Acoustic metamaterial structure unit with double negative mass band gaps and acoustic metamaterial

Abstract

The invention aims to provide an acoustic metamaterial structure unit with double negative mass band gaps and an acoustic metamaterial with the double negative mass band gaps. Comprising an electromagnetic inertia actuator which drives a mass block to generate inertia force through electromagnetic force, a shunt circuit for tuning band gap characteristics and an accelerometer for converting vibration acceleration signals into voltage signals. And a signal output end of the accelerometer is electrically connected with the shunt circuit and an excitation coil of the electromagnetic inertia actuator in sequence to form a feedback loop. The vibration suppression device is used for conducting low-frequency vibration reduction on a base body so as to solve the problems that an existing vibration suppression band is narrow in width and poor in adjustability.

Description

[Technical Field]

[0001] This invention belongs to the field of low-frequency vibration control technology, specifically relating to an acoustic metamaterial structural unit with a dual negative mass bandgap and an acoustic metamaterial. [Background Technology]

[0002] Low-frequency vibrations are a common challenge in fields such as aerospace and marine engineering, negatively impacting the performance and lifespan of equipment such as aerospace vehicles and ships. Due to their long wavelengths and strong penetrating power, low-frequency vibrations are difficult to block, making them challenging to effectively control using traditional vibration control techniques.

[0003] Acoustic metamaterials refer to novel acoustic materials or structures composed of specially designed artificial acoustic microstructure units arranged periodically in an elastic medium. They possess extraordinary physical properties not found in naturally occurring materials, such as negative mass density, negative refractive index, and negative modulus. Existing research has shown that acoustic metamaterials constructed based on localized resonant units can generate elastic wave bandgap (frequency ranges where no intrinsic elastic wave dispersion curve exists) near their resonant frequency. Within the bandgap frequency range, the propagation of elastic waves can be significantly suppressed. Utilizing these bandgap characteristics, effective control of low-frequency vibrations and noise in structures can be achieved.

[0004] Mainstream research on active acoustic metamaterials generally employs piezoelectric materials, which suffer from limitations such as small mechanical strain values, short driving strokes, high brittleness, high-pressure actuation, and short lifespan, significantly restricting their potential for practical applications. Currently, traditional vibration suppression research based on electromagnetic inertial actuators focuses on attenuating local vibration energy at the focal length, unlike acoustic metamaterials which can achieve global energy reduction. Furthermore, existing electromagnetic inertial actuator-based research typically employs a "electromagnetic inertial actuator + shunt circuit" configuration, achieving only single-bandgap characteristics with a very narrow suppression bandwidth and low degrees of freedom, failing to meet the increasingly complex vibration suppression requirements of broadband loads. [Summary of the Invention]

[0005] The purpose of this invention is to provide an acoustic metamaterial structural unit and an acoustic metamaterial with a dual negative mass bandgap for low-frequency vibration reduction of the matrix, so as to solve the problems of narrow bandwidth and poor adjustability of existing vibration suppression methods.

[0006] The present invention adopts the following technical solution: an acoustic metamaterial structural unit with a dual negative mass bandgap, including an electromagnetic inertial actuator that drives a mass block to generate inertial force through electromagnetic force, a shunt circuit that tunes the bandgap characteristics, and an accelerometer that converts vibration acceleration signals into voltage signals;

[0007] The signal output terminal of the accelerometer is sequentially connected to the shunt circuit and the excitation coil of the electromagnetic inertial actuator to form a feedback loop;

[0008] The equivalent transfer function between the output voltage and the input voltage of the shunt circuit satisfies the following form:

[0009]

[0010] In the formula, s is the Laplace operator; v(s) is the excitation coil voltage of electromagnetic inertial actuator 1; v a (s) is the output voltage of the accelerometer; ω t γ is the resonant angular frequency of the shunt circuit; γ, R, and C are the DC gain, equivalent real impedance, and equivalent capacitance of the shunt circuit, respectively.

[0011] Furthermore, the shunt circuit is implemented through an analog circuit, which includes a capacitive device, an inductive device, a resistive device, and a voltage amplifier connected in series. The excitation coil is electrically connected to the capacitive device, the input terminal of the voltage amplifier is electrically connected to the output terminal of the accelerometer, and the output terminal of the voltage amplifier is electrically connected to the resistive device.

[0012] Furthermore, capacitive devices include discrete capacitor elements or equivalent capacitive reactance circuits synthesized based on operational amplifiers; inductive devices include discrete inductive elements or equivalent inductive reactance circuits synthesized based on operational amplifiers; resistive devices include resistive elements, mechanically adjustable resistors, and digital potentiometers; and voltage amplifiers include transistor amplifier circuits, field-effect transistor amplifier circuits, integrated operational amplifier circuits, and multi-stage amplifier circuits.

[0013] Furthermore, the shunt circuit is implemented using digital circuitry, which includes:

[0014] The output of the accelerometer is connected in series with a digital-to-analog converter, a microcontroller, an analog-to-digital converter, and a power amplifier, and finally matched with the impedance of the excitation coil.

[0015] The analog-to-digital converter is electrically connected between the accelerometer signal output terminal and the microcontroller to sample the accelerometer output voltage V. a (s);

[0016] The digital-to-analog converter (DAC) is electrically connected between the microcontroller and the power amplifier, converting the control signal calculated by the microcontroller into an analog voltage. The power amplifier is located between the DAC and the excitation coil of the electromagnetic inertial actuator, outputting the excitation coil voltage v(s). The microcontroller is configured with a discrete transfer function as the control law, and calculates the control signal based on the accelerometer output voltage acquired by the DAC, outputting it to the DAC.

[0017] The second technical solution of the present invention is an acoustic metamaterial with a double negative mass bandgap, based on an acoustic metamaterial structural unit with a double negative mass bandgap, comprising a matrix, on which a plurality of acoustic metamaterial structural units with a double negative mass bandgap are periodically arranged.

[0018] In the acoustic metamaterial structural unit with a double negative mass bandgap, the electromagnetic inertial actuator and accelerometer are symmetrically distributed on both sides of the substrate, and the contact surface between the electromagnetic inertial actuator and accelerometer and the substrate forms a mechanical impedance match.

[0019] Furthermore, the substrate is a beam, plate, or shell.

[0020] The third technical solution of the present invention is a control method for controlling the low-frequency vibration reduction of the substrate 4 by the acoustic metamaterial with a dual negative mass bandgap as described in claim 5 or 6, comprising the following:

[0021] S1. Configure a fixed negative mass density bandgap frequency range: that is, configure the natural angular frequency of the electromagnetic inertial actuator to be the target vibration suppression angular frequency ω1 of the matrix;

[0022] S2. Periodically arrange an acoustic metamaterial structural unit with a double negative mass bandgap on the substrate to construct an acoustic metamaterial.

[0023] S3. Design the impedance of the shunt circuit and configure an adjustable negative mass density bandgap frequency range:

[0024] The equivalent capacitance C of the shunt circuit is configured as a fixed value; the resonant angular frequency ω of the shunt circuit is configured as follows. t ω2 is the target vibration suppression angular frequency of the substrate; the equivalent real impedance R of the shunt circuit is configured, and the DC gain γ of the shunt circuit is configured.

[0025] Furthermore, when the shunt circuit 3 is a digital circuit, the impedance design is achieved through the control law after discretization of the microcontroller's equivalent transfer function; the discretized control law is then placed into the microcontroller to complete the impedance design.

[0026] Furthermore, when the shunt circuit is an analog circuit, according to Configure the capacitance of capacitive devices and the inductance of inductive devices, and configure the real impedance R and DC gain γ by configuring the resistance of resistive devices and the voltage amplifier gain.

[0027] The beneficial effects are as follows: This invention proposes an acoustic metamaterial structural unit and acoustic metamaterial that can simultaneously achieve independent negative mass density bandgap in two frequency bands—near the natural angular frequency of the electromagnetic inertial actuator and the resonant angular frequency of the shunt circuit. This innovative design effectively broadens the bandgap frequency range for blocking elastic waves, achieving a revolutionary breakthrough in the field of vibration control and providing unprecedented high-degree-of-freedom, wide-band vibration reduction capabilities for engineering applications. Traditional acoustic metamaterials often only function in a single fixed frequency band, while the dual bandgap design of this invention, through synergistic action, constructs a first negative mass density bandgap at the natural angular frequency of the electromagnetic inertial actuator, achieving targeted vibration suppression of fixed vibration sources such as rotating machinery and engines; and can flexibly adjust the shunt circuit according to actual needs, forming a second negative mass density bandgap at the electric resonant angular frequency, achieving precise suppression of variable frequency vibration or wideband random vibration, greatly expanding the effective vibration suppression bandwidth and control freedom. The dual negative mass density bandgap characteristics of this invention enable it to cope with more complex and variable engineering vibration environments.

[0028] In terms of implementation, this invention provides both analog and digital shunt circuit schemes, offering users unprecedented controllability. The analog scheme employs classic capacitor-inductor networks, offering advantages such as simple structure, stable operation, and low power consumption, making it particularly suitable for long-term deployments or applications in harsh environments. The digital scheme, implemented through programmable circuits, not only allows for real-time adjustment of bandgap parameters but also integrates with advanced control algorithms, enabling the system to possess self-learning and adaptive capabilities. These two schemes can be used independently or collaboratively; the analog circuit ensures basic vibration suppression performance, while the digital circuit enables intelligent control, forming a complementary advantage. This flexible design concept greatly expands the applicability of the technology, allowing for optimal implementation solutions from precision instruments to large structures, and from static environments to dynamic scenarios. [Attached Image Description]

[0029] Figure 1 This is a structural diagram of an acoustic metamaterial structural unit with a dual negative mass bandgap according to the present invention;

[0030] Figure 2 This is a structural diagram of an acoustic metamaterial structure unit with a dual negative mass bandgap, which employs an analog shunt circuit in this invention.

[0031] Figure 3 This is a structural diagram of an acoustic metamaterial structure unit with a dual negative mass bandgap, which employs a digital shunt circuit in this invention.

[0032] Figure 4 This is a schematic diagram of a specific structure of an acoustic metamaterial with a dual negative mass bandgap connected to a matrix to form an acoustic metamaterial in an embodiment of the present invention.

[0033] Figure 5 This is a comparison of the vibration transmissibility of the matrix beam before and after vibration suppression control is performed using the characteristics of an acoustic metamaterial with a double negative mass bandgap in an example of the present invention.

[0034] Among them, 1. Electromagnetic inertial actuator, 2. Accelerometer, 3. Shunt circuit, 4. Base, 5. Capacitive device, 6. Inductive device, 7. Resistive device, 8. Voltage amplifier, 9. Power amplifier, 10. Digital-to-analog converter, 11. Microcontroller, 12. Analog-to-digital converter.

Detailed Implementation Methods

[0035] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0036] This invention provides an acoustic metamaterial structural unit with a dual negative mass bandgap for vibration damping of a matrix 4, such as... Figure 1 As shown, it includes an electromagnetic inertial actuator 1 that generates inertial force by driving a mass block with electromagnetic force, a shunt circuit 3 with tuned bandgap characteristics, and an accelerometer 2 that converts vibration acceleration signals into voltage signals.

[0037] The electromagnetic inertial actuator 1 includes: an inertial body, which is movable along the axial degree of freedom; a base, which is fixedly connected to the base 4 through a mechanical impedance matching interface; an elastic element, which connects the inertial body and the base; a magnetic component, which generates a static bias magnetic field; and an excitation coil, which forms an electromagnetic coupling with the magnetic field of the magnetic component and generates an axial electromagnetic force in response to the drive current.

[0038] The shunt circuit 3 is located between the accelerometer 2 and the electromagnetic inertial actuator 1. The signal output terminal of the accelerometer 2 is sequentially connected to the shunt circuit 3 and the excitation coil of the electromagnetic inertial actuator 1 to form a feedback loop to generate bandgap characteristics in the target frequency band and suppress the vibration of the substrate 4.

[0039] The circuit equivalent transfer function between the output voltage and the input voltage of shunt circuit 3 satisfies the following form:

[0040]

[0041] In the formula, s is the Laplace operator; v(s) is the excitation coil voltage of electromagnetic inertial actuator 1; v a (s) is the output voltage of accelerometer 2; ω t γ is the resonant angular frequency of shunt circuit 3; γ, R, and C are the DC gain, equivalent real impedance, and equivalent capacitance of shunt circuit 3, respectively.

[0042] In some embodiments, such as Figure 2As shown, the shunt circuit 3 is implemented through an analog circuit, which includes a capacitive device 5, an inductive device 6, a resistive device 7, and a voltage amplifier 8 connected in series. The excitation coil is electrically connected to the capacitive device 5, the input terminal of the voltage amplifier 8 is electrically connected to the output terminal of the accelerometer 2, and the output terminal of the voltage amplifier 8 is electrically connected to the resistive device 7, forming a feedback loop to generate bandgap characteristics near the resonant angular frequency of the shunt circuit, thus suppressing substrate vibration.

[0043] In some embodiments, the capacitive device 5 includes discrete capacitor elements or an equivalent capacitive reactance circuit synthesized based on an operational amplifier, which has the advantages of small size, low cost, and good stability; the inductive device 6 includes discrete inductive elements or an equivalent inductive reactance circuit synthesized based on an operational amplifier, which has the advantages of high Q value, large inductance value, and low noise; the resistive device 7 includes resistive elements, mechanically adjustable resistors, and digital potentiometers, which are flexible in use and have high adjustment accuracy; the voltage amplifier 8 includes transistor amplifier circuits, field-effect transistor amplifier circuits, integrated operational amplifier circuits, and multi-stage amplifier circuits, which are highly versatile and have good adjustability.

[0044] The accelerometer output is electrically connected to the voltage amplifier input. The voltage amplifier output is connected in series with the excitation coils of a resistive device, an inductive device, a capacitive device, and an electromagnetic inertial actuator to form a feedback loop that generates a bandgap characteristic near the resonant angular frequency of the shunt circuit, thereby suppressing the vibration of the substrate.

[0045] In some embodiments, such as Figure 3 As shown, the shunt circuit 3 is implemented using digital circuitry, which includes an analog-to-digital converter (ADC) 10, a microcontroller unit, a digital-to-analog converter (DAC) 12, and a power amplifier. The output of the accelerometer 2 is connected in series with the ADC 10, microcontroller 11, DAC 12, and power amplifier 9, and finally electrically connected to the excitation coil. It should be noted that the relationship between the aforementioned digital circuit components and the acoustic metamaterial structural units is not absolutely one-to-one. Through multi-channel components or time-division multiplexing technology, a single component can serve multiple structural units. For example, a single ADC with eight conversion channels can be used for parallel synchronous acquisition of accelerometer signals in eight structural units.

[0046] The analog-to-digital converter 12 is electrically connected between the signal output terminal of the accelerometer 2 and the microcontroller 11, sampling the output voltage V of the accelerometer 2. a(s); The digital-to-analog converter 10 is electrically connected between the microcontroller 11 and the power amplifier 9, converting the control signal calculated by the microcontroller 11 into an analog voltage; the power amplifier 9 is located between the digital-to-analog converter 10 and the excitation coil of the electromagnetic inertial actuator 1, and outputs the excitation coil voltage v(s); the microcontroller 11 configures the discrete transfer function as the control law to realize the required impedance design of the shunt circuit 3, and calculates the control signal based on the output voltage of the accelerometer 2 collected by the analog-to-digital converter 12 and outputs it to the digital-to-analog converter 10.

[0047] The discretization methods for the transfer function of shunt circuit 3 include the backward difference method, the bilinear transform method, and the zero-order hold method. The bilinear transform method is preferred.

[0048] This invention provides an acoustic metamaterial with a dual negative mass bandgap, based on acoustic metamaterial structural units with dual negative mass bandgap, such as... Figure 4 As shown, it includes a substrate 4, on which multiple acoustic metamaterial structural units with double negative mass band gaps are periodically arranged for low-frequency vibration reduction of the substrate 4; electromagnetic inertial actuators 1 and accelerometers 2 in the acoustic metamaterial structural units with double negative mass band gaps are symmetrically distributed on both sides of the substrate 4, and the contact surfaces of the electromagnetic inertial actuators 1 and accelerometers 2 with the substrate 4 form mechanical impedance matching.

[0049] Specifically, the distance between any two adjacent structural units in the multiple acoustic metamaterial structural units with double negative mass bandgap is equal; the matrix of any two adjacent structural units in the multiple acoustic metamaterial structural units with double negative mass bandgap is integrally connected. Preferably, the acoustic metamaterial structural units with double negative mass density bandgap characteristics are preferably arranged at the extreme value of the matrix amplitude to intervene in the region of concentrated vibration energy. Through the cancellation force or energy dissipation with opposite phase, the vibration amplitude is efficiently suppressed, and a better vibration reduction effect can be achieved.

[0050] In some embodiments, the substrate 4 is a beam, plate, or shell. For example, it may be a beam, plate, or shell of equipment such as ships, spacecraft, or submarines. Preferably, the substrate is made of stainless steel. Using the active piezo-acoustic metamaterial of the present invention for low-frequency vibration reduction of the substrate can improve the performance, service life, and stealth of equipment such as ships, spacecraft, or submarines.

[0051] The present invention also provides a control method for controlling the low-frequency vibration reduction of a substrate 4 by an acoustic metamaterial with a dual negative mass bandgap, which includes the following:

[0052] S1. Configure a fixed negative mass density bandgap frequency range: Perform mechanical design on the electromagnetic inertial actuator, configuring the natural angular frequency of the electromagnetic inertial actuator to be the target damping angular frequency ω1 of the base 4, i.e., ω d =ω1;

[0053] S2. Periodically arrange an acoustic metamaterial structural unit with a double negative mass bandgap on the substrate 4 to construct an acoustic metamaterial.

[0054] S3. Perform impedance design on shunt circuit 3, and configure an adjustable negative mass density bandgap frequency range:

[0055] The equivalent capacitance C of the shunt circuit 3 is configured as a fixed value, typically 1 to 100 nF;

[0056] In order to facilitate adjustment of the circuit's resonant angular frequency and damping;

[0057] Configure the resonant angular frequency ω of shunt circuit 3 t The target vibration suppression angular frequency of the substrate 4 is ω2, i.e., ω t =ω2;

[0058] The equivalent real impedance R of the shunt circuit 3 is configured and is generally adjusted between 0 and 2000. The larger the equivalent real impedance R, the stronger the damping of the shunt circuit 3 and the better the control stability, but the weaker the bandgap vibration suppression effect.

[0059] Configure the shunt circuit with DC gain γ. The larger the DC gain γ, the stronger the bandgap damping effect, but the worse the stability.

[0060] In some embodiments, when the shunt circuit 3 is a digital circuit, the impedance design is achieved by the control law after the discretization of the equivalent transfer function of the microcontroller 11.

[0061] Specifically, the configuration parameter ω t After determining R, γ, and C, the transfer function discretization algorithm is first used to discretize the transfer function of claim 1 to obtain the control law of the microcontroller 11:

[0062]

[0063] In the formula, a n These are the coefficients of the feedback filter, b m These are the coefficients of the feedforward filter, where p represents the order of the feedforward filter, q represents the order of the feedback filter, k is the sampling time, x(k) is the voltage signal acquired by the analog-to-digital converter 12 at time k, and y(k) is the control signal output by the microcontroller 11. Specifically, a n b m p and q are all calculated through a discretization process.

[0064] The discrete control law is fed into the microcontroller 11 to complete the impedance design.

[0065] In some embodiments, when the shunt circuit 3 is an analog circuit, the impedance design of C and ω... tParameters such as γ and R are achieved by configuring the capacitance of capacitive device 5, the inductance of inductive device 6, the resistance of resistive device 7, and the gain of voltage amplifier 8.

[0066] Specifically, according to Configure the capacitance of capacitive device 5 and the inductance of inductive device 6, and configure the equivalent real impedance R and DC gain γ by configuring the resistance of resistive device 7 and the gain of voltage amplifier 8.

[0067] Example

[0068] Figure 4 This is a schematic diagram of a specific structure of the acoustic metamaterial with a double negative mass bandgap of the present invention. Figure 4 As shown, in this embodiment, eight acoustic metamaterial structural units with a dual negative mass bandgap are periodically arranged on both sides of the matrix beam to form an acoustic metamaterial composite beam structure. In each acoustic metamaterial structural unit with a dual negative mass bandgap, the accelerometer is an ADXL354 series capacitive MEMS accelerometer, the electromagnetic inertial actuator is an electromagnetic horn, and the microcontroller is an STM32; the digital-to-analog converter and analog-to-digital converter are AD7606 and DAC80508 respectively. Each unit has eight conversion channels, therefore only one channel of the AD7606 and DAC80508 is used in each structural unit. The power amplifier is based on the operational amplifier OPA454. In each structural unit, the accelerometer and electromagnetic inertial actuator are attached to both sides of the matrix structure using 502 adhesive, and are electrically connected sequentially to the analog-to-digital converter, microcontroller, digital-to-analog converter, and power amplifier. The acoustic metamaterial has eight structural units.

[0069] Specifically, the physical parameters of the base beam and the electromagnetic inertial actuator in this embodiment are shown in Table 1.

[0070] Table 1. Relevant structural and electrical parameters of acoustic metamaterials

[0071]

[0072] Then, the above-mentioned acoustic metamaterial is controlled using the control method of the present invention.

[0073] Preferably, in this embodiment, after the microcontroller unit starts up, it first performs an initialization operation, enables the interrupt instruction, and enters an infinite loop to wait for the sampling signal of the analog-to-digital converter. Each time the analog-to-digital converter completes a sampling, it sends an interrupt signal to the microcontroller unit, enters the interrupt handling program to calculate the output voltage signal, and finally outputs the control voltage to the power amplifier through the digital-to-analog converter unit.

[0074] To facilitate understanding of the dual negative mass density bandgap characteristics of the invention, the bandgap range is derived and demonstrated in conjunction with this embodiment:

[0075] for Figure 4 The composite beam structure shown is dynamically modeled based on Euler-Bernoulli beam theory. Considering free boundary conditions and neglecting mechanical damping in the system, the dynamic equations of the composite beam system are:

[0076]

[0077] In the formula, EI is the bending stiffness of the beam matrix, m is the mass per unit length of the beam matrix, and δ(xx) j ) is the Dirac function, m d ω d u(x) j ,t),f a (x j x and t are respectively x j The inertial mass, natural frequency, lateral displacement relative to the beam, and electromagnetic force of the electromagnetic inertial actuator are considered.

[0078] According to Newton's second law, x j The electromagnetic inertial actuator at that location has the following dynamic equations:

[0079]

[0080] According to claim 1, the excitation coil voltage of the electromagnetic inertial actuator and the output voltage of the accelerometer satisfy a transfer function:

[0081]

[0082] Ignoring the back electromotive force generated in the coil, according to the Ampere force formula, the electromagnetic force of the electromagnetic inertial actuator can be expressed as:

[0083]

[0084] In the formula, Γ=1 / (L d s+R d ), L d R d These represent the parasitic inductance and parasitic resistance of the excitation coil, respectively; their values ​​are very small and can be ignored. φ is the motor constant of the electromagnetic inertial actuator. The dynamic equations of the coupled composite beam system, the electromagnetic inertial actuator, and the electromagnetic force formula of the electromagnetic inertial actuator, after simplification, yield the equivalent mass density m of the composite beam in modal space. eq :

[0085]

[0086] For ease of analysis, let R = 0, and the equivalent mass density of the system can be simplified to:

[0087]

[0088] Expanding the Laplacian operator and setting the real part to less than 0, it can be proven that the range of the corresponding negative mass density bandgap includes:

[0089] ① A fixed negative mass density bandgap introduced by the mechanical structure of the electromagnetic inertial actuator:

[0090]

[0091] In the formula, ω is the angular frequency of the vibration or elastic wave. The above formula shows that at the natural angular frequency ω of the electromagnetic inertial brake... d The right side has a fixed range of negative mass density bandgap, which can be used to block and attenuate vibrations within the bandgap frequency.

[0092] ② Adjustable negative mass density bandgap introduced by the electromagnetic force of an electromagnetic inertial actuator:

[0093] When ω d <ω t At that time, there is a band gap range:

[0094] Band gap 1:

[0095] Band gap 2:

[0096] When ω d >ω t At that time, there is a band gap range:

[0097] Band gap 1:

[0098] Band gap 2:

[0099] In summary, the acoustic metamaterial of this invention possesses the following bandgap characteristics: it has a dual negative mass density bandgap, located at the mechanical natural angular frequency ω of the electromagnetic inertial actuator. d The resonant angular frequency ω of the shunt circuit t Nearby; due to the natural angular frequency ω of the electromagnetic inertial actuator d It is difficult to change, therefore the bandgap range in its vicinity is fixed; due to the resonant angular frequency ω of the shunt circuit. t The bandgap range can be easily adjusted by changing the impedance design.

[0100] This embodiment only presents a portion of the above derivation process. The remaining derivation process is well-known to those skilled in the art and will not be described in detail here.

[0101] In this embodiment, an excitation signal was output from a signal generator to induce vibration in the beam structure. Accelerometers were used to measure the excitation point and ends of the beam structure. 120Hz and 150Hz were selected as target frequencies for vibration control. Data was acquired using an NI data acquisition device, and finally, MATLAB was used for data processing to obtain the transmissivity curve shown in Figure 0. It can be seen that after attaching the acoustic metamaterial structural unit of this invention, a fixed bandgap 1 caused by the electromagnetic horn mechanical structure was first generated in the vicinity of 150Hz, resulting in a significant attenuation of the vibration transmissivity in the nearby frequency band. After applying control at 120Hz, an adjustable bandgap 1 was generated near 120Hz due to the negative mass density effect, achieving a vibration attenuation of approximately 34dB.

Claims

1. An acoustic metamaterial structural unit with a dual negative mass bandgap, characterized in that, It includes an electromagnetic inertial actuator (1) that generates inertial force by driving a mass block with electromagnetic force, a shunt circuit (3) with tuned bandgap characteristics, and an accelerometer (2) that converts vibration acceleration signals into voltage signals. The signal output terminal of the accelerometer (2) is connected in sequence to the shunt circuit (3) and the excitation coil of the electromagnetic inertial actuator (1) to form a feedback loop; The circuit equivalent transfer function between the output voltage and the input voltage of the shunt circuit (3) satisfies the following form: In the formula, s is the Laplace operator; v(s) is the excitation coil voltage of electromagnetic inertial actuator 1; v a (s) is the output voltage of the accelerometer (2); ω t γ is the resonant angular frequency of the shunt circuit (3); γ, R, and C are the DC gain, equivalent real impedance, and equivalent capacitance of the shunt circuit (3), respectively.

2. The acoustic metamaterial structural unit with a dual negative mass bandgap according to claim 1, characterized in that, The shunt circuit (3) is implemented by an analog circuit, which includes a capacitive device (5), an inductive device (6), a resistive device (7), and a voltage amplifier (8) connected in series. The excitation coil is electrically connected to the capacitive device (5), the input terminal of the voltage amplifier (8) is electrically connected to the output terminal of the accelerometer (2), and the output terminal of the voltage amplifier (8) is electrically connected to the resistive device (7).

3. The acoustic metamaterial structural unit with a dual negative mass bandgap according to claim 2, characterized in that, The capacitive device (5) includes discrete capacitor elements or equivalent capacitive reactance circuits synthesized based on operational amplifiers; the inductive device (6) includes discrete inductive elements or equivalent inductive reactance circuits synthesized based on operational amplifiers; the resistive device (7) includes resistive elements, mechanically adjustable resistors, and digital potentiometers; and the voltage amplifier (8) includes transistor amplifier circuits, field-effect transistor amplifier circuits, integrated operational amplifier circuits, and multi-stage amplifier circuits.

4. The acoustic metamaterial structural unit with a dual negative mass bandgap according to claim 1, characterized in that, The shunt circuit (3) is implemented by a digital circuit, which includes: The output terminal of the accelerometer (2) is connected in series with a digital-to-analog converter (10), a microcontroller (11), an analog-to-digital converter (12), and a power amplifier (9), and finally matched with the impedance of the excitation coil. The analog-to-digital converter (12) is electrically connected between the signal output terminal of the accelerometer (2) and the microcontroller (11), and samples the output voltage v of the accelerometer (2). a (s); The digital-to-analog converter (10) is electrically connected between the microcontroller (11) and the power amplifier (9), converting the control signal calculated by the microcontroller (11) into an analog voltage; the power amplifier (9) is located between the digital-to-analog converter (10) and the excitation coil of the electromagnetic inertial actuator (1), and outputs the excitation coil voltage v(s); the microcontroller (11) configures the discrete transfer function as the control law, and calculates the control signal based on the output voltage of the accelerometer (2) collected by the analog-to-digital converter (12) and outputs it to the digital-to-analog converter (10).

5. An acoustic metamaterial with a dual negative mass bandgap, based on the acoustic metamaterial structural unit with a dual negative mass bandgap as described in any one of claims 1-4, characterized in that, It includes a substrate (4) on which multiple acoustic metamaterial structural units with double negative mass band gaps are periodically arranged; The electromagnetic inertial actuator (1) and accelerometer (2) in the acoustic metamaterial structural unit with dual negative mass bandgap are symmetrically distributed on both sides of the substrate (4), and the contact surfaces of the electromagnetic inertial actuator (1) and the accelerometer (2) with the substrate (4) form a mechanical impedance match.

6. The acoustic metamaterial with a dual negative mass bandgap according to claim 1, characterized in that, The substrate (4) is a beam, plate or shell.

7. A control method, characterized in that, The method for controlling the low-frequency vibration reduction of a matrix using the acoustic metamaterial with a dual negative mass bandgap as described in claim 5 or 6 includes the following: S1. Configure a fixed negative mass density bandgap frequency range: that is, configure the natural angular frequency of the electromagnetic inertial actuator as the target vibration suppression angular frequency ω1 of the substrate (4); S2. Periodically arrange the acoustic metamaterial structural units with a double negative mass bandgap on the substrate (4) to build an acoustic metamaterial; S3. Perform impedance design on the shunt circuit (3) and configure an adjustable negative mass density bandgap frequency range: The equivalent capacitance C of the shunt circuit (3) is configured to be a fixed value; the resonant angular frequency ω of the shunt circuit (3) is configured to be... t The target vibration suppression angular frequency ω2 of the substrate (4) is set; the equivalent real impedance R of the shunt circuit (3) is configured, and the DC gain γ of the shunt circuit (3) is configured.

8. The control method according to claim 7, characterized in that, When the shunt circuit 3 is a digital circuit, the impedance design is achieved by the control law after the equivalent transfer function of the microcontroller (11) is discretized; the discretized control law is placed into the microcontroller (11) to complete the impedance design.

9. The control method according to claim 7, characterized in that, When the shunt circuit (3) is an analog circuit, according to Configure the capacitance of the capacitive device (5) and the inductance of the inductive device (6), and configure the real impedance R and DC gain γ by configuring the resistance of the resistive device (7) and the gain of the voltage amplifier (8).

Images