Broadband vibration control method and device based on acoustic black holes and distributed vibration absorbers

Abstract

The invention relates to the technical field of broadband vibration control, in particular to a broadband vibration control method and device based on acoustic black holes and distributed vibration absorbers. The method comprises the following steps: constructing a three-dimensional model of the acoustic black hole, and importing the three-dimensional model of the acoustic black hole into finite element analysis software; design parameters of the distributed vibration absorber are defined, and a spring-mass-damping system model of a distributed vibration absorber unit is established; based on a collaborative tuning strategy of a gradient descent method, collaborative optimization is carried out on acoustic black hole and distributed vibration absorber parameters, and broadband vibration control is realized; based on a finite element analysis result, analyzing a transmission path and efficiency of energy between the acoustic black hole and the distributed vibration absorber by utilizing a mathematical model for analyzing vibration energy transmission and dissipation; a vibration signal of the acoustic black hole is collected through an acceleration sensor, and the broadband vibration control effect is verified. The design not only pays attention to the suppression of vibration energy, but also considers the energy dissipation efficiency and the lightweight demand of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of broadband vibration control. Specifically, it relates to a broadband vibration control method and device based on acoustic black holes and distributed vibration absorbers. Background Art

[0002] In modern engineering design, vibration control is crucial for improving the stability of mechanical structures, extending their service life, and enhancing overall performance. However, traditional vibration control technologies often face the problem of narrowband effects, that is, they can only provide effective vibration suppression within a specific frequency range and are difficult to meet the requirements of broadband vibration control. Especially in high-precision fields such as aerospace and automotive manufacturing, structures need to withstand vibrations from multiple sources with complex spectra, including vibration components in the low-frequency to high-frequency range. In this case, single types of vibration absorption or damping measures are insufficient. For example, traditional vibration absorbers are mainly optimized for a specific frequency and have poor vibration suppression effects outside that frequency range; while damping materials can dissipate energy, but their efficiency varies significantly with frequency and is particularly limited in the high-frequency band. Therefore, a broadband vibration control method and device based on acoustic black holes and distributed vibration absorbers are provided. Summary of the Invention

[0003] The purpose of the present invention is to provide a broadband vibration control method and device based on acoustic black holes and distributed vibration absorbers to solve the problems of narrowband vibration control limitations, high-frequency vibration aggregation and dissipation requirements, and insufficient low-frequency vibration absorption mentioned in the above background art.

[0004] To achieve the above object, the present invention aims to provide a broadband vibration control method based on acoustic black holes and distributed vibration absorbers, including the following steps: S1. Construct a three-dimensional model of an acoustic black hole and import the three-dimensional model of the acoustic black hole into finite element analysis software; S2. Define the design parameters of the distributed vibration absorber and establish a spring-mass-damper system model of the distributed vibration absorber unit; S3. Based on the collaborative tuning strategy of the gradient descent method, co-optimize the parameters of the acoustic black hole and the distributed vibration absorber to achieve broadband vibration control, and introduce dynamic frequency band weights and predicted transfer functions into the co-optimization process; S4. Based on the finite element analysis results, use a mathematical model for analyzing the transmission and dissipation of vibration energy to analyze the transmission path and efficiency of energy between the acoustic black hole and the distributed vibration absorber; S5. Collect the vibration signals of the acoustic black hole through an acceleration sensor to verify the broadband vibration control effect.

[0005] As a further improvement of the technical solution, in S1, a three-dimensional model of the acoustic black hole is constructed and imported into the finite element analysis software, including the following steps: S1.1. Determine the shape of the core layer of the acoustic black hole and set the central thickness; S1.2. Design a thickness distribution function by establishing parameters with the thickness decreasing exponentially along the radial direction; S1.3. Based on the wave theory, use the flexural wave equation to analyze how the vibration wave propagates in the acoustic black hole region with a gradually decreasing thickness; S1.4. Analyze the behavior of vibration waves with different frequencies in the acoustic black hole structure; S1.5. Use ANSYS finite element analysis software to perform three-dimensional modeling.

[0006] As a further improvement of the technical solution, in S1.3, based on the wave theory, use the flexural wave equation to analyze how the vibration wave propagates in the acoustic black hole region with a gradually decreasing thickness, including the following steps: S1.31. Define the thin plate material parameters, including Young's modulus , density , Poisson's ratio ; S1.32. Based on the thin plate wave theory, construct a flexural wave control equation; S1.33. Analyze the changes in wave speed and wavelength according to the relationship between the wave speed of the flexural wave and the thickness of the acoustic black hole structure; S1.34. Use the separation of variables method to solve the flexural wave control equation to obtain the displacement field of the vibration wave.

[0007] As a further improvement of the technical solution, in S2, define the design parameters of the distributed absorber and establish a spring-mass-damper system model for the distributed absorber unit, including the following steps: S2.1. Define the design parameters of the distributed absorber, including the mass of the mass block , spring stiffness , damping coefficient , tuning frequency ; S2.2. Based on the interaction between the mass block, spring and damper, construct a spring-mass-damper system model; S2.3. Perform modal analysis on the main structure to obtain the natural frequencies and mode shapes of the main structure; S2.4. According to the modal analysis results, adjust the mass of the mass block and the stiffness of the spring so that the tuning frequency of the distributed absorber covers the target frequency band.

[0008] As a further improvement of this technical solution, in S3, based on the collaborative tuning strategy of the gradient descent method, the parameters of the acoustic black hole and the distributed vibration absorber are collaboratively optimized, including the following steps: S3.1. Map the parameters of the acoustic black hole and the distributed vibration absorber into real number vectors; S3.2. Set the initial parameter combination; S3.3. Based on the current parameter combination, construct a finite element model of the acoustic black hole and the distributed vibration absorber, and obtain the transfer function within the entire target frequency band ; S3.4. According to the transfer function , and superimpose the lightweight penalty term to calculate the objective function value, and introduce the dynamic frequency band weight and the predicted transfer function into the objective function to optimize the objective function; S3.5. Optimize the objective function value through the gradient descent method.

[0009] As a further improvement of this technical solution, in S3.4, according to the transfer function , and superimpose the lightweight penalty term to calculate the objective function value as: ; Wherein, represents the objective function; represents the set of all parameters of the acoustic black hole and the distributed vibration absorber to be optimized; represents the starting frequency of the target optimization; represents the termination frequency of the target optimization; represents the lightweight penalty term; represents the total structure mass; represents the set of all parameters of the acoustic black hole and the distributed vibration absorber to be optimized; Based on the influence of the vibration energy of each frequency band on the system performance, construct the dynamic frequency band weight ; Define the damping coefficient as a function of the strain rate : ; Wherein, represents the linear viscous damping coefficient; represents the first-order nonlinear viscous damping coefficient; represents the second-order nonlinear viscous damping coefficient; and , , are incorporated into the parameter set ; At different temperatures Perform finite element simulation to generate a dataset ; Use the data in the dataset to train a deep neural network so that the deep neural network outputs a predicted frequency response function ; In summary, introduce the dynamic frequency band weight and the predicted transfer function into the objective function to optimize the objective function

[0010] As a further improvement of this technical solution, in S4, based on the finite element analysis results, use a mathematical model for analyzing the transfer and dissipation of vibration energy to analyze the transfer path and efficiency of energy between the acoustic black hole and the distributed vibration absorber, including the following steps S4.1. Export vibration response data from ANSYS finite element software S4.2. Convert the vibration response data into tensor form, perform Fourier transform on the time series data in the vibration response data, convert the time domain data into frequency domain response data, analyze the frequency domain response data, and extract the vibration characteristics in the key frequency range S4.3. Define the kinetic energy density and potential energy density of the element, calculate the kinetic energy density and potential energy density element by element in the finite element mesh to obtain the energy distribution within the system S4.4. Calculate the input power according to the external excitation force and the velocity at the excitation point, perform Fourier transform on the input power to obtain the frequency domain input power spectrum S4.5. Analyze the energy transfer path based on power flow S4.6. Divide the structure into an acoustic black hole area, a distributed vibration absorber area, and a transfer path area, and establish a segmented energy balance equation S4.7. Discretize the energy transfer equation and solve it using the finite difference method

[0011] As a further improvement of this technical solution, in S5, collect the vibration signal of the acoustic black hole through an acceleration sensor to verify the broadband vibration control effect, including the following steps S5.1. Obtain the original vibration signal data and perform preprocessing and analysis S5.2. Perform fast Fourier transform on the preprocessed vibration signal to convert it into a frequency domain signal, and calculate the power spectral density based on the frequency domain signal S5.3. Compare the vibration responses with and without the acoustic black hole area + distributed vibration absorber, and calculate the attenuation amount of vibration energy at each frequency point S5.4. Calculate the transfer function of the system based on the input excitation and output response, use the transfer function to integrate the power flow vector along the structure propagation direction, and identify the main energy transfer path S5.5. Collect the vibration attenuation process and record the acceleration time-domain signal in the acoustic black hole region; S5.6. Extract the initial vibration amplitude from the collected time-domain signal, track the change of the vibration amplitude over time, find the time when the amplitude decays to a% of the initial value, compare the decay times under different conditions, and evaluate the energy dissipation efficiency of the system; S5.7. Perform Hilbert transform on the acceleration time-domain signal, extract the envelope, analyze the envelope decay rate, and verify the broadband dissipation characteristics of the acoustic black hole region + distributed vibration absorber.

[0012] As a further improvement of this technical solution, in S5.7, performing Hilbert transform on the acceleration time-domain signal, extracting the envelope, analyzing the envelope decay rate, and verifying the broadband dissipation characteristics of the combination of the acoustic black hole region + distributed vibration absorber include the following steps: S5.71. Decompose the collected acceleration time-domain signal into K intrinsic mode functions by variational mode decomposition to separate the vibration components in different frequency bands; S5.72. Perform Hilbert transform on each intrinsic mode function component respectively to generate an analytic signal; S5.73. Establish an initial decay model based on linear viscoelastic theory, and introduce a non-linear correction term in the model for adjustment to construct a piecewise decay model to distinguish the decay rates in different frequency bands; S5.74. Verify the energy dissipation ability of the combination of the acoustic black hole region + distributed vibration absorber in the broadband range by comparing the decay rates of the envelopes under different frequency components.

[0013] On the other hand, the present invention provides a broadband vibration control device based on an acoustic black hole and a distributed vibration absorber, including a sensor, a storage, a processor, and a computer program stored in the memory and operable on the processor. When the processor executes the computer program, the steps of the broadband vibration control method based on an acoustic black hole and a distributed vibration absorber described in any one of the above are implemented.

[0014] Compared with the prior art, the beneficial effects of the present invention: 1. In the broadband vibration control method and device based on acoustic black hole and distributed vibration absorber, by combining acoustic black hole (ABH) and distributed vibration absorber (DVA), this method can achieve effective vibration control in a wide frequency range. The acoustic black hole (ABH) is designed to aggregate and dissipate high-frequency vibration energy, while the distributed vibration absorber (DVA) absorbs low-frequency vibration. The collaborative optimization strategy further ensures the best cooperation of the two within the target frequency band, achieving effective suppression of the vibration of the entire structure. In addition, introducing dynamic frequency band weights and predicted transfer functions into the optimization process can specifically strengthen the vibration control of key frequency bands, thereby improving the anti-vibration performance of the overall system.

[0015] 2. In the broadband vibration control method and device based on acoustic black hole and distributed vibration absorber, not only the suppression of vibration energy is concerned, but also the energy dissipation efficiency and lightweight requirements of the system are considered. By accurately simulating and analyzing the transfer path and efficiency of energy between ABH and DVA, and using a non-linear damping model to more accurately reflect the actual energy consumption characteristics of materials, the system can reduce unnecessary mass increase while ensuring efficient energy absorption. Especially using the deep neural network (DNN) as a surrogate model to quickly evaluate the effects of different design schemes greatly reduces the computational cost, improves the design optimization efficiency, and helps to achieve the lightweight of the structure under the established vibration suppression target. Brief Description of the Drawings

[0016] Figure 1 is the overall method flow chart of the present invention; Figure 2 is the vibration test comparison chart of this embodiment. Detailed Embodiments

[0017] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work shall fall within the protection scope of the present invention.

[0018] Embodiment 1: Please refer to Figure 1-2 As shown, this embodiment provides a broadband vibration control method based on acoustic black hole and distributed vibration absorber, including the following steps: S1. Construct a three-dimensional model of the acoustic black hole (ABH) and import the three-dimensional model of the acoustic black hole (ABH) into finite element analysis software; In this embodiment, constructing a three-dimensional model of the acoustic black hole (ABH) and importing the three-dimensional model of the acoustic black hole (ABH) into finite element analysis software includes the following steps: S1.1. Determine the shape (circular or square) of the core layer of the acoustic black hole (ABH) and set the central thickness; S1.2. Design a thickness distribution function with the thickness decreasing exponentially along the radial direction, ensuring that the minimum thickness at the edge is 0.4 mm; S1.3. Based on wave theory, use the flexural wave equation to analyze how vibration waves propagate in the region of the acoustic black hole (ABH) with a gradually decreasing thickness; Among them, by regulating the wave speed and energy density through the gradual change of thickness and combining with the dissipation of the damping layer, the ABH realizes the efficient control of high-frequency vibration energy; Based on wave theory, use the flexural wave equation to analyze how vibration waves propagate in the region of the acoustic black hole (ABH) with a gradually decreasing thickness, including the following steps: S1.31. Define the parameters of the thin plate material, and the parameters of the thin plate material include Young's modulus , density , Poisson's ratio ; S1.32. Based on the thin plate wave theory, construct the flexural wave control equation: , where is the flexural rigidity, which is related to the cube of the thickness , is the displacement in the direction perpendicular to the plate surface. Since the thickness of the ABH region changes with position, substitute into the equation to obtain the flexural wave equation in a non-uniform medium, and introduce a variable coefficient term to characterize the influence of the thickness gradient on wave propagation. The new flexural wave equation becomes: ; where represents the position variable; S1.33. Analyze the changes in wave speed and wavelength according to the relationship between the wave speed of the flexural wave and the thickness of the acoustic black hole (ABH) structure. The relationship between the wave speed and the thickness is: . The decreasing thickness leads to a decrease in wave speed and a shortening of the wavelength. At the edge of the ABH region, the thickness approaches zero, and the wave speed drops sharply, forming an "equivalent black hole" effect, which makes the vibration wave unable to escape and accumulate energy in this region; S1.34. Use the method of separation of variables to solve the flexural wave control equation to obtain the displacement field of the vibration wave, The displacement field can be decomposed into the product form of time and space parts; and substitute the above into the flexural wave equation, and solve the equations of the time part and the space part respectively. The time part is usually a simple harmonic equation, while the space part needs to consider the geometric shape and boundary conditions; The boundary conditions need to satisfy: continuity condition: at the junction of the ABH and non-ABH regions, the displacement and stress are continuous; radiation condition: set an absorption damping layer at the edge of the ABH to simulate energy dissipation; S1.4. Analyze the behavior of vibration waves with different frequencies in an Acoustic Black Hole (ABH) structure, especially how high-frequency components are concentrated and dissipated in the damping layer; S1.5. Use ANSYS finite element analysis software for 3D modeling. In ANSYS finite element software, map the thickness function to a circular or annular region to generate a geometrically tapered 3D thin plate model.

[0019] S2. Define the design parameters of the Distributed Vibration Absorber (DVA), and establish a spring - mass - damper system model for the Distributed Vibration Absorber (DVA) unit; In this embodiment, the core is to achieve broadband vibration absorption through the synergistic effect of spring - mass - damper units; Define the design parameters of the Distributed Vibration Absorber (DVA), and establish a spring - mass - damper system model for the Distributed Vibration Absorber (DVA) unit, including the following steps: S2.1. Define the design parameters of the Distributed Vibration Absorber (DVA), including the mass of the mass block , the spring stiffness , the damping coefficient , the tuning frequency ; S2.2. Based on the interactions between the mass block, spring, and damper, construct a spring - mass - damper system model. The spring - mass - damper system model is established based on Newton's laws of motion and linear dynamics theory. By describing the interactions between the mass block, spring, and damper (damping ring), analyze the vibration characteristics of the system (the system refers to the specific engineering structure or device that applies the acoustic black hole and distributed vibration absorber for broadband vibration control). Its core principle is to simplify the mechanical system into an aggregate of mass (inertial element), spring (elastic element), and damper (energy - dissipating element). Among them, the spring provides a restoring force proportional to the displacement, and the damper generates a resistance force proportional to the velocity. The motion of the mass block is dominated by Newton's second law. The mathematical expression of this model is a second - order linear differential equation: , represents the external excitation force, represents the displacement of the Distributed Vibration Absorber (DVA); Install multiple DVA units at different positions of the main structure according to spatial distribution. Each unit is independently modeled as a single - degree - of - freedom system, and the overall vibration absorption effect is analyzed through the superposition principle; the tuning frequencies of each DVA unit are distributed at non - linear intervals (such as Gaussian or exponential distribution) to expand the vibration absorption bandwidth and enhance robustness; S2.3. Perform modal analysis on the main structure to obtain the natural frequencies and mode shapes of the main structure, where the main structure refers to the actual physical structure or system that requires vibration control. This main structure can be any object that may experience vibration and thus requires vibration damping treatment; S2.4. Adjust the mass of the mass block and the stiffness of the spring so that the tuning frequency of the distributed vibration absorber (DVA) covers the target frequency band. If the modal analysis shows that the main structure has a significant vibration mode near 150 Hz, then adjust the tuning frequency of the DVA to be close to 150 Hz.

[0020] S3. Based on the collaborative tuning strategy of the gradient descent method, co-optimize the parameters of the acoustic black hole (ABH) and the distributed vibration absorber (DVA) to achieve the best vibration suppression effect within the entire frequency band, and introduce the dynamic frequency band weight and the predicted transfer function into the co-optimization process; In this embodiment, by co-optimizing the parameters of the acoustic black hole (ABH) and the distributed vibration absorber (DVA), construct an objective function to minimize the vibration energy within the target frequency band (100 - 2000 Hz); Based on the collaborative tuning strategy of the gradient descent method, co-optimize the parameters of the acoustic black hole (ABH) and the distributed vibration absorber (DVA), including the following steps: S3.1. Map the parameters of the acoustic black hole (ABH) and the distributed vibration absorber (DVA) to real number vectors; S3.2. Set the initial parameter combination (based on empirical values or random initialization, where the initial parameter combination refers to a set of initial values set for these parameters before co-optimizing the parameters of the acoustic black hole (ABH) and the distributed vibration absorber (DVA)); S3.3. Based on the current parameter combination, construct a finite element model of the acoustic black hole (ABH) and the distributed vibration absorber (DVA), perform a harmonic response analysis, and obtain the transfer function within the entire target frequency band , where the transfer function represents the amplitude relationship between the input excitation and the output vibration response at frequency ; S3.4. According to the transfer function , calculate the vibration energy within the entire target frequency band , and superimpose the lightweight penalty term to calculate the objective function value; According to the transfer function , and superimpose the lightweight penalty term to calculate the objective function value as: ; Among them, represents the objective function, and by optimizing the parameters to make minimize, achieving the balance between low-frequency vibration suppression and structural lightweighting; represents the parameter sets of all acoustic black holes (ABHs) and distributed vibration absorbers (DVAs) to be optimized, and adjusting to make the transfer function and the target mass reach the optimal values; represents the starting frequency of the target optimization; represents the termination frequency of the target optimization; represents the lightweighting penalty term; represents the total structural mass, including the mass of the ABH structure substrate, the mass blocks of the DVA, and the total mass of the additional damping layer; represents the parameter sets of all acoustic black holes and distributed vibration absorbers to be optimized; The introduction of the dynamic frequency band weight is for differential optimization control according to the harm degrees of vibration energy at different frequencies. In practical applications, the influence of vibration energy on the system performance varies significantly at different frequency bands: some frequency bands (such as the structural resonance frequency or the key operation frequency band) may cause serious fatigue damage or noise problems, while other frequency bands have lower harm. Through dynamic weight allocation (for example, assigning higher weights to the resonance frequency bands), the optimization process can preferentially suppress the vibration energy in the high-harm frequency bands while taking into account the overall broadband performance; Determine the influence of vibration energy at each frequency band on the system performance through experiments or simulations (collect the system vibration response using a laser vibrometer / acceleration sensor and obtain the natural frequencies and vibration modes through FFT analysis); Based on the influence of vibration energy at each frequency band on the system performance, construct the dynamic frequency band weight (determined by the frequency band energy ratio and the harm level) : ; Among them, represents the input vibration energy spectrum, reflecting the vibration energy distribution at different frequency bands; represents the key frequency band indicator function (set to 1 for the resonance frequency band and 0.2 for the rest); represents the adjustment parameter for amplifying the importance of the key frequency band; Define the damping coefficient as a function of the strain rate Define the damping coefficient as a function of the strain rate Actually means adjusting the damping coefficient according to the actual performance of the material at different strain rates. Specifically, it is to establish a mathematical model that takes into account the influence of the strain rate on the damping coefficient, so that the damping coefficient Not only depends on the properties of the material itself (linear viscous damping coefficient ), but also is proportional to the magnitude of the strain rate and its square (i.e., includes terms and ). This approach more accurately reflects the non - linear energy - dissipation characteristics of the material in practical applications, thereby improving the design accuracy of vibration suppression effect. In the dynamic equation of the vibration system, the damping coefficient directly affects the energy - dissipation characteristics of the system, thereby changing the magnitude and phase of the transfer function and further affecting the vibration energy term in the objective function. Defining the damping coefficient as a function of the strain rate mainly aims to accurately characterize the non - linear energy - dissipation characteristics of the material under dynamic loads. The traditional linear damping model assumes that the damping coefficient is a fixed value. However, in practical engineering, the energy - dissipation ability of damping materials often has a non - linear relationship with the strain rate: at high strain rates (mechanical shock or high - frequency vibration), the response of the internal microstructure of the material (molecular - chain friction, interface slip) will increase, resulting in a significant change in the damping coefficient with the increase of . By establishing the model, the energy - dissipation law of the material from static to dynamic can be more realistically reflected, thereby improving the simulation accuracy in scenarios such as vibration suppression and noise control; this modeling method can also optimize the structural design parameters (damper layout) to enable it to still maintain high - efficiency energy - absorption ability under complex environments such as broadband vibration and temperature changes): ; Among them, represents the linear viscous damping coefficient, which reflects the basic energy - dissipation ability of the material at low strain rates or static conditions (i.e., when the strain rate is close to zero); represents the first - order non - linear viscous damping coefficient, which reflects the energy - dissipation characteristics of the material at medium strain rates (i.e., when the strain rate starts to increase but is not extremely high). As the strain rate increases, the damping coefficient will increase linearly; represents the second - order non - linear viscous damping coefficient, which reflects the energy - dissipation characteristics of the material at high strain rates (such as high - frequency vibration or impact load). When the strain rate further increases, the damping coefficient will increase rapidly in a square relationship; and , , are incorporated into the parameter set (which directly affects the magnitude of the transfer function); Perform finite - element simulations at different temperatures to generate the data set ; Training a deep neural network (DNN) using the data in the dataset so that the DNN outputs a predicted frequency response function , where is the prediction of the DNN for ; The trained DNN, as a surrogate model, can quickly predict the frequency response of the system for any given parameter combination, thus replacing time-consuming finite element simulations and efficiently evaluating the effects of different design schemes during the optimization process to achieve the rapid design and optimization of a broadband vibration control system; the introduction of the surrogate model to predict the transfer function is aimed at solving the problems of high computational cost and low efficiency in traditional optimization that rely on finite element simulations. The surrogate model trained by machine learning (such as neural networks) can predict the system vibration response under different parameter combinations ( ) and environmental conditions with extremely low time consumption, and replacing complex physical simulations has the following advantages: the surrogate model can complete parameter evaluation within seconds, while finite element simulations usually take several hours; explicitly incorporating the influence of temperature on material properties (such as the damping loss factor) makes the optimization results environmentally robust; the surrogate model can capture the non-linear coupling effects between parameters and avoid the dependence on local solutions of traditional gradient methods; by embedding the surrogate model into the objective function, both the optimization accuracy can be guaranteed and the computational resource requirements can be significantly reduced, providing a feasible path for complex multi-objective optimization; In summary, introducing the dynamic frequency band weight and the predicted transfer function into the objective function to optimize the objective function, and the optimized objective function is: ; where represents the optimized objective function; S3.5. Optimizing the objective function value by the gradient descent method: calculating the gradient of the objective function with respect to the parameters (i.e., the rate of change of the function), updating the parameters along the opposite direction of the gradient to gradually reduce the objective function value, and the update step size is controlled by the learning rate; repeating this process until the objective function converges to the minimum value or meets the preset stopping conditions (such as the number of iterations or the error threshold).

[0021] S4. Based on the finite element analysis results, using a mathematical model for analyzing the vibration energy transfer and dissipation to analyze the transfer path and efficiency of energy between the acoustic black hole (ABH) and the distributed vibration absorber (DVA); In this embodiment, based on the finite element analysis results, using a mathematical model for analyzing the vibration energy transfer and dissipation to analyze the transfer path and efficiency of energy between the acoustic black hole (ABH) and the distributed vibration absorber (DVA) includes the following steps: S4.1. Export the vibration response data from ANSYS finite element software, including the displacement field, velocity field, stress tensor, etc. of each node; S4.2. Convert the vibration response data into tensor form, perform Fourier transform on the time series data in the vibration response data, convert the time domain data into frequency domain response data, analyze the frequency domain response data, and extract the vibration characteristics within the key frequency range, including resonance frequency, modal shape, etc.; S4.3. Define the kinetic energy density and potential energy density of the element, calculate the kinetic energy density and potential energy density element by element in the finite element mesh to obtain the energy distribution within the system; Kinetic energy density is: ; Potential energy density is: ; Among them, represents the velocity field; represents the material density; represents the stress tensor; represents the strain tensor; S4.4. Calculate the input power according to the external excitation force and the velocity at the excitation point, perform Fourier transform on the input power to obtain the frequency domain input power spectrum; Input power is: ; Among them, is the excitation force, is the complex conjugate of the velocity; represents taking the real part of the complex number; S4.5. Analyze the energy transfer path based on power flow; Among them, analyzing the energy transfer path based on power flow includes the following steps: S4.51. Perform Fourier transform on the input power to obtain the frequency domain input power spectrum; S4.52. Define the power flow vector, integrate the power flow vector along the structure propagation direction (radial or axial) , represents the th component of the velocity vector, to obtain the energy transfer path; S4.53. Compare the power flow density differences between the acoustic black hole (ABH) region and the distributed vibration absorber (DVA) region, and analyze the energy distribution ratio; S4.54. Calculate the dissipated power of the acoustic black hole (ABH) and the power of the kinetic energy of the distributed vibration absorber (DVA) element converted into heat energy.

[0022] Dissipated power of the acoustic black hole (ABH) is: ; Among them, is the loss factor of the damping material; represents the volume element; The power of converting the kinetic energy of the distributed vibration absorber (DVA) unit into heat energy : ; Among them, is the DVA damping coefficient, is the velocity of the mass block; represents the number of DVA units; represents the index of the DVA unit.

[0023] S4.6. Divide the structure into an acoustic black hole (ABH) region (mainly responsible for the aggregation of high-frequency vibration energy), a distributed vibration absorber (DVA) region (mainly responsible for the absorption of low-frequency vibration energy), and a transmission path region (the transition region connecting ABH and DVA), and establish a segmented energy balance equation; The segmented energy balance equation is: ; ; Among them, represents the power transmitted from ABH to DVA; represents the energy of the acoustic black hole (ABH) region; represents the energy of the distributed vibration absorber (DVA) region; represents the energy loss of the acoustic black hole (ABH) region; represents the energy loss of the distributed vibration absorber (DVA) region; S4.7. Discretize the energy transfer equation and solve it using the finite difference method: Divide the continuous physical domain into a series of discrete grid points, and then approximate the derivative terms in the original equation with difference quotients at these points, thereby converting the differential equation into a set of algebraic equations that can be independently solved at each grid point. Then, set appropriate boundary conditions according to the actual situation, and gradually update the values at each grid point through an iterative algorithm until the solution converges, that is, the change between adjacent iterative steps is less than the preset threshold, so as to simulate and analyze how the energy in the system is transmitted and dissipated with the change of time and space.

[0024] S5. Collect the vibration signals of the acoustic black hole (ABH) through an acceleration sensor to verify the broadband vibration control effect; In this embodiment, collecting the vibration signals of the acoustic black hole (ABH) through an acceleration sensor to verify the broadband vibration control effect includes the following steps: S5.1. Obtain the original vibration signal data and perform preprocessing and analysis; S5.2. Perform a fast Fourier transform on the preprocessed vibration signal to convert it into a frequency-domain signal. Based on the frequency-domain signal, calculate the power spectral density to evaluate the energy distribution of each frequency component; Convert the time-domain signal into a frequency-domain power spectral density It is: ; where, is the number of sampling points; is the sampling frequency; represents performing a fast Fourier transform operation; S5.3. Compare the vibration responses with and without the acoustic black hole (ABH) region + distributed vibration absorber (DVA), and calculate the attenuation amount of vibration energy at each frequency point, that is, calculate the difference in power spectral density between the initial state and the optimized state; S5.4. Based on the input excitation and output response, calculate the transfer function of the system. Using the transfer function, integrate the power flow vector along the structural propagation direction to identify the main energy transfer paths; S5.5. Use an impact hammer to apply a transient excitation, collect the vibration decay process, and record the acceleration time-domain signal located in the acoustic black hole (ABH) region; S5.6. Extract the initial vibration amplitude from the collected time-domain signal, track the change of the vibration amplitude over time, find the time when the amplitude decays to a% of the initial value, and compare the decay times under different conditions (such as only ABH, only DVA, ABH + DVA combination) to evaluate the energy dissipation efficiency of the system; S5.7. Perform a Hilbert transform on the acceleration time-domain signal, extract the envelope, analyze the envelope decay rate, and verify the broadband dissipation characteristics of the acoustic black hole (ABH) region + distributed vibration absorber (DVA); where, performing a Hilbert transform on the acceleration time-domain signal, extracting the envelope, analyzing the envelope decay rate, and verifying the broadband dissipation characteristics of the acoustic black hole (ABH) region + distributed vibration absorber (DVA) combination include the following steps: S5.71. Use variational mode decomposition (VMD) to decompose the collected acceleration time-domain signal into K intrinsic mode functions (IMFs) to separate the vibration components in different frequency bands: , where, represents the index of the intrinsic mode function, represents the total number of IMFs obtained by decomposition; S5.72. Perform a Hilbert transform on each intrinsic mode function component respectively to generate an analytic signal : , where, represents the imaginary unit, indicating the imaginary part direction, Denotes the Hilbert transform, which converts a real signal into an imaginary part, constructs a complex signal to eliminate negative frequency components, and extracts the instantaneous envelope of each component , and the modulus of the analytic signal is the instantaneous amplitude envelope; S5.73. Establish an initial attenuation model based on linear viscoelastic theory and introduce a non-linear correction term into the model Adjust and construct a piecewise attenuation model to distinguish the attenuation rates in different frequency bands. The traditional linear viscoelastic model assumes that the damping coefficient is a fixed value. However, in practical applications, the energy dissipation capacity (i.e., damping) of materials often varies with frequency. Especially under high-frequency and low-frequency conditions, differences in the response mechanisms of the internal microstructure of materials (such as molecular chain friction, interfacial slip, etc.) will lead to different energy dissipation efficiencies. During actual vibration processes, not only steady-state vibrations (continuous and stable vibrations) exist, but transient processes (brief vibrations during impact or rapid loading) may also occur. Under these different types of vibration modes, the energy dissipation characteristics of the system will also be different, and a more accurate model is needed to describe this dynamic behavior; The piecewise attenuation model is: ; wherein, Denotes the critical time; Denotes the time variable; Denotes the initial amplitude; Denotes the transient attenuation coefficient, which controls the exponential decay rate and reflects characteristics such as material damping and structural energy dissipation; Denotes the non-linear correction coefficient, which characterizes the amplitude correction term caused by non-linear effects (frictional hysteresis, material plastic deformation) during the transient stage; Denotes the steady-state attenuation coefficient, which reflects the attenuation rate dominated by linear damping after the system enters the steady state; S5.74. Verify the energy dissipation capacity of the combination of the acoustic black hole (ABH) region + distributed vibration absorber (DVA) in a wide frequency range by comparing the attenuation rates of the envelope lines under different frequency components.

[0025] This embodiment provides experimental verification: Vibration tests are respectively carried out by pasting traditional ABH and ABH + DVA structures with equivalent mass on a 1 mm aluminum plate. Under the same excitation, the vibration velocity of the ABH + damping ring + DVA scheme is significantly less than that of the traditional ABH scheme, as Figure 2 shown.

[0026] Embodiment 2: This embodiment provides a broadband vibration control device based on an acoustic black hole and a distributed vibration absorber, including a sensor, a storage, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the broadband vibration control method based on the acoustic black hole and the distributed vibration absorber described in any one of the above are implemented.

[0027] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and the descriptions in the specification are only preferred examples of the present invention and are not used to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and all these changes and improvements fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A broadband vibration control method based on acoustic black holes and distributed vibration absorbers, characterized in that It includes the following steps: S1. Construct a three-dimensional model of the acoustic black hole and import the three-dimensional model of the acoustic black hole into finite element analysis software; S2. Define the design parameters of the distributed vibration absorber and establish a spring-mass-damper system model for the distributed vibration absorber unit; S3. Based on the collaborative tuning strategy of the gradient descent method, co-optimize the parameters of the acoustic black hole and the distributed vibration absorber to achieve broadband vibration control, and introduce the dynamic frequency band weight and the predicted transfer function into the co-optimization process; S4. Based on the finite element analysis results, use a mathematical model for analyzing the transfer and dissipation of vibration energy to analyze the transfer path and efficiency of energy between the acoustic black hole and the distributed vibration absorber; S5. Collect the vibration signals of the acoustic black hole through an acceleration sensor to verify the broadband vibration control effect.

2. The broadband vibration control method based on acoustic black holes and distributed vibration absorbers according to claim 1, characterized in that: In the above S1, constructing a three-dimensional model of the acoustic black hole and importing the three-dimensional model of the acoustic black hole into finite element analysis software includes the following steps: S1.

1. Determine the shape of the core layer of the acoustic black hole and set the central thickness; S1.

2. Design a thickness distribution function by establishing parameters with the thickness decreasing exponentially along the radial direction; S1.

3. Based on the wave theory, use the bending wave equation to analyze how the vibration wave propagates in the region of the acoustic black hole with a gradually decreasing thickness; S1.

4. Analyze the behavior of vibration waves with different frequencies in the acoustic black hole structure; S1.

5. Use ANSYS finite element analysis software for three-dimensional modeling.

3. The broadband vibration control method based on acoustic black holes and distributed vibration absorbers according to claim 2, characterized in that: In the above S1.3, based on the wave theory, using the bending wave equation to analyze how the vibration wave propagates in the region of the acoustic black hole with a gradually decreasing thickness includes the following steps: S1.

31. Define the thin plate material parameters, where the thin plate material parameters include Young's modulus , density , Poisson's ratio ; S1.

32. Based on the thin plate wave theory, construct a bending wave control equation; S1.

33. Analyze the changes in wave speed and wavelength according to the relationship between the wave speed of the bending wave and the thickness of the acoustic black hole structure; S1.

34. Use the method of separation of variables to solve the bending wave control equation to obtain the displacement field of the vibration wave.

4. The broadband vibration control method based on an acoustic black hole and a distributed vibration absorber according to claim 3, characterized in that: In the above S2, defining the design parameters of the distributed vibration absorber and establishing a spring-mass-damper system model for the distributed vibration absorber unit includes the following steps: S2.

1. Define the design parameters of the distributed vibration absorber, including the mass of the mass block , the spring stiffness , the damping coefficient , the tuning frequency ; S2.

2. Based on the interaction between the mass block, the spring and the damper, construct a spring-mass-damper system model; S2.

3. Conduct a modal analysis of the main structure to obtain the natural frequencies and mode shapes of the main structure. S2.

4. Adjust the mass of the mass block according to the modal analysis results and the stiffness of the spring so that the tuning frequency of the distributed vibration absorber covers the target frequency band.

5. The broadband vibration control method based on an acoustic black hole and a distributed vibration absorber according to claim 4, characterized in that: In the above S3, based on the collaborative tuning strategy of the gradient descent method, co-optimize the parameters of the acoustic black hole and the distributed vibration absorber, including the following steps: S3.

1. Map the parameters of the acoustic black hole and the distributed vibration absorber into real number vectors; S3.

2. Set the initial parameter combination; S3.

3. Build a finite element model of the acoustic black hole and the distributed vibration absorber based on the current parameter combination, and obtain the transfer function within the entire target frequency band ; S3.

4. Calculate the objective function value according to the transfer function , and superimpose the lightweight penalty term to optimize the objective function by introducing the dynamic frequency band weight and the predicted transfer function into the objective function; S3.

5. Optimize the objective function value through the gradient descent method.

6. The broadband vibration control method based on acoustic black holes and distributed vibration absorbers according to claim 5, characterized in that: In the said S3.4, according to the transfer function , and superimpose the lightweight penalty term to calculate the objective function value as: ； Among them, represents the objective function; represents all the parameter sets of acoustic black holes and distributed vibration absorbers to be optimized; represents the starting frequency of the objective optimization; represents the termination frequency of the objective optimization; represents the lightweight penalty term; represents the total mass of the structure; represents all the parameter sets of acoustic black holes and distributed vibration absorbers to be optimized; Construct a dynamic frequency band weight based on the influence of vibration energy in each frequency band on system performance ; Define the damping coefficient as a function of the strain rate as follows : ； Among them, represents the linear viscous damping coefficient; represents the first-order non-linear viscous damping coefficient; represents the second-order non-linear viscous damping coefficient; and and and are included in the parameter set ; Perform finite element simulations at different temperatures to generate a data set ; Training a deep neural network using the data in the dataset to make the deep neural network output a predicted frequency response function ; In summary, introducing the dynamic frequency band weight and the predicted transfer function into the objective function to optimize the objective function.

7. The broadband vibration control method based on acoustic black hole and distributed vibration absorber according to claim 6, characterized in that: In the above S4, based on the finite element analysis results, using a mathematical model for analyzing the transfer and dissipation of vibration energy to analyze the transfer path and efficiency of energy between the acoustic black hole and the distributed vibration absorber includes the following steps: S4.

1. Export the vibration response data from the ANSYS finite element software; S4.

2. Convert the vibration response data into a tensor form, perform Fourier transform on the time series data in the vibration response data, convert the time domain data into frequency domain response data, analyze the frequency domain response data, and extract the vibration characteristics within the key frequency range; S4.

3. Define the kinetic energy density and potential energy density of the element, calculate the kinetic energy density and potential energy density element by element in the finite element mesh to obtain the energy distribution within the system; S4.

4. Calculate the input power based on the external excitation force and the velocity at the excitation point, perform Fourier transform on the input power to obtain the frequency domain input power spectrum; S4.

5. Analyze the energy transfer path based on power flow; S4.

6. Divide the structure into an acoustic black hole region, a distributed vibration absorber region, and a transfer path region, and establish a segmented energy balance equation; S4.

7. Discretize the energy transfer equation and solve it using the finite difference method.

8. The broadband vibration control method based on acoustic black holes and distributed vibration absorbers according to claim 7, characterized in that: In the above-mentioned S5, the vibration signal of the acoustic black hole is collected by an acceleration sensor to verify the broadband vibration control effect, including the following steps: S5.

1. Obtain the original vibration signal data and perform preprocessing and analysis; S5.

2. Perform fast Fourier transform on the preprocessed vibration signal to convert it into a frequency domain signal, and calculate the power spectral density based on the frequency domain signal; S5.

3. Compare the vibration responses with and without the acoustic black hole region + distributed vibration absorber, and calculate the attenuation amount of the vibration energy at each frequency point; S5.

4. Calculate the transfer function of the system based on the input excitation and output response, and use the transfer function to integrate the power flow vector along the structure propagation direction to identify the main energy transfer path; S5.

5. Collect the vibration attenuation process and record the acceleration time domain signal located in the acoustic black hole region; S5.

6. Extract the initial vibration amplitude from the collected time domain signal, track the change of the vibration amplitude over time, find the time when the amplitude decays to a% of the initial value, and compare the decay times under different conditions to evaluate the energy dissipation efficiency of the system; S5.

7. Perform Hilbert transform on the acceleration time domain signal, extract the envelope, analyze the envelope decay rate, and verify the broadband dissipation characteristics of the acoustic black hole region + distributed vibration absorber.

9. The broadband vibration control method based on acoustic black holes and distributed vibration absorbers according to claim 8, characterized in that: In the above-mentioned S5.7, performing Hilbert transform on the acceleration time domain signal, extracting the envelope, analyzing the envelope decay rate, and verifying the broadband dissipation characteristics of the combination of the acoustic black hole region + distributed vibration absorber include the following steps: S5.

71. Use variational mode decomposition to decompose the collected acceleration time domain signal into K intrinsic mode functions to separate the vibration components in different frequency bands; S5.

72. Perform Hilbert transform on each intrinsic mode function component respectively to generate an analytic signal; S5.

73. Establish an initial decay model based on the linear viscoelastic theory and introduce a nonlinear correction term in the model for adjustment to construct a segmented decay model to distinguish the decay rates in different frequency bands; S5.

74. Verify the energy dissipation ability of the combination of the acoustic black hole region + distributed vibration absorber within the broadband range by comparing the envelope decay rates under different frequency components.

10. A broadband vibration control device based on an acoustic black hole and a distributed vibration absorber, comprising a sensor, a storage, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it implements the steps of the broadband vibration control method based on the acoustic black hole and the distributed vibration absorber described in any one of claims 1 to 9.

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