaterial plate, a defect structure and a multi-modal parallel resonance circuit.

[0025] As Figure 1As shown, the piezoelectric metamaterial plate includes a piezoelectric metamaterial substrate 1, which in this embodiment has a rectangular shape with dimensions of 260 mm x 200 mm x 1.5 mm and is made of aluminum alloy (density 2700 kg / m³) for good mechanical properties and processability. The piezoelectric metamaterial substrate 1 is uniformly divided into multiple rectangular units, each with dimensions of 30 mm x 20 mm and a gap of 10 mm between the rectangular units. The piezoelectric metamaterial substrate 1 is provided with a piezoelectric sheet array, which is composed of multiple first piezoelectric sheets 2, with one first piezoelectric sheet 2 covering each rectangular unit. The first piezoelectric sheets 2 are made of PZT-5H piezoelectric sheets, each with dimensions of 30 mm x 20 mm x 0.4 mm. The gaps between the first piezoelectric sheets 2 are filled with an epoxy resin insulating layer to prevent short circuits between adjacent first piezoelectric sheets 2. The piezoelectric metamaterial plate is excited by the piezoelectric metamaterial substrate 1 at one end, considering only transverse bending vibration. The positive poles of all first piezoelectric sheets 2, i.e., the upper surface electrodes (with consistent polarization direction), are welded to a common positive bus, and the negative poles of all first piezoelectric sheets 2, i.e., the lower surface electrodes, are welded to a common negative bus.

[0026] The geometric center of the piezoelectric metamaterial plate is provided with a defect structure, which includes four cavities 3 and a cross-shaped cantilever plate 4. As shown in the specific embodiment Figure 1 As shown, the cross-shaped cantilever plate 4 (made of aluminum plate, composite material plate, etc.) has a 2x2 unit rectangular cavity 3 between the piezoelectric metamaterial substrate 1, located in the four unit areas of (3, 3), (3, 4), (4, 3), and (4, 4) on the metamaterial substrate 1, with each missing unit (cavity 3) having dimensions of 30 mm x 20 mm. The cross-shaped cantilever plate 4 is arranged between the gaps of the 2x2 cavity 3 and communicates with the metamaterial substrate 1, and the four cantilevers of the cross-shaped cantilever plate 4 are each provided with a long strip-shaped second piezoelectric sheet 6 (PZT-5H piezoelectric sheet) with dimensions of 16 mm x 8 mm x 0.4 mm, arranged in a cross shape ("+" shape). The four second piezoelectric sheets 6 intersect at the center of the 2x2 area to form a "+" shape, with the center point located at the geometric center of the cross-shaped cantilever plate 4 (i.e., the square mass block 5). At the cross center point (i.e., the geometric center of the cross-shaped cantilever plate 4), a square mass block 5 is connected, made of aluminum alloy with dimensions of 15 mm x 15 mm x 15 mm. This mass block serves to increase the strain of the end of the cross-shaped cantilever plate 4 when vibrating, thereby improving energy harvesting efficiency. Each second piezoelectric sheet 6 is connected in series with a resistor for energy harvesting.

[0027] Each first piezoelectric sheet 2 is connected with a multi-modal parallel resonant circuit (the multi-modal parallel resonant circuit is a two-port circuit, and the upper and lower surfaces of each first piezoelectric sheet 2 are connected with one end of the multi-modal parallel resonant circuit of the circuit, respectively), and all the multi-modal parallel resonant circuits are independent of each other. The multi-modal parallel resonant circuit includes a plurality of parallel branches, and each parallel branch includes a current flow branch and a resonant branch connected in series. As shown in Figure 2 , each first piezoelectric sheet 2 is equivalent to a series connection of a voltage source and an equivalent capacitor . In this embodiment, a high-order resonant circuit (multi-modal parallel resonant circuit) composed of a current flow branch and a resonant branch is used to generate a plurality of decoupled bandgaps.

[0028] Figure 2 The L-C series circuit in the yellow part in the figure is a current flow branch, which includes a first inductor and a capacitor connected in series. The subscript , represents the number of the branch, and the number of the bandgap / modal is represented by . The current flow branch acts as an electrical switch. When the first inductor in the branch is tuned to , the current flow branch works at an electrical resonance frequency . At the electrical resonance frequency , the impedance of the current flow branch tends to zero, which is approximately a short circuit. In comparison, the impedance of the current flow branch at the resonant frequency tends to infinity, which is approximately an open circuit.

[0029] Figure 2 The L-R series circuit in the purple part in the figure is a resonant branch, which includes a second inductor and a resistor connected in series. The inductor is tuned in the manner of . When the current flow branch behaves as a short circuit, the second inductor forms an electrical resonance with the equivalent capacitor inside the first piezoelectric sheet 2, and the electrical resonance frequency is . According to the working principle of the piezoelectric metamaterial structure, a bandgap will be generated at the frequency . Therefore, by combining the electrical switch function of the current flow branch and the resonance function of the resonant branch, the multi-modal parallel resonant circuit can create independent bandgaps that are decoupled from each other at by adjusting the parameters of the first inductor and the second inductor in the multi-modal parallel resonant circuit.

[0030] A central 2x2 empty cell region (65mmx65mm) forms a structural stiffness discontinuity, which creates a defect state within the bandgap frequency range of the metamaterial plate. When the external excitation frequency matches the defect state frequency, the vibration energy is localized around the cross-shaped cantilevered plate 4 region (near the geometric center) surrounding the empty cell (cavity 3). Four long strip-shaped second piezoelectric patches 6 are arranged in a cross shape, covering the empty cell gap, and directly capturing the high strain region caused by the defect state. The second piezoelectric patches 6 generate electric charges due to strain gradient under bending vibration (positive piezoelectric effect), and the output voltage amplitude is improved by the reverse polarization pairing (the polarization directions of adjacent cells are opposite). On the basis of generating multiple tunable bandgaps, local mutations (spatial defects) of parameters / configurations in the circuit or structure can introduce defect states within a specific bandgap. This defect (such as the stiffness discontinuity caused by the cantilever beam structure) causes the vibration energy that is originally prohibited by the bandgap to be strongly localized at the defect state frequency. At the same time, the energy is highly concentrated in the defect region (such as the tip of the cantilever beam), resulting in a prominent amplitude vibration and strain at this location, which has important applications in the fields of sensing, energy harvesting, etc.

[0031] The current flow branch decouples different order electric resonances, ensuring that each resonance branch only works at its specified frequency. For example, when (ω = 500 x 2 ), the impedance amplitude (Z) of a tuning branch drops to near zero, isolating the corresponding resonance branch. Reducing the capacitance can enhance the sharpness of this switching feature. This decoupling ensures robustness, and a disturbance in the inductance of one branch will not affect the other branches, maintaining the normal operation of the remaining branches. Multiple bandgaps can be independently tuned, unlike the situation in traditional high-order circuits where resonances are coupled to each other. By allowing precise control of the defect mode frequency within a wide frequency band, the flexibility of the system is enhanced. And due to the robustness provided by the decoupled branches, the reliability in complex vibration scenarios is improved. In summary, the embodiments of the present application provide a piezoelectric metamaterial plate system combining high-order resonant circuits and structural defects, including a piezoelectric metamaterial plate, a defect structure, and a multi-modal parallel resonant circuit. By introducing a multi-modal parallel resonant circuit, any number of adjustable local resonance bandgaps can be achieved. At the same time, due to the local stiffness discontinuity caused by the structural defect in the cross-shaped cantilevered plate 4 region, the bandgap formation mechanism is destroyed at the defect, thereby re-creating a passband for the propagation of elastic waves within multiple bandgaps. Elastic waves with frequencies conforming to the passband will converge at the structural defect, forming a defect mode. Utilizing the energy concentration effect under the defect mode, the strain of the cross-shaped cantilevered plate 4 will be significantly improved, thereby utilizing the piezoelectric patches attached to its surface for wide-frequency vibration energy harvesting.

[0032] In summary, the embodiments of the present application provide a piezoelectric metamaterial plate system combining high-order resonant circuits and structural defects, including a piezoelectric metamaterial plate, a defect structure, and a multi-modal parallel resonant circuit. By introducing a multi-modal parallel resonant circuit, any number of adjustable local resonance bandgaps can be achieved. At the same time, due to the local stiffness discontinuity caused by the structural defect in the cross-shaped cantilevered plate 4 region, the bandgap formation mechanism is destroyed at the defect, thereby re-creating a passband for the propagation of elastic waves within multiple bandgaps. Elastic waves with frequencies conforming to the passband will converge at the structural defect, forming a defect mode. Utilizing the energy concentration effect under the defect mode, the strain of the cross-shaped cantilevered plate 4 will be significantly improved, thereby utilizing the piezoelectric patches attached to its surface for wide-frequency vibration energy harvesting.

[0033] ​The foregoing presents the basic principles of the present application, the main features and the advantages of the present application. It should be understood by those skilled in the art that the present application is not limited by the above-mentioned embodiments, and the above-mentioned embodiments and descriptions in the specification are only to illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection of the present application is defined by the appended claims and their equivalents.

Claims

1. A piezoelectric metamaterial panel system combining high order resonant circuits with structural defects, characterized by, The piezoelectric metamaterial plate comprises a piezoelectric metamaterial substrate (1) provided with an array of piezoelectric sheets on the surface, the array of piezoelectric sheets is composed of a plurality of first piezoelectric sheets (2), and each first piezoelectric sheet (2) is connected with one multi-modal parallel resonant circuit; A defect structure is arranged at the geometric center of the piezoelectric metamaterial plate, the defect structure comprises four cavities (3), and a cross-shaped cantilever plate (4) is arranged between the four cavities (3), four cantilever arms of the cross-shaped cantilever plate (4) are each provided with a second piezoelectric sheet (6), and a mass block (5) is arranged at the center position of the cross-shaped cantilever plate (4); The multi-modal parallel resonant circuit comprises a plurality of parallel branches, each parallel branch comprises a current flow branch and a resonant branch connected in series.

2. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 1, wherein, The gap between the first piezoelectric sheets (2) is filled with an epoxy insulating layer to avoid short circuit of adjacent first piezoelectric sheets (2).

3. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 2, wherein, The piezoelectric metamaterial substrate (1) and the mass block (5) are made of aluminum alloy.

4. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 3, wherein, The first piezoelectric sheets (2) and the second piezoelectric sheets (6) are PZT-5H piezoelectric sheets.

5. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 4, wherein, The electrode connection mode of the array of piezoelectric sheets is as follows: Positive connection: the upper surface electrodes of all the first piezoelectric sheets (2) are connected to a common positive bus; Negative connection: the lower surface electrodes of all the first piezoelectric sheets (2) are connected to a common negative bus.

6. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 5, wherein, Each second piezoelectric sheet (6) is connected in series with one resistor for energy collection.

7. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 6, wherein, The current circulation branch includes a first inductor in series and a capacitor , , denotes the number of branches, is the number of target bands.

8. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 7, wherein, The resonance branch comprises a second inductance in series and a resistance .

9. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 8, wherein, The piezoelectric sheet array is equivalent to a series voltage source and an equivalent capacitance .

10. The piezoelectric metamaterial panel system incorporating high order resonant circuits with structural defects of claim 9, wherein, A bandgap is generated by adjusting parameters of a first inductance and parameters of a second inductance in the multi-modal parallel resonant circuit, comprising the steps of: When the branch with the first inductance is tuned to , the current flow branch works at the electrical resonance frequency , the current flow branch is approximately short-circuited; Second inductor With an equivalent capacitance Forming an electrical resonance, the electrical resonance frequency being And a bandgap at the electrical resonance frequency Is generated.

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