Non-hermitian elastic system and applications thereof

Abstract

The application discloses a non-Hermite elastic system and application thereof. The system comprises a first resonator, a second resonator and a coupling module. The coupling module is composed of a sensing-actuating feedback system, which comprises a first sensor and a first actuator arranged on the first resonator, and a second sensor and a second actuator arranged on the second resonator. The sensor is used for detecting the deformation amount of the corresponding resonator. The actuator is used for driving the corresponding resonator to deform. The excitation signals of the first actuator and the second actuator are obtained by multiplying the sensing signals of the first sensor and the second sensor by a transfer function. The transfer function makes the two natural frequencies of the non-Hermite elastic system consistent near the singular point. The bifurcation value of the system natural frequency near the singular point in the application is very sensitive to the parameter change of the system, so that a cantilever beam mass measurement device and a crack propagation detection device with super-high sensitivity can be obtained.

Description

Technical Field

[0001] This invention belongs to the fields of non-Hermitian system design, microelectromechanical sensors and non-destructive testing technology, and specifically relates to a non-Hermitian elastic system and its application. Background Technology

[0002] In recent years, sensors designed based on the singular point theory of non-Hermitian systems have attracted widespread attention. Compared with traditional linear sensors, this type of sensor has a completely different working mechanism, utilizing the characteristic frequency splitting near the singular point of a non-Hermitian system to establish a correlation between load disturbances and the characteristic frequency splitting. Theoretically, for a second-order singular point, the magnitude of the characteristic frequency splitting near it is proportional to the square root of the load disturbance. Therefore, compared with traditional sensors, sensors designed based on the singular point theory of non-Hermitian systems exhibit extremely high sensitivity to small changes in load, which has been experimentally proven in fields such as optics and electronics. However, such sensors have not yet been realized in mechanical or elastic systems, and no reasonable design scheme has been proposed.

[0003] Compared to disciplines like optics and electronics, realizing non-Hermitian mechanical or elastic systems is relatively difficult. Non-Hermitian systems overcome the symmetry limitations of traditional Hermitian systems and may exhibit energy loss or gain characteristics under certain conditions, typically requiring the design of systems capable of energy exchange with the external environment. In the field of solid-state structures, research related to singularities is currently mainly limited to parity-time (PT) symmetric or quasi-PT symmetric non-Hermitian systems. However, both PT-symmetric and quasi-PT-symmetric systems have stringent realization conditions; for example, each harmonic oscillator must have the same natural frequency, while simultaneously ensuring a strict balance between gain and dissipation. However, in practical applications, manufacturing errors and material degradation can disrupt the system's symmetry, increasing the difficulty of applying such sensors.

[0004] Conversely, anti-PT symmetric non-Hermitian systems do not require the natural frequencies of the harmonic oscillators to be identical. However, the main challenge in designing anti-PT symmetric systems lies in establishing purely imaginary coupling between the harmonic oscillators. Similar to anti-PT symmetric systems, anti-PT symmetric pseudo-Hermitian systems further alleviate the constraints on coupling symmetry imposed by anti-PT symmetric non-Hermitian systems. In addition to the non-Hermitian systems mentioned above, non-Hermitian systems with unidirectional coupling have been designed, and the concept of an exceptional surface has been proposed. The advantage of this system is that it combines the robustness required for practical applications with its high sensitivity. Currently, in the field of solid-state structures, none of these three systems have been realized, nor have any reasonable design schemes been proposed. The fundamental challenge lies in how to design purely imaginary and non-reciprocal coupling between the harmonic oscillators.

[0005] Therefore, whether for theoretical research on non-Hermitian elastic systems or for designing mechanical sensors based on non-Hermitian singularity theory, there is an urgent need to propose a reliable structural design scheme that can realize non-Hermitian singularity phenomena. Summary of the Invention

[0006] The purpose of this invention is to build a general platform for realizing non-Hermitian elastic systems with multiple symmetry characteristics, and further apply this system to the design of highly sensitive mechanical sensors and crack detection technology based on the theory of non-Hermitian singularities.

[0007] In a first aspect, the present invention provides a non-Hermitian elastic system, comprising a first resonator, a second resonator, and a coupling module. The coupling module includes a first sensor and a first actuator disposed on the first resonator, and a second sensor and a second actuator disposed on the second resonator. The sensor is used to detect the deformation of the corresponding resonator. The actuator is used to drive the corresponding resonator to deform.

[0008] The excitation signals of the first actuator and the second actuator are obtained by multiplying the sensing signals of the first sensor and the second sensor by a transfer function. The transfer function makes the two natural frequencies of the non-Hermitian elastic system tend to coincide at the singularity point (i.e., they overlap near the singularity point). Specifically, it makes the difference between the two natural frequencies of the mechanical system less than a threshold value, at which point the two natural frequencies of the mechanical system are considered to coincide.

[0009] Preferably, the transfer function is implemented using a sensing-actuation feedback circuit based on electrical signal amplification and summation.

[0010] Preferably, the non-Hermitian elastic system is essentially an anti-parity pseudo-Hermitian system. Without considering dissipation effects, it has only two transfer functions, H1 and H2, used to control the non-reciprocal coupling between the two resonators. The excitation signal of the second actuator is obtained by multiplying the sensing signal of the first sensor by the transfer function H1. The excitation signal of the first actuator is obtained by multiplying the sensing signal of the second sensor by the transfer function H2. Adjusting the transfer functions to make the two natural frequencies of the non-Hermitian elastic system tend to be consistent involves: keeping the product of transfer functions H1 and H2 negative; and adjusting transfer functions H1 and / or H2, increasing the absolute value of the product of transfer functions H1 and H2 until the two natural frequencies of the non-Hermitian elastic system are less than or equal to a threshold.

[0011] Preferably, the transfer functions H1 and H2 are either pure real numbers or pure imaginary numbers.

[0012] Preferably, when the dissipation coefficient of the resonator is large, there need to be four transfer functions, namely transfer functions H 11 H 12 H 21 H 22 The excitation signal of the first actuator is multiplied by the transfer function H by the sensing signal of the first sensor. 11 The sensing signal from the second sensor is superimposed and multiplied by the transfer function H. 21 The excitation signal of the second actuator is obtained by multiplying the sensing signal of the first sensor by the transfer function H. 12 The sensing signal from the second sensor is superimposed and multiplied by the transfer function H. 22 The process of obtaining and adjusting the transfer function to change the stiffness, dissipation coefficient, and coupling strength of the non-Hermitian elastic system is as follows: by adjusting the transfer function H... 11 By changing the stiffness or dissipation coefficient of the first resonator, the transfer function H can be adjusted. 22 By changing the stiffness or dissipation coefficient of the second resonator, the transfer function H can be adjusted. 12 and H 21 Change the coupling strength between the two resonators.

[0013] Excitation signals of the first actuator and the second actuator , Sensing signals from the first sensor and the second sensor , The following relationship must be satisfied:

[0014] .

[0015] As a preferred option, the transfer function H 11 H 12H 21 H 22 It can be a pure real number or a pure imaginary number.

[0016] Preferably, the sensing signals from the first and second sensors are wirelessly uploaded to the controller. The controller then wirelessly sends control signals to the first and second actuators.

[0017] Preferably, the resonator is an elastic structure. The natural frequencies of the first actuator and the second actuator are different when decoupled. The elastic structure can be a cantilever beam or other elastic structures, such as an elastic half-space.

[0018] Preferably, when using a cantilever beam as a resonator, the sensor is positioned on the upper surface of the cantilever beam near the fixed end; the actuator is positioned at the end of the lower surface of the cantilever beam.

[0019] Preferably, both the sensor and the actuator are piezoelectric elements.

[0020] Secondly, the present invention provides an application of the aforementioned non-Hermitian elastic system as a mass measurement device.

[0021] Preferably, the mass measurement process involves: detecting the changes in the two natural frequencies of the non-Hermitian elastic system and calculating the bifurcation change value of the system's natural frequencies at the singular point. The bifurcation change value is the change in the current difference between the two natural frequencies of the non-Hermitian elastic system relative to the initial difference. The mass change of the object placed on the first or second resonator is determined based on the bifurcation change value of the system's natural frequencies near the singular point.

[0022] Thirdly, the present invention provides an application of the aforementioned non-Hermitian elastic system as a crack propagation monitoring device.

[0023] Preferably, the structure containing the crack under test is used as one resonator, and another resonator is also installed. Coupling modules are placed on the two resonators to form an anti-parity pseudo-Hermitian elastic system. The changes in the two natural frequencies of the non-Hermitian elastic system at the singular point are detected, and the bifurcation change value of the system's natural frequencies is calculated. The bifurcation change value is the change in the current difference between the two natural frequencies of the non-Hermitian elastic system relative to the initial difference. The size change of the crack under test is determined based on the bifurcation change value of the system's natural frequencies near the singular point.

[0024] Fourthly, this invention provides an application of the aforementioned non-Hermitian elastic system as a non-Hermitian elastic experimental platform; the natural frequencies of the first actuator and the second actuator are equal under decoupling conditions. When testing a time-parity symmetric non-Hermitian elastic system, the transfer function H... 11 H12 H 21 H 22 Both are non-zero. Using a sensing-actuation feedback method, equal gains and dissipation coefficients are generated on the two resonators, with equal coupling strengths. When testing a non-Hermitian elastic system with a singular surface, the transfer function H... 11 H 21 H 22 All are 0, transfer function H 12 Not zero.

[0025] Fifthly, the present invention provides a method for constructing a non-Hermitian elastic system, comprising:

[0026] A flexible system comprising multiple discrete resonators and coupling modules is established. The coupling module consists of a sensing-actuation feedback system. Preferably, the coupling module comprises: a first sensor and a first actuator mounted on a first resonator; a second sensor and a second actuator mounted on a second resonator; and a circuit control system linking the sensors and actuators.

[0027] Establish a transfer function. The transfer function is the ratio of the excitation signal to the sensing signal, generated by the amplifier circuit. The transfer function adjusts the excitation signals of the first actuator and the second actuator based on the signals measured by the first sensor and the second sensor.

[0028] The transfer function is adjusted so that the two natural frequencies of the elastic system near the singular point tend to be consistent. Specifically, the difference between the two natural frequencies of the elastic system near the singular point is less than a threshold. At this time, the two natural frequencies of the elastic system are considered to coincide.

[0029] The beneficial effects of this invention are:

[0030] 1. This invention provides a non-Hermitian elastic system that can be adjusted to a singular point through electrical means. At this point, the bifurcation value of the system's natural frequency is highly sensitive to changes in the system's parameters, thereby obtaining an ultra-high sensitivity cantilever beam mass measurement device and crack detection device.

[0031] 2. The non-Hermitian elastic system provided by this invention has the characteristic of highly adjustable mechanical properties. In particular, the coupling strength and coupling mode between the two resonators can be arbitrarily controlled by electrical means (transfer function). Therefore, the non-Hermitian elastic system provided by this invention can be used as a general platform to realize various non-Hermitian elastic systems with different symmetries, such as PT-symmetric, anti-PT-symmetric, anti-P pseudo-Hermitian systems, etc., and even non-Hermitian systems with singular surfaces can be realized. Attached Figure Description

[0032] Figure 1This is a schematic diagram of the structure of the non-Hermitian elastic system provided in Embodiment 1 of the present invention.

[0033] Figure 2 The graph shows the changes of the real and imaginary parts of the two natural frequencies as a function in Embodiment 1 of the present invention (where (a) corresponds to the change of the real part of the first-order natural frequency as a function, (b) corresponds to the change of the imaginary part of the first-order natural frequency as a function, (c) corresponds to the change of the real part of the fourth-order natural frequency as a function, and (d) corresponds to the change of the imaginary part of the fourth-order natural frequency as a function).

[0034] Figure 3 This is a schematic diagram of the quality change monitoring device in Embodiment 2 of the present invention.

[0035] Figure 4 This is a schematic diagram of the sensitivity of the mass change monitoring device in Embodiment 2 of the present invention.

[0036] Figure 5 This is a diagram showing the bifurcation of the natural frequency of the mass change monitoring device in Embodiment 2 of the present invention when the mass of the object being measured changes by 1%.

[0037] Figure 6 This is a schematic diagram of the crack change monitoring device in Embodiment 3 of the present invention.

[0038] Figure 7 This is a schematic diagram of the sensitivity of the crack change monitoring device in Embodiment 3 of the present invention.

[0039] Figure 8 This is a diagram showing the bifurcation of the natural frequency of the crack change monitoring device in Embodiment 3 of the present invention when the mass of the object being tested changes by 1%.

[0040] Figure 9 This is a schematic diagram of the structure of the non-Hermitian elastic system provided in Embodiment 4 of the present invention.

[0041] Figure 10 The real and imaginary parts of the natural frequency of the first cantilever beam under the decoupled condition in Embodiment 4 of the present invention are given by the transfer function H. 11 A diagram illustrating the changes.

[0042] Figure 11 This is the frequency-output curve of the first cantilever beam under the decoupling condition in Embodiment 4 of the present invention.

[0043] Figure 12 This is a schematic diagram illustrating the influence of different dissipation coefficients on the natural frequency of the system under coupling conditions in Embodiment 4 of the present invention.

[0044] Figure 13 This is a schematic diagram illustrating how an active method is used in Embodiment 4 of the present invention to eliminate the influence of dissipation effects on singularities in non-Hermitian systems.

[0045] Figure 14 This is a schematic diagram of the structure of the non-Hermitian elastic experimental platform provided in Embodiment 5 of the present invention. Detailed Implementation

[0046] The following description, in conjunction with the accompanying drawings, further illustrates the detailed content and specific embodiments of the present invention, so that those skilled in the art can more fully understand the technical solution of the present invention and thereby clarify the scope of protection of the present invention.

[0047] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0048] Example 1

[0049] like Figure 1 As shown, a non-Hermitian elastic system includes two resonators and a coupling module. In this embodiment, the resonators are cantilever beam structures. In other embodiments, the resonators are not limited to cantilever beam structures and are also applicable to other types of structures. For example, the resonators can also be beams with fixed ends, elastic half-spaces, etc.

[0050] The resonator includes a first cantilever beam of varying lengths (i.e., Figure 1 Beam 1) and the second cantilever beam (i.e. Figure 1 (Beam 2 in the diagram). The length of the first cantilever beam is greater than the length of the second cantilever beam. The coupling module consists of a sensing-actuation feedback system, including a first sensor and a first actuator mounted on the first cantilever beam, and a second sensor and a second actuator mounted on the second cantilever beam. The first sensor, first actuator, second sensor, and second actuator are all connected to an amplifier circuit. The amplifier circuit receives the voltage signals measured by the first and second sensors and provides voltage signals to the first and second actuators according to their corresponding transfer functions.

[0051] Each cantilever beam has piezoelectric sheets attached to its upper and lower surfaces. The piezoelectric sheets on the upper surface of the cantilever beam act as sensors to detect the beam's bending deformation; the piezoelectric sheets on the lower surface of the cantilever beam act as actuators to generate the required bending deformation.

[0052] Through an intelligent digital feedback system including a microcontroller, the first and second cantilever beams can be coupled together. Specifically, the bending deformation of the first cantilever beam will generate a voltage V on the sensor on its surface. SThis voltage, after being amplified by the amplifier circuit, is applied as voltage V to the actuator on the surface of the second cantilever beam. A The actuator applies a corresponding bending moment to the second cantilever beam, causing it to bend and deform, and vice versa. Voltage V A With V S The ratio of the two cantilever beams is called the transfer function. The expressions for the transfer function H1 from the first cantilever beam to the second cantilever beam and the transfer function H2 from the second cantilever beam to the first cantilever beam are: , V a1 V a2 The voltages generated by the corresponding sensors due to the bending of the first and second cantilever beams are respectively; V s1 V s2 These are the voltages input to the actuators in the first and second cantilever beams, respectively.

[0053] This embodiment achieves dynamic coupling between two beams through this design, and this coupling can exist in any form, such as real or imaginary coupling, reciprocal or non-reciprocal coupling, etc.

[0054] In the frequency domain, for Figure 1 From the structure shown, the coupled vibration equations of the system can be derived as follows:

[0055]

[0056] in,

[0057]

[0058] and , The system's natural frequency is the one where the first cantilever beam and the second cantilever beam are coupled. The amplitude matrix; and These represent the amplitudes of the first and second cantilever beams, respectively. For Hamiltonian; and represents the equivalent stiffness and equivalent mass matrix of the system, respectively; m and q represent the vibration mode order of the first cantilever beam and the vibration mode order of the second cantilever beam, respectively.

[0059] Further derivation yields the Hamiltonian. for:

[0060]

[0061] in, and P1 and P2 represent the m-th and q-th natural frequencies of the first cantilever beam and the second cantilever beam, respectively, under decoupling conditions. P1 and P2 are constants related to the structural material and geometry, which can be obtained through fitting. The non-reciprocal coupling strength between the second cantilever beam and the first cantilever beam (i.e., the effect of the deformation of the second cantilever beam on the first cantilever beam). The non-reciprocal coupling strength between the first cantilever beam and the second cantilever beam (i.e., the effect of the deformation of the first cantilever beam on the second cantilever beam).

[0062] The structure designed in this embodiment can be used to design anti-parity pseudo-Hermitian systems, requiring that the two harmonic oscillators have unequal natural frequencies and non-reciprocal coupling characteristics. Therefore, the following requirements must be met: and To meet the above conditions, this embodiment uses two aluminum cantilever beams with different dimensions as resonators: 50mm×10mm×0.8mm and 40mm×10mm×0.8mm, respectively. The Poisson's ratio is 0.33, and the Young's modulus is 70 GPa. The dissipation coefficient of aluminum is small and negligible. Both the actuator and sensor are 10mm×6mm×0.52mm in size, and their centers are located at the x-axis of the cantilever beam. i =l i / 8 and x i =l i At position / 2, i=1,2,l i This is the length of the cantilever beam. The piezoelectric element is a PZT-5H piezoelectric ceramic sheet.

[0063] The product of the two transfer functions is negative, and the adjustment process is as follows: the absolute value of the product increases from small to large until a singularity is reached. Since it is impossible to accurately reach the singularity in actual adjustment, in this embodiment, a singularity is considered to have been reached when the difference between the two natural frequencies of the system is less than or equal to a set threshold.

[0064] In some embodiments, the transfer function can be simply selected as: In this embodiment, the coupled vibration of two cantilever beams was simulated in three dimensions using the commercial finite element software COMSOL Multiphysics.

[0065] Using equations (1)-(3), based on coupled mode theory, the natural frequencies of the system near the singular point can be derived as follows:

[0066]

[0067] in,

[0068]

[0069] and Let represent the natural frequencies of the first and second cantilever beams in the uncoupled state, respectively. The transfer function required to reach the singularity. The values ​​of A and B can be determined through numerical simulation results at two points near the singular point. Through numerical simulation and coupled modal theory, the curves of the system's natural frequencies as a function of the transfer function can be obtained, see... Figure 2 The two natural frequencies of the system gradually move closer to each other as the transfer function increases. When the coupling reaches a critical value, the two natural frequencies eventually merge to form a singularity. Before reaching the singularity (e.g. Figure 2 (As shown in the gray area), the system is in an unbroken phase and has a real natural frequency. Exceeding this critical point (e.g.) Figure 2 After the white area in the middle, the system enters a broken phase, and the imaginary part of the natural frequency begins to bifurcate into two branches, at which point the natural frequencies are complex conjugates of each other. It should be particularly noted that in the structure designed in this embodiment, singularities exist not only in low-order modes but also in high-order modes. The structure designed in this embodiment is based on the ultra-sensitive characteristic of the system's natural frequencies near the singularities to parameter changes, enabling ultra-high precision detection of micro-masses and micro-cracks.

[0070] In some embodiments, the functions that the non-Hermitian elastic system can achieve include, but are not limited to: (a) highly adjustable coupling strength and coupling mode between structures, including reciprocal coupling, non-reciprocal coupling, pure real number coupling, pure imaginary number coupling and general complex number coupling; (b) precise control of structural mechanical properties, such as stiffness, gain coefficient and dissipation coefficient.

[0071] In some embodiments, the coupling module further includes a signal amplification circuit. The amplification factor of the signal amplification circuit is consistent with the transfer function. The signal output interface of the sensor is connected to the input interface of the corresponding signal amplification circuit; the output interface of the signal amplification circuit is connected to the input interface of the second actuator.

[0072] Example 2

[0073] A mass change monitoring device based on a non-Hermitian elastic system is used to measure minute mass changes.

[0074] The mass change monitoring device includes the non-Hermitian elastic system provided in Example 1. In the non-Hermitian elastic system, the first cantilever beam serves as the load-bearing structure for the object being measured, and the top of the first cantilever beam, which serves as the load-bearing structure for the object being measured, has a placement position for the object being measured.

[0075] A mass block m is placed at the test object placement location as the test object. The system is excited using fourth-order modes, and the relationship between mass perturbation and natural frequency changes near singular points is observed. Figure 3 As shown, the initial mass of the mass block is 8 mg, accounting for 0.28% of the total mass of the non-Hermitian elastic system. After the mass block is loaded, the transfer functions H1 and / or H2 need to be continuously adjusted to keep the system near the singular point and maintain its high sensitivity. Changes in mass can cause the natural frequency to bifurcate near the singular point.

[0076] However, whether in numerical simulation or practical application, it is almost impossible to make the system precisely at the singular point. Therefore, the initial natural frequency bifurcation is almost inevitable. Before starting to detect the change in mass, the difference between the two initial natural frequencies of the system is recorded as the initial natural frequency bifurcation value. Then, the numerical change of the natural frequency bifurcation value is continuously monitored and used as the basis for judging the change in the mass of the object being measured.

[0077] The monitoring results of this embodiment are as follows: Figure 4 and 5 As shown, the initial natural frequency bifurcation value is 43 Hz, and the corresponding transfer function is 9.365. Figure 4 The blue discrete points represent the bifurcation variation values ​​of the system's natural frequency. The curve showing the change in mass disturbance. The bifurcation change value of the system's natural frequency. ; The initial difference between the two natural frequencies of the system. These are the current differences between the two natural frequencies of the system.

[0078] In contrast. Figure 4 The results obtained using the traditional impedance method are also presented (i.e., the red line in the figure; the working principle of the traditional method is that the natural frequency of the cantilever beam shifts with mass disturbance, and the shift is linearly related to the mass disturbance). The results show that the structure designed in this embodiment has extremely high sensitivity to minute mass changes, while the traditional method is almost unable to detect the same mass change. For example, see... Figure 5 For a 1% mass disturbance, the structural natural frequency bifurcation value provided in this embodiment will increase by 49 Hz, while the natural frequency offset measured by the traditional method is only 0.2 Hz. This embodiment improves the measurement sensitivity by 244 times.

[0079] Example 3

[0080] A crack change monitoring device based on a non-Hermitian elastic system is disclosed for monitoring minute changes in cracks on a beam. The crack change monitoring device includes the non-Hermitian elastic system provided in Example 1. The monitored beam with a crack is used as the first cantilever beam in the non-Hermitian elastic system. An additional cantilever beam is provided as the second cantilever beam.

[0081] In some embodiments, the second cantilever beam is disposed near the first cantilever beam. The main controller is wiredly connected to the sensors and actuators.

[0082] In other embodiments, the second cantilever beam is positioned away from the first cantilever beam, and the main controller is wirelessly connected to some or all of the sensors and actuators. The main controller receives signals from the sensors and controls the input voltage of the actuators via wireless communication. In some further embodiments, a power supply module and a sub-controller that communicates wirelessly with the main controller can be mounted on the cantilever beam.

[0083] like Figure 6 As shown, in this embodiment, a slender surface crack is monitored at the outer end of the beam. The crack is located 40 mm from the fixed end and has an initial size of 5 mm (length) × 0.3125 mm (width) × 0.2 mm (depth). For the fourth-order mode, an initial natural frequency bifurcation value of 22 Hz can be obtained by adjusting the transfer function H to 9.508. Figure 7 The variation of the natural frequency bifurcation amplitude with crack propagation is demonstrated. Compared with the traditional impedance method (i.e., measuring the shift of the structure's natural frequency), this embodiment significantly improves the detection sensitivity for crack propagation. For example, when the crack length increases by 1%, the natural frequency bifurcation value measured by the structure of this invention reaches 139 Hz (an increment of 117 Hz), while the traditional impedance method only detects a frequency shift of 0.8 Hz. Figure 8 Therefore, in this situation, the detection sensitivity of the system provided in this embodiment is 145 times higher than that of traditional methods. The crack change monitoring device proposed in this embodiment exhibits ultra-high sensitivity for monitoring the propagation of micro-cracks, making it particularly suitable for early monitoring of crack initiation, and providing a new solution for structural health monitoring.

[0084] Example 4

[0085] A non-Hermitian elastic system, this embodiment is applicable to materials with a large dissipation coefficient.

[0086] Example 1's design scheme for obtaining singularities is only applicable to materials with low dissipation coefficients, such as aluminum. However, when the dissipation coefficient is high, the singularity phenomenon will no longer exist, such as... Figure 12 As shown, where E i and E r These are the real and imaginary parts of Young's modulus, respectively. The size of the imaginary part can be used to characterize the magnitude of the dissipation coefficient.

[0087] The difference between this embodiment and Embodiment 1 lies in the method of obtaining the input voltages of the first and second actuators in the coupling module. This embodiment includes four transfer functions H. 11 H 12 H 21 H 22 Transfer function H 11 H 12 The signal measured by the first sensor is used as input. The transfer function H... 21 H 22 The signal measured by the second sensor is used as input. Transfer function H 11 and transfer function H 21 The outputs of both control the input voltage of the first actuator. Transfer function H 12 and transfer function H 22 The outputs of the two actuators jointly control the input voltage of the second actuator.

[0088] Compared to Example 1, this example adds the association between the sensor and the actuator on the same beam; that is, the detection voltage on the sensor is applied to the actuator on the same beam through an amplification circuit. Therefore, the excitation voltage of the actuator on the two cantilever beams consists of two parts, the expression of which is:

[0089]

[0090] in, , These represent the excitation voltages of the actuators attached to the first and second cantilever beams, respectively. , These represent the detection voltages on the sensors on the first and second cantilever beams, respectively. Let represent the transfer function, specifically the ratio of the excitation voltage applied to the j-th cantilever beam to the detection voltage applied to the i-th cantilever beam, where i=1,2 and j=1,2.

[0091] This embodiment not only enables coupling between two cantilever beams but also allows for active control of parameters such as the stiffness, dissipation coefficient, and gain coefficient of the cantilever beams. When the transfer function is real, the beam stiffness, i.e., the real part of Young's modulus, can be adjusted; when the transfer function is imaginary, the beam's dissipation or gain coefficient, i.e., the imaginary part of Young's modulus, can be adjusted. Numerical simulation results show that for a single cantilever beam (without coupling), when the transfer function is purely imaginary, the imaginary part of the beam's natural frequency can be continuously adjusted, such as... Figure 10 As shown by the pink line, the real part has almost no effect, as... Figure 10As shown by the blue line, this embodiment demonstrates that it can effectively and actively change the dissipation or gain coefficient of the cantilever beam without affecting its stiffness. Furthermore, the response frequency curve also verifies the rationality of this embodiment; for example, for materials with high dissipation coefficients, the Q value is typically small, such as... Figure 11 As shown by the black line, the proposed solution in this embodiment can significantly improve the Q value, see... Figure 11 As shown by the yellow line, the dissipation coefficients corresponding to the red and yellow lines are the same, while the dissipation coefficients corresponding to the remaining red, green, and blue lines are (…). The values ​​are 0.001, 0.0001, and 0, respectively. Furthermore, by actively eliminating the dissipation effect of materials, systems that originally did not possess singularities ( Figure 12 and 13 The red line in the diagram is adjusted to exhibit properties similar to those of systems with singularities (see [link]). Figure 13 (The yellow line in the diagram), thereby achieving an ultra-high sensitivity to system disturbances. From Figure 12 As can be seen from this, when the dissipation coefficient is small, the system still possesses characteristics similar to a dissipative system. Figure 12 The green and blue lines in the diagram correspond to cases with small and no dissipation effects, respectively.

[0092] In some embodiments, the coupling module further includes a signal amplification circuit and a summing circuit. Each transfer function corresponds to a signal amplification circuit. The sensing signal output from the first sensor is input to the transfer function H. 11 H 12 The corresponding signal amplification circuit. The input transfer function H of the sensing signal output from the second sensor. 21 H 22 The corresponding signal amplification circuit. Transfer function H 11 H 21 The output signal of the corresponding signal amplification circuit is superimposed by a summing circuit and then input to the first actuator. Transfer function H 12 H 22 The output signal of the corresponding signal amplification circuit is superimposed by the summing circuit and then input to the second actuator.

[0093] Example 5

[0094] A non-Hermitian elastic experimental platform based on a non-Hermitian elastic system. The non-Hermitian elastic experimental platform includes a resonator and a coupling module. The resonator includes a first cantilever beam of equal length (i.e.,...). Figure 14 Beam 1) and the second cantilever beam (i.e. Figure 14(Beam 2 in the diagram). The coupling module includes a first sensor and a first actuator mounted on the first cantilever beam, and a second sensor and a second actuator mounted on the second cantilever beam. The first sensor, the first actuator, the second sensor, and the second actuator are all connected to an amplifier circuit. The amplifier circuit receives the voltage signals measured by the first and second sensors and provides voltage signals to the first and second actuators according to their corresponding transfer functions.

[0095] This embodiment includes four transfer functions H. 11 H 12 H 21 H 22 Transfer function H 11 H 12 The signal measured by the first sensor is used as input. The transfer function H... 21 H 22 The signal measured by the second sensor is used as input. Transfer function H 11 and transfer function H 21 The outputs of both control the input voltage of the first actuator. Transfer function H 12 and transfer function H 22 The outputs of the two actuators jointly control the input voltage of the second actuator.

[0096] The excitation voltage of the actuators on the two cantilever beams consists of two parts, and its expression is as follows:

[0097]

[0098] in, and These represent the excitation voltages of the actuators attached to the first and second cantilever beams, respectively. and These represent the detection voltages on the sensors on the first and second cantilever beams, respectively. Let represent the transfer function, specifically the ratio of the excitation voltage applied to the j-th cantilever beam to the detection voltage applied to the i-th cantilever beam, where i=1,2 and j=1,2.

[0099] In some embodiments, the non-Hermitian elastic experimental platform can be used as a time-parity-symmetric (PT-symmetry) non-Hermitian elastic system, in which case the Hamiltonian is required. It has the following forms:

[0100]

[0101] The two cantilever beams have the same natural frequency, which is 1 / 2. ; The imaginary unit; This represents the gain or dissipation coefficient of the cantilever beam. The coupling strength is given by the equation denoted as . For a time-parity symmetric system, the two harmonic oscillators must have the same natural frequency, the same coupling strength, and the same gain and dissipation. When the system is at a singular point, the following conditions must be met: Therefore, it can be adopted Figure 14 The design shown has two beams with identical material and geometry, and the sensors and actuators are attached at the same locations to ensure that the natural frequencies of the two beams are the same. Furthermore, the beam dissipation and gain coefficients, along with the beam coupling strength, are controlled by a circuit to meet certain requirements. This condition is sufficient.

[0102] In other embodiments, the non-Hermitian elastic experimental platform can be a non-Hermitian elastic system with an exceptional surface. The transfer function H in this case... 11 H 21 H 22 All are 0; only the input voltage of the actuator on the second cantilever beam changes according to the transfer function H as the voltage measured by the sensor in the first cantilever beam changes. 12 Change proportionally.

[0103] In a non-Hermitian elastic system with an exceptional surface, the Hamiltonian must satisfy the following condition:

[0104]

[0105] That is, the natural frequencies of the two oscillators must be the same, but they must have unidirectional coupling characteristics and do not require gain or dissipation. Among these, The natural frequency of the cantilever beam; The strength of unidirectional coupling.

Claims

1. A non-Hermitian elastic system, characterized in that: It includes a first resonator, a second resonator, and a coupling module; the coupling module includes a first sensor and a first actuator disposed on the first resonator, and a second sensor and a second actuator disposed on the second resonator; The sensor is used to detect the deformation of the corresponding resonator; The actuator is used to drive the corresponding resonator to deform. The excitation signals of the first actuator and the second actuator are obtained through the sensing signals of the first sensor and the second sensor and the transfer function; the transfer function makes the two natural frequencies of the non-Hermitian elastic system tend to coincide at the singular point; The excitation signals for the first and second actuators are obtained using either of the following two methods: Option 1: There are two transfer functions, namely transfer functions H1 and H2; the excitation signal of the second actuator is obtained by multiplying the sensing signal of the first sensor by the transfer function H1; the excitation signal of the first actuator is obtained by multiplying the sensing signal of the second sensor by the transfer function H2; the process of adjusting the transfer functions to make the two natural frequencies of the non-Hermitian elastic system tend to be consistent is as follows: keep the product of transfer functions H1 and H2 negative, and adjust the absolute value of the product of transfer functions H1 and / or transfer function H2 from small to large until the two natural frequencies of the non-Hermitian elastic system are less than or equal to the threshold. Option 2: There are four transfer functions in total, namely transfer function H 11 H 12 H 21 H 22 Excitation signals for the first actuator and the second actuator , Sensing signals from the first sensor and the second sensor , The following relationship must be satisfied: ； By adjusting the transfer function H 11 By changing the stiffness or dissipation coefficient of the first resonator, the transfer function H can be adjusted. 22 By changing the stiffness or dissipation coefficient of the second resonator, the transfer function H can be adjusted. 12 and H 21 Change the coupling strength between the two resonators.

2. The non-Hermitian elastic system according to claim 1, characterized in that: The sensing signals from the first and second sensors are wirelessly uploaded to the controller; the controller wirelessly sends control signals to the first and second actuators.

3. The non-Hermitian elastic system according to claim 1, characterized in that: The resonator is an elastic structure; the natural frequencies of the first resonator and the second resonator are different when decoupled.

4. The application of the non-Hermitian elastic system as described in claim 3 as a mass measurement device.

5. The application as described in claim 4, characterized in that: The changes in the two natural frequencies of a non-Hermitian elastic system are detected, and the bifurcation change value of the system's natural frequencies at the singular point is calculated. The bifurcation change value of the system's natural frequencies near the singular point is the change in the current difference between the two natural frequencies of the non-Hermitian elastic system relative to the initial difference. The change in the mass of the object under test placed on the first or second resonator is determined based on the bifurcation change value of the system's natural frequencies.

6. The application of the non-Hermitian elastic system as described in claim 3 as a crack change detection device.

7. The application as described in claim 6, characterized in that: The structure containing the crack under test is used as one of the resonators, and another resonator is set up. A coupling module is set on the two resonators to form a non-Hermitian elastic system. The changes of the two natural frequencies of the non-Hermitian elastic system at the singular point are detected, and the bifurcation change value of the system's natural frequencies is calculated. The bifurcation change value of the system's natural frequencies is the change of the current difference between the two natural frequencies of the non-Hermitian elastic system relative to the initial difference. The size change of the crack under test is determined based on the bifurcation change value of the system's natural frequencies.

8. The application of the non-Hermitian elastic system as described in claim 1 as a non-Hermitian elastic experimental platform, characterized in that: Scheme 2 is adopted to obtain the excitation signals of the first and second actuators; the natural frequencies of the first and second resonators are equal under decoupling conditions; when testing a time-parity symmetric non-Hermitian elastic system, the transfer function... H 11 , H 12 , H 21 , H 22 All are non-zero; when testing a non-Hermitian elastic system with singular surfaces, the transfer function H 11 , H 21 , H 22 All are 0, transfer function H 12 Not zero.

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