Active metamaterial beam based on temperature regulation

Abstract

The application discloses an active metamaterial beam based on temperature regulation, which comprises a metamaterial beam body and a plurality of "j" shaped beam cells arranged in a zigzag shape and formed by arching upward from the metamaterial beam body, wherein an actuator is arranged on the opening of the beam cell and the opening between the beam cells, and the actuator is connected with the sidewalls on both sides of the opening; the actuator is an elastic component, a damping component or a combination of the elastic component and the damping component; the stiffness coefficient and / or the damping coefficient of the actuator can change with the change of temperature, so that the active metamaterial beam can adapt to a wider application scenario.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunable metamaterials, and particularly relates to an active metamaterial beam based on temperature regulation. Background Art

[0002] Currently, many novel phononic crystals, metamaterials, and / or metasurfaces have been proposed and implemented for controlling elastic waves in structures, especially for controlling flexural waves in beam and plate structures. Currently, passive metamaterials proposed for flexural waves in beams and / or plates include columnar types, zigzag beam types, multi-material types, stepped beam types, variable-thickness beam types, and various metamaterials based on the "rainbow" effect, etc. However, these passive metamaterials have an obvious drawback, that is, the working frequency range is limited, which seriously hinders their applications.

[0003] In the prior art, two technical routes have emerged to solve the above problems. One is the topology optimization technology. Although this technology has been successfully applied to many phononic crystals and metamaterials, for metamaterials and phononic crystals applied to controlling flexural waves in beams and plates, the corresponding topology optimization work is still relatively few. Although the optimized phononic crystals and metamaterials have a wider working frequency range, they are still no longer adjustable after being fabricated.

[0004] The other technical route is the active control technology. Based on this technology, phononic crystals and metamaterials can obtain a wider working frequency range. Active regulation can be achieved through various driving strategies, such as using electric, magnetic, optical, mechanical force, and thermal driving strategies. For the control of flexural waves, based on the above various driving strategies, a large number of tunable metamaterial beams / plates have been proposed. It should be noted that different driving strategies are beneficial to different application scenarios, and no single strategy can be applicable to all application scenarios. Therefore, more tunable acoustic crystals and metamaterials need to be designed and proposed to adapt to a wider range of application scenarios. Summary of the Invention

[0005] The present invention aims to provide an active metamaterial beam based on temperature regulation to adapt to a wider range of application scenarios.

[0006] The active metamaterial beam based on temperature regulation in the present invention includes a metamaterial beam body, and a plurality of "Ji"-shaped beam cells arranged in a zigzag shape and formed by the upward arching of the metamaterial beam body. Among them, actuators are provided at the openings of the beam cells and at the openings between the beam cells, and the actuator is simultaneously connected to the two side walls at the opening.

[0007] The actuator is an elastic component, a damping component, or a combination of an elastic component and a damping component; the stiffness coefficient and / or damping coefficient of the actuator can change with the change of temperature.

[0008] Furthermore, the actuator is positioned across the opening.

[0009] Furthermore, the actuator is made of a thermosensitive polymer.

[0010] Furthermore, the thermosensitive polymer is the 3D printing material "VeroPureWhite".

[0011] Furthermore, the material thickness of the beam cell is consistent with that of the metamaterial beam body.

[0012] Furthermore, the metamaterial beam body is made of metal.

[0013] Furthermore, the metamaterial beam body is made of aluminum alloy.

[0014] Furthermore, all the turning points on the beam cell are right angles.

[0015] Furthermore, the width of the beam cell is a = 2(h + l), where h represents the thickness of the metamaterial beam body and l is the width inside the upper arch of the beam cell.

[0016] Furthermore, the total height of the beam cell is 3 to 5 times the thickness of the metamaterial beam body.

[0017] Furthermore, the number of beam cells is at least 6.

[0018] An actuator applicable to the aforementioned temperature-controlled active metamaterial beam.

[0019] This invention proposes a novel tunable metamaterial beam that utilizes the change in stiffness and damping coefficients of its actuators with temperature to actively control the overall band structure of the metamaterial beam.

[0020] In some embodiments, the thermosensitive polymer is used to manufacture the actuator, whose mechanical behavior can be regulated by temperature. Compared with existing tunable metamaterial beams, the metamaterial beam of this invention can be passively and actively regulated based on changes in ambient temperature, or it can be regulated based on active heating and cooling, which expands the application range of the metamaterial beam of this invention. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the analytical model of the temperature-controlled active metamaterial beam (a) and its beam cell (b) in an embodiment of the present invention.

[0022] Figure 2 Different α values ​​in the embodiments of the present invention k A schematic diagram of the real (a) and imaginary (b) parts of the band structure of the metamaterial beam under the condition H = 4h.

[0023] Figure 3 The lower limit (a) and upper limit (b) of the first bandgap of metamaterial beams with different H values ​​in the embodiments of the present invention vary with α. k And the changing curve.

[0024] Figure 4 for Figure 2 A schematic diagram of the eigenmodes of the beam cell at midpoints A(a), B(b), and C(c).

[0025] Figure 5 Different α values ​​in the embodiments of the present invention C A schematic diagram of the real (a) and imaginary (b) parts of the band structure of the metamaterial beam under the condition H = 4h.

[0026] Figure 6 The graph shows the storage modulus (left) and loss coefficient (right) of the 3D printing material "VeroPureWhite" measured in this embodiment of the invention as a function of temperature at different excitation frequencies.

[0027] Figure 7 This is a two-dimensional structural diagram of the actuator (a) made of the material "VeroPureWhite" and the metamaterial beam (b) integrating the actuator in an embodiment of the present invention.

[0028] Figure 8 This is a schematic diagram of the real part (a) and imaginary part (b) of the band structure of the metamaterial beam with integrated actuator in an embodiment of the present invention at different temperatures.

[0029] Figure 9 The images shown are actual photographs of the experimental setup in this embodiment of the invention, wherein (a) shows the experimental sample prepared, (b) shows the entire experimental apparatus used to measure the transmission spectrum, and (c) shows the measured temperature inside the heating container and the measured temperature in the room at different specified temperatures.

[0030] Figure 10 This is a schematic diagram of the transmission spectrum of metamaterial beams without actuators with different H values ​​measured in an embodiment of the present invention.

[0031] Figure 11 This is a schematic diagram of the transmission spectrum of metamaterial beams with different H values ​​measured in the embodiments of the present invention at room temperature (≈27℃) and 47℃.

[0032] Figure 12 This is a comparison of the transmission spectra of metamaterial beams with different H values ​​at 75.5°C and 27.5°C during the process of raising the temperature to above the glass transition temperature and then cooling it to room temperature in an embodiment of the present invention, with the transmission spectra of the corresponding metamaterial beams at 47°C and 26.6°C in the third heating-cooling cycle. Detailed implementation mode

[0033] The analysis model of the active metamaterial beam based on temperature regulation in this embodiment is as shown in Figure 1 part (a). It includes the metamaterial beam body and multiple "Ji"-shaped beam cells arranged in a zigzag shape and formed by the upward arching of the metamaterial beam body. In the figure, the number of "Ji"-shaped beam cells is selected but not limited to 6. Actuators are arranged at the openings of the beam cells and the openings between the beam cells. In the model, the actuators are equivalent to parallel spring components and damping components; the actuators are arranged across the openings and are simultaneously connected to the side walls on both sides of the openings.

[0034] In the figure, the variables h, l, H, and a respectively represent the thickness, the gap width at the opening of the beam cell, the total height, and the lattice constant (the total width of the beam cell). The spring stiffness and damping coefficient are respectively denoted as k and c. Based on such a design, if the spring stiffness k and the damping coefficient c can be changed, the behavior of the metamaterial beam in this embodiment is adjustable.

[0035] In order to characterize the above-mentioned adjustable metamaterial beam, in this embodiment, the spectral element analysis method (SEM) simulation calculation is used to obtain the complex band structure of the metamaterial beam. Figure 1 Part (b) is the beam cell model used in the SEM calculation in this embodiment. Each straight line represents an Euler-Bernoulli beam, and the numbers 1-8 represent 8 nodes. The entire beam cell model includes five Euler-Bernoulli beam components, three spring components, and three damping components. Other parameter settings include that the parameters h and l are selected as h = 2 mm and l = 4 mm, and the width b along the y-axis direction in the figure is set to 10.0 mm unless otherwise specified. The lattice constant is a = 2×(h + l) = 12.0 mm; the main material is selected as aluminum alloy (6061), its Young's modulus is E₁ = 70.0 GPa, the Poisson's ratio is ν = 0.33, and the mass density is ρ = 2700.0 kg / m 2 . The spring stiffness and damping coefficient are respectively denoted as k and c. The spring stiffness coefficient k is normalized to α k = k / k cri , where k cri = E₁A / l, and A is the cross-section of the main beam. The damping coefficient c is normalized to

[0036] In this embodiment, under different α k conditions, the complex band structures of the adjustable metamaterial beam with different H values are calculated. Among them, α c is fixed at . The results represented by H = 4h are as shown in Figure 2 . The shaded area represents the forbidden band. The results show that the bandwidth of the first forbidden band (1st gap) decreases with the increase of α k . Specifically, when αk From 5.0×10 -4 When the α value is increased to 2.0 × 10⁻², the bandwidth of the first bandgap decreases from 21.47 kHz to 9.16 kHz, while the second bandgap (the 2nd gap in the figure) hardly changes with α. k And change. Furthermore, when α k When the value reaches the critical value, a new forbidden band will appear at the position between the original first forbidden band and the second forbidden band (re-labeled as the third forbidden band in the figure), and the width of this forbidden band will increase with α. k The energy band structure of metamaterial beams with different H values ​​also exhibits a similar pattern, but for simplicity, it is not discussed here.

[0037] Furthermore, under different H values, the lower and upper limits of the first bandgap vary with α. k The changing curve is as follows Figure 3 As shown. Figure 3 As shown in part (a), with α k As α increases, the lower limit of the first forbidden band shows an upward trend. Furthermore, the lower limit affects α. k There is a sensitive area; and such Figure 4 As shown in section (b), the upper limit of the first bandgap is almost unaffected by α. k The effects of this. Therefore, the results plotted in part (b) of the figure can be used to guide the selection of metamaterial beams and / or the design of suitable spring component characteristics in this embodiment. Figure 4 The text appears to be a mix of Chinese characters and symbols, possibly related to a document or document. A direct translation wouldn't be meaningful without further context or clarification. Figure 2 The intrinsic modes at points A, B, and C on the three lowest dispersion curves in part (c) explain the above phenomenon well. The results in the figure show that the spring element deforms less at point A and more significantly at point B. However, the spring hardly deforms at point C. Figure 4 The eigenmodes shown explain well why the upper limit of the first bandgap does not change with the spring stiffness, while the lower limit changes with α. k The increase shifts towards higher frequencies.

[0038] To demonstrate the influence of the damping coefficient on the behavior of metamaterial beams, simulations were also performed at different α values. c Under horizontal conditions, the complex energy band structure of metamaterial beams with different H values, and α k Set to a very small value, such as α k =3.0 × 10 -5 For example, Figure 5The results are presented for the case of H = 4h. The results show that damping has a significant impact on evanescent waves, with a greater effect on the real part of the evanescent wave vector than on the imaginary part. Specifically, the propagation term (real part of the wave vector) of the evanescent wave increases significantly with increasing damping, while the attenuation term (imaginary part of the wave vector) decreases slightly. Traveling waves are relatively insensitive to damping, especially with small damping values; therefore, the bandgap is almost unaffected by damping. When the damping exceeds a critical value, such as α in this example... c =1.0×10 -3 The band gap begins at the intersection of the lower limit of the first bandgap line from bottom to top in the diagram, widening the frequency range of the high attenuation region. As the damping increases, this gap widens, which is also reflected in... Figure 5 These findings are consistent with previous work regarding the degree of separation of the eight curves shown in section (a).

[0039] The above parameter analysis confirms that Figure 1 The band structure of the metamaterial beam proposed in this study is highly sensitive to k and c. Therefore, as long as k and c can be actively controlled, the band structure of the metamaterial beam can be controlled.

[0040] To achieve the desired active control mechanism, this embodiment further selects, but is not limited to, the 3D printing material "VeroPureWhite" to manufacture the exemplary actuator (which can be viewed as a spring and damping component). The reason behind this is that, as long as the temperature remains below the corresponding glass transition temperature, the stored Young's modulus and dissipation factor of this material can be reversibly adjusted by temperature. Furthermore, even actuators with complex structures can be 3D printed using this material. However, in practice, other materials, such as some other thermosensitive polymer materials, can also be used to manufacture actuators depending on specific needs.

[0041] First, the storage modulus (Young's modulus) and loss factor of the "VeroPureWhite" material were measured using a dynamic mechanical analyzer (DMAQ850, USA). The test specimens were 3D-printed sheets measuring 18 × 4 × 1.5 mm. During the measurement, one end of the specimen was fixed, and the temperature was raised from room temperature to 48°C. Each specimen underwent 3-5 cycles of heating and cooling to check reversibility. The measurement results are as follows: Figure 6 As shown, the energy storage modulus and loss factor change significantly with temperature, and this change is almost reversible within the temperature range of interest. Therefore, using this material, the envisioned active control mechanism can be realized based on temperature control.

[0042] In this embodiment, an exemplary actuator design based on the "VeroPureWhite" material is as follows: Figure 7As shown in section (a), the adjustable metamaterial beam integrating this actuator is as follows: Figure 7 As shown in section (b). To characterize the metamaterial beam at different temperatures, the band structure of the metamaterial beam was calculated based on representative cells using finite element analysis (FEM). In the numerical simulation, the actuator was tested using the storage modulus and loss factor at a frequency of 200.0 Hz. Furthermore, the Poisson's ratio of the "VeroPureWhite" material was measured to be ν² = 0.4185, and the measured mass density was ρ² = 1185 kg / m³. The main sawtooth structure (excluding the actuator) was made of aluminum alloy (6061).

[0043] For ease of explanation, Figure 8 The band structure calculated at H=4h is given for three different temperatures. Figure 8 Part (a) represents the real part of the complex band structure, where the shaded area represents the entire band gap, and the corresponding imaginary part is as follows: Figure 8 As shown in section (b). It should be noted that the imaginary part given here represents the time-varying decay of the wave, which is consistent with... Figure 3 The imaginary part in the equation represents the different attenuation of the wave as the propagation distance changes. Figure 8 The results show that as temperature increases, the bandgap shifts downwards overall, and the bandwidths of each bandgap also change. Furthermore, the attenuation within the passband increases with increasing temperature because the damping of the actuator increases with temperature. Therefore, it can be seen that... Figure 7 The actuator designed in (a) can serve as a good example. Figure 1 The springs and damping elements proposed in the paper.

[0044] To verify the performance of the metamaterial beam designed in this embodiment, a sample was fabricated and corresponding sample tests were conducted. Figure 9 (a) shows the test specimen used in the experiment, with an inset showing a magnified view from different angles. The main body of the metamaterial beam, 1.2 m long, was fabricated using wire cutting. The actuators were 3D-fabricated using "VeroPureWhite" material and then glued to the main sawtooth beam. The overall experimental setup is as follows. Figure 9(b) shows that in the experiment, a sweep signal with a frequency in the range of [5.0, 150.0] kHz and a duration of 40 ms was generated by a signal generator (Tektronix, AFG31021), further amplified, and then output to a phase conversion device (self-made). A piezoelectric plate (PZT) was attached to the upper and lower surfaces of the metamaterial beam, respectively, and two signals with opposite voltages were output to this pair of piezoelectric plates (PZT). To reduce wave reflection, a damping material (Blue tack) was attached to both ends of the metamaterial beam. The out-of-plane vibration velocity was measured using a laser scanning vibrometer (Polytec, OFV 505, Germany). A heater consisting of a heating container and a voltage regulator was used to generate the required thermal environment, with a heating range from room temperature to 85°C.

[0045] The temperature inside the heating container was measured using a thermocouple thermometer with four probes. Three probes (channels #1, #2, and #3) were inserted into the heating container to assess the internal temperature field, while the remaining probe (channel #4) was placed outside to measure room temperature for comparison. Figure 9 As shown in (c), the temperature inside the heating container and the room temperature were measured during the experiment. The results show that the temperature field inside the heating container is approximately uniform, close to the temperature required for the experiment. In the experiment, the measurement results of a straight beam with a thickness of h were used as a reference. Then, the propagation behavior of the bending wave in the metamaterial beam designed in this embodiment was evaluated by comparing the measured amplitude of the out-of-plane velocity with the reference velocity amplitude.

[0046] In the experiment, the transmission spectrum of the metamaterial beam without actuators was first measured to verify the established experimental equipment and procedures. Furthermore, the measurement results can also serve as a reference for the experimental results below. Figure 10 The transmission spectra of three sawtooth metamaterial beams without actuators are shown, with the shaded areas representing the first and second band gaps obtained from finite element calculations. Comparison results show that the calculated band gaps agree well with the measured results, confirming the effectiveness of the established experimental setup and procedure.

[0047] Subsequently, the transmittance of each metamaterial beam was measured at room temperature and 47°C. Each specimen underwent three heating-to-cooling cycles to evaluate the reversibility of the designed metamaterial beam. To ensure the temperature within the heating container remained close to the specified value, the holding time was set to 30 minutes. The wave transmittance measurements of the metamaterial beams with different H values ​​are shown below. Figure 11 As shown, the shaded area represents the bandgap calculated by the finite element method at a temperature T = 47℃. The results show that the measurement results have good reversibility, and the bandgap changes significantly with temperature. Furthermore, the lower limit of the first bandgap shifts downwards, while the upper limit hardly changes with temperature, which is consistent with... Figure 4The theoretical results are consistent. However, in the numerical simulation, the Young's modulus of the actuator was set to the measured value of its material at 200Hz. In reality, the Young's modulus of resin ("VeroPureWhite" refers to a resin-based material) typically increases with frequency, leading to a slight discrepancy between the numerically calculated bandgap and the experimental results. The results show that the numerically calculated bandgap position is slightly lower than the measured bandgap. Both the calculation and measurement results demonstrate that the bandgap of the metamaterial beam designed in this embodiment can be temperature-manipulated, and this manipulation is reversible.

[0048] To verify the performance of the designed metamaterial beam at temperatures exceeding the glass transition temperature of the actuator material, the transmittance was specifically measured at a temperature of approximately 75°C after the third heating-to-cooling cycle in the aforementioned experiment. The sample was then cooled to room temperature, and the transmittance was measured again. The corresponding experimental results are plotted in [the table / plot]. Figure 12 The results were included in the third heating-to-cooling cycle for comparison. Figure 12 The results show that as the temperature rises to around 75°C, the transmission spectrum changes significantly compared to 47°C. On the other hand, unexpectedly, the transmission spectrum at room temperature before and after the glass transition is almost the same. In other words, although the actuator undergoes a glass transition, its transmission spectrum can be considered almost reversible after cooling.

[0049] In this embodiment, a novel adjustable metamaterial beam is created by combining springs and damping elements. The wave propagation behavior in this adjustable metamaterial beam was characterized using SEM, and the results confirmed its excellent performance. Then, an actuator was designed as both the spring and damping elements and 3D printed using the thermosensitive material "VeroPureWhite". The toothed metamaterial beam integrating this actuator was tested under multiple thermal load cycles. Experimental results show that even when the loading temperature is slightly higher than the glass transition temperature of the actuator, its transmission spectrum changes significantly with temperature and exhibits good reversibility. Both numerical and experimental results confirm that the designed metamaterial beam possesses good and flexible adjustability.

[0050] It is worth noting that although this embodiment only uses beam cells of equal height and width as an example, it is clear from the principles and effects of the present invention that, since the effect comes from the change in the properties of the actuator itself, other forms of "U"-shaped beam cells can be used in other embodiments of the present invention, such as beam cells of unequal height and / or unequal width. In these embodiments, the actuator can also play a regulatory role. Similarly, the number of beam cells is not limited to the six in this example and can be added or reduced according to actual needs.

[0051] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An actively metamaterial beam based on temperature regulation, comprising a metamaterial beam body and a plurality of "ji"-shaped beam cells arranged in a zigzag shape and formed by the upward arching of the metamaterial beam body, wherein An actuator is provided at the opening of the beam cell and at the opening between beam cells, and the actuator is connected to both side walls of the opening. The actuator is an elastic component, a damping component, or a combination of elastic and damping components; The stiffness coefficient and / or damping coefficient of the actuator can vary with temperature.

2. The metamaterial beam according to claim 1, characterized in that, The actuator is positioned across the opening.

3. The metamaterial beam according to claim 1, characterized in that, The actuator is made of a thermosensitive polymer.

4. The metamaterial beam according to claim 1, characterized in that, The material thickness of the beam cell is consistent with that of the metamaterial beam body.

5. The metamaterial beam according to claim 1, characterized in that, The metamaterial beam body is made of metal.

6. The metamaterial beam according to claim 1, characterized in that, All the turning points on the beam cell are right angles.

7. The metamaterial beam according to claim 1, characterized in that, The width of the beam cell is a = 2(h + l), where h represents the thickness of the metamaterial beam body and l is the width of the upper arched part of the beam cell.

8. The metamaterial beam according to claim 1, characterized in that, The total height of the beam cell is 3 to 5 times the thickness of the metamaterial beam body.

9. The metamaterial beam according to claim 1, characterized in that, The number of beam cells is at least 6.

10. An actuator, characterized in that, This actuator is applicable to temperature-controlled active metamaterial beams as described in any of claims 1-9.

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