Broadband vibration control method and device based on acoustic black hole and distributed absorber

Abstract

The present application relates to the technical field of broadband vibration control, and particularly relates to a broadband vibration control method and device based on an acoustic black hole and a distributed vibration absorber. 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; defining design parameters of the distributed vibration absorber, and establishing a spring-mass-damper system model of a distributed vibration absorber unit; based on a gradient descent method collaborative tuning strategy, the parameters of the acoustic black hole and the distributed vibration absorber are collaboratively optimized to achieve broadband vibration control; based on the finite element analysis results, a mathematical model for analyzing vibration energy transmission and dissipation is used to analyze the transmission path and efficiency of energy between the acoustic black hole and the distributed vibration absorber; and the vibration signal of the acoustic black hole is collected by an acceleration sensor to verify the broadband vibration control effect. The present application not only focuses on the suppression of vibration energy, but also considers the energy dissipation efficiency and lightweight requirements of the system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of broadband vibration control, in particular to a broadband vibration control method and device based on acoustic black hole and distributed vibration absorber. BACKGROUND

[0002] In modern engineering design, vibration control is crucial for improving the stability of mechanical structures, prolonging the service life, and enhancing the overall performance. However, traditional vibration control techniques often face the problem of narrowband effect, i.e., they can only provide effective vibration suppression within a specific frequency range, making it difficult to meet the demand for broadband vibration control. In particular, in high-precision fields such as aerospace and automobile manufacturing, structures need to withstand vibrations from multiple sources with complex frequency spectra, including vibration components in the low to high frequency range. In this case, a single type of vibration absorption or damping measure is not sufficient. For example, traditional vibration absorbers are mainly optimized for a specific frequency, and their vibration suppression effect is not good for frequencies beyond that range. While damping materials can dissipate energy, their efficiency varies significantly with frequency, and their performance is particularly limited at high frequencies. Therefore, a broadband vibration control method and device based on acoustic black hole and distributed vibration absorber are provided. SUMMARY

[0003] The purpose of the present application is to provide a broadband vibration control method and device based on acoustic black hole and distributed vibration absorber to solve the problems of narrowband vibration control limitation, high-frequency vibration accumulation and dissipation demand, and insufficient low-frequency vibration absorption mentioned in the background.

[0004] To achieve the above-mentioned purpose, the present application aims to provide a broadband vibration control method based on acoustic black hole and distributed vibration absorber, comprising the following steps:

[0005] S1, constructing a three-dimensional model of an acoustic black hole and importing the three-dimensional model of the acoustic black hole into a finite element analysis software;

[0006] S2, defining the design parameters of the distributed vibration absorber, and establishing a spring-mass-damper system model of the distributed vibration absorber unit;

[0007] S3, based on the gradient descent method of collaborative tuning strategy, the parameters of the acoustic black hole and the distributed vibration absorber are collaboratively optimized to achieve broadband vibration control, and the dynamic frequency band weight and the predicted transfer function are introduced into the process of collaborative optimization;

[0008] S4, based on the results of finite element analysis, the mathematical model of analyzing vibration energy transmission and dissipation is used to analyze the transmission path and efficiency of energy between the acoustic black hole and the distributed vibration absorber;

[0009] S5, the vibration signal of the acoustic black hole is collected by the acceleration sensor to verify the effect of broadband vibration control.

[0010] As a further improvement of the technical solution, in S1, a three-dimensional model of the acoustic black hole is constructed, and the three-dimensional model of the acoustic black hole is imported into the finite element analysis software, including the following steps:

[0011] S1.1, determine the shape of the core layer of the acoustic black hole, and set the center thickness;

[0012] S1.2, design a thickness distribution function with the thickness decreasing exponentially along the radial direction;

[0013] S1.3, based on wave theory, analyze how vibration waves propagate in the acoustic black hole area with gradually decreasing thickness by using bending wave equation;

[0014] S1.4, analyze the behavior of vibration waves of different frequencies in the acoustic black hole structure;

[0015] S1.5, use ANSYS finite element analysis software for three-dimensional modeling.

[0016] As a further improvement of the technical solution, in S1.3, based on wave theory, analyze how vibration waves propagate in the acoustic black hole area with gradually decreasing thickness by using bending wave equation, including the following steps:

[0017] S1.31, define thin plate material parameters, including Young's modulus , density , Poisson's ratio ;

[0018] S1.32, based on thin plate wave theory, construct bending wave control equation;

[0019] S1.33, analyze the change of wave speed and wavelength according to the relationship between wave speed and acoustic black hole structure thickness;

[0020] S1.34, solve the bending wave control equation by separation of variables method to get the displacement field of vibration wave.

[0021] As a further improvement of the technical solution, in S2, define the design parameters of the distributed vibration absorber, and establish the spring-mass-damper system model of the distributed vibration absorber unit, including the following steps:

[0022] S2.1, define the design parameters of the distributed vibration absorber, including mass , spring stiffness , damping coefficient , tuning frequency ;

[0023] S2.2, constructing a spring-mass-damper system model based on the interaction between the mass, spring and damper;

[0024] S2.3, performing modal analysis on the main structure to obtain the natural frequency and mode shape of the main structure;

[0025] S2.4, adjusting the mass of the mass block and the stiffness of the spring according to the modal analysis results , so that the tuning frequency of the distributed vibration absorber covers the target frequency band.

[0026] As a further improvement of the technical solution, in the S3, the gradient descent method-based collaborative tuning strategy is used to collaboratively optimize the acoustic black hole and the distributed vibration absorber parameters, including the following steps:

[0027] S3.1, mapping the parameters of the acoustic black hole and the distributed vibration absorber into a real number vector;

[0028] S3.2, setting an initial parameter combination;

[0029] S3.3, constructing a finite element model of the acoustic black hole and the distributed vibration absorber based on the current parameter combination, and obtaining the transfer function in the entire target frequency band ;

[0030] S3.4, calculating the objective function value according to the transfer function , and adding a lightweight penalty term , introducing the dynamic frequency band weight and the predicted transfer function into the objective function to optimize the objective function;

[0031] S3.5, optimizing the objective function value by the gradient descent method.

[0032] As a further improvement of the technical solution, in the S3.4, the objective function value is calculated according to the transfer function , and a lightweight penalty term is added:

[0033] ;

[0034] wherein, represents the objective function; represents the set of all acoustic black hole and distributed vibration absorber parameters to be optimized; represents the starting frequency of the target optimization; represents the end frequency of the target optimization; represents the lightweight penalty term; represents the total mass of the structure; ​represents all the sets of acoustic black hole and distributed absorber parameters to be optimized;

[0035] Based on the influence of vibration energy of each frequency band on the performance of the system, a dynamic frequency band weight is constructed ;

[0036] The damping coefficient is defined as a function of the strain rate :

[0037] ;

[0038] wherein, represents the linear viscous damping coefficient; represents the first-order nonlinear viscous damping coefficient; represents the second-order nonlinear viscous damping coefficient; and , , is included in the parameter set ;

[0039] Finite element simulation is performed at different temperatures to generate a data set ;

[0040] The data in the data set is used to train a deep neural network, so that the deep neural network outputs a predicted frequency response function ;

[0041] As described above, the dynamic frequency band weight and the predicted transfer function are introduced into the objective function to optimize the objective function.

[0042] As a further improvement of the technical solution, in the S4, based on the finite element analysis result, the mathematical model for analyzing vibration energy transmission and dissipation is used to analyze the transmission path and efficiency of energy between the acoustic black hole and the distributed absorber, including the following steps:

[0043] S4.1, export vibration response data from ANSYS finite element software;

[0044] 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;

[0045] S4.3, define kinetic energy density and potential energy density of the unit, calculate kinetic energy density and potential energy density of each unit in the finite element grid to obtain the energy distribution in the system;

[0046] S4.4, calculate input power based on external excitation force and velocity at excitation point, and perform Fourier transform on input power to obtain frequency domain input power spectrum;

[0047] S4.5, analyze energy transmission path based on power flow;

[0048] S4.6, divide structure into acoustic black hole region, distributed absorber region and transmission path region, and establish segmented energy balance equation;

[0049] S4.7, discretize energy transmission equation and solve using finite difference method.

[0050] As a further improvement of the technical solution, in S5, the vibration signal of the acoustic black hole is collected by the acceleration sensor to verify the broadband vibration control effect, including the following steps:

[0051] S5.1, obtain vibration signal raw data and perform preprocessing and analysis;

[0052] S5.2, perform fast Fourier transform on the preprocessed vibration signal to convert it to a frequency domain signal, and calculate power spectral density based on the frequency domain signal;

[0053] S5.3, compare vibration responses with and without acoustic black hole region + distributed absorber, and calculate vibration energy attenuation at each frequency point;

[0054] S5.4, calculate the transfer function of the system based on input excitation and output response, and use the transfer function to integrate power flow vectors along the propagation direction of the structure to identify the main energy transmission path;

[0055] S5.5, collect vibration attenuation process and record acceleration time domain signal located in the acoustic black hole region;

[0056] S5.6, extract initial vibration amplitude from the collected time domain signal, track the change of vibration amplitude with time, find the time when the amplitude decays to a% of the initial value, compare the decay time under different conditions, and evaluate the energy dissipation efficiency of the system;

[0057] S5.7, perform Hilbert transform on the acceleration time domain signal, extract envelope, analyze envelope decay rate, and verify the broadband dissipation characteristics of the acoustic black hole region + distributed absorber combination.

[0058] As a further improvement of the technical solution, in S5.7, the acceleration time domain signal is subjected to Hilbert transform to extract the envelope, analyze the envelope decay rate, and verify the broadband dissipation characteristics of the acoustic black hole region + distributed absorber combination, including the following steps:

[0059] S5.71, the collected acceleration time domain signal is decomposed into K intrinsic mode functions by using variational mode decomposition, and the vibration components of different frequency bands are separated;

[0060] S5.72, Hilbert transform is performed on each intrinsic mode function component to generate an analytical signal;

[0061] S5.73, an initial attenuation model is established based on linear viscoelastic theory, and a nonlinear correction term is introduced into the model for adjustment to construct a segmented attenuation model, so as to distinguish the attenuation rates of different frequency bands;

[0062] S5.74, the energy dissipation capability of the acoustic black hole region + distributed vibration absorber combination in a wide frequency range is verified by comparing the attenuation rates of the envelope lines under different frequency components.

[0063] On the other hand, the application provides a wide-frequency vibration control device based on acoustic black hole and distributed vibration absorber, comprising a sensor, a storage, a processor and a computer program stored in the storage and executable on the processor, wherein the processor executes the computer program to realize the steps of the wide-frequency vibration control method based on acoustic black hole and distributed vibration absorber according to any one of the above.

[0064] Compared with the prior art, the application has the following beneficial effects:

[0065] 1. In the wide-frequency vibration control method and device based on acoustic black hole and distributed vibration absorber, the acoustic black hole (ABH) and the distributed vibration absorber (DVA) are combined, and the method can realize effective vibration control in a wide frequency range. The acoustic black hole (ABH) is designed to concentrate and dissipate high-frequency vibration energy, while the distributed vibration absorber (DVA) is designed to absorb low-frequency vibration. The synergistic optimization strategy further ensures the optimal cooperation of the two in the target frequency band, realizing effective suppression of the whole structure vibration. In addition, the dynamic frequency band weight and the predicted transfer function are introduced into the optimization process, which can specifically strengthen the vibration control of the key frequency band, thereby improving the anti-vibration performance of the whole system.

[0066] 2. In the wide-frequency vibration control method and device based on acoustic black hole and distributed vibration absorber, not only the vibration energy suppression is concerned, but also the energy dissipation efficiency and lightweight demand of the system are considered. By accurately simulating and analyzing the energy transfer path and efficiency between ABH and DVA, and using a nonlinear damping model to more accurately reflect the actual energy dissipation characteristics of the material, the system can reduce unnecessary mass increase while ensuring efficient energy absorption. Especially using deep neural network (DNN) as a proxy model to quickly evaluate the effect of different design schemes, greatly reducing the calculation cost and improving the design optimization efficiency, which is helpful to realize the lightweight of the structure under the given vibration suppression target. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 for the overall method flowchart of the present application;

[0068] Figure 2 for the vibration test comparison chart of the present embodiment. DETAILED DESCRIPTION

[0069] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0070] Embodiment 1: please refer to Figures 1-2 As shown in the figure, the present embodiment provides a broadband vibration control method based on acoustic black hole and distributed vibration absorber, including the following steps:

[0071] S1, construct a three-dimensional model of acoustic black hole (ABH), and import the three-dimensional model of acoustic black hole (ABH) into finite element analysis software;

[0072] In the present embodiment, the three-dimensional model of acoustic black hole (ABH) is constructed, and the three-dimensional model of acoustic black hole (ABH) is imported into finite element analysis software, including the following steps:

[0073] S1.1, determine the shape of the core layer of acoustic black hole (ABH) (circular or square), and set the center thickness;

[0074] S1.2, design a thickness distribution function with the thickness decreasing along the radial direction according to the exponential law, and ensure that the minimum thickness of the edge is 0.4mm;

[0075] S1.3, based on wave theory, analyze how vibration waves propagate in the area of acoustic black hole (ABH) with gradually decreasing thickness by using bending wave equation;

[0076] Among them, the wave speed and energy density are controlled by the thickness gradient, combined with the damping layer dissipation, and the ABH realizes efficient control of high-frequency vibration energy;

[0077] Based on wave theory, bending wave equation is used to analyze how vibration waves propagate in the area of acoustic black hole (ABH) with gradually decreasing thickness, including the following steps:

[0078] S1.31, define the thin plate material parameters, including Young's modulus , density , Poisson's ratio ;

[0079] S1.32, based on the thin plate wave theory, the bending wave control equation is constructed: wherein, is the bending stiffness, and the thickness is related to the third power of the thickness, is the displacement perpendicular to the plate surface, since the thickness of the ABH region varies with position, the is substituted into the equation to obtain the bending wave equation under the non-uniform medium, and a variable coefficient term is introduced to represent the effect of the thickness gradient on wave propagation, and the new bending wave equation becomes: ; wherein, represents the position variable;

[0080] S1.33, according to the relationship between the wave speed of the bending wave and the thickness of the acoustic black hole (ABH) structure, the change of the wave speed and the wavelength is analyzed, and the wave speed is related to the thickness as: The decrease in thickness leads to a decrease in wave speed and a shortening of 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 prevents the vibration wave from escaping and concentrates energy in this region;

[0081] S1.34, the separation of variables method is used to solve the bending wave control equation, and the displacement field of the vibration wave is obtained,

[0082] The displacement field can be decomposed into the product of the time and space parts; and the above is substituted into the bending wave equation, and the equations of the time part and the space part are solved respectively, the time part is usually a simple harmonic equation, and the space part needs to consider the geometric shape and boundary conditions;

[0083] The boundary conditions need to meet: continuity condition: at the junction of the ABH and the non-ABH region, the displacement and stress are continuous; radiation condition: an absorption damping layer is set at the edge of the ABH to simulate energy dissipation;

[0084] S1.4, analyze the behavior of vibration waves of different frequencies in the acoustic black hole (ABH) structure, especially how the high-frequency components are concentrated and dissipated in the damping layer;

[0085] S1.5, use ANSYS finite element analysis software to perform three-dimensional modeling, in the ANSYS finite element software, map the thickness function to a circular or annular region to generate a geometrically graded three-dimensional thin plate model.

[0086] S2, define the design parameters of the distributed vibration absorber (DVA), and establish a spring-mass-damper system model of the distributed vibration absorber (DVA) unit;

[0087] In this embodiment, the core is to realize wideband vibration absorption through the synergistic effect of the spring-mass-damper unit;

[0088] Defining design parameters of a distributed vibration absorber (DVA), establishing a spring-mass-damper system model of a DVA unit, including the following steps:

[0089] S2.1, defining the design parameters of the distributed vibration absorber (DVA), including the mass of the mass , spring stiffness , damping coefficient , tuning frequency ;

[0090] S2.2, building a spring-mass-damper system model based on the interaction between the mass, spring and damper, the spring-mass-damper system model is established based on Newton's law of motion and linear dynamics theory, and the vibration characteristics of the system (the specific engineering structure or device using the acoustic black hole and the distributed vibration absorber for broadband vibration control) are analyzed by describing the interaction between the mass, spring and damper (damping ring). The core principle is to simplify the mechanical system into a collection of mass (inertial element), spring (elastic element) and damper (energy dissipation element), where the spring provides a restoring force proportional to displacement, the spring provides a restoring force proportional to displacement, and the damper generates a resistance proportional to velocity. The motion of the mass is dominated by Newton's second law, and 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);

[0091] A plurality of DVA units are installed at different positions of the main structure according to the spatial distribution, each unit is independently modeled as a single degree of freedom system, and the overall vibration absorption effect is analyzed by superposition principle; the tuning frequencies of each DVA unit are distributed in a non-linear interval (such as Gaussian or exponential distribution) to expand the vibration absorption bandwidth and enhance the robustness;

[0092] S2.3, modal analysis of the main structure, obtaining the natural frequency and mode shape of the main structure, the main structure refers to the actual physical structure or system that needs to be vibration controlled. This main structure can be any object that may experience vibration and therefore needs to be damped;

[0093] S2.4, according to the modal analysis results, adjusting the mass of the mass 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 significant vibration mode near 150Hz, adjust the tuning frequency of the DVA close to 150Hz.

[0094] S3: A collaborative tuning strategy based on the gradient descent method coordinates the optimization of the acoustic black hole (ABH) and distributed vibration absorber (DVA) parameters to achieve the best vibration suppression effect across the entire frequency band. Dynamic frequency band weights and predicted transfer functions are introduced into the collaborative optimization process.

[0095] In this embodiment, by collaboratively optimizing the parameters of the acoustic black hole (ABH) and the distributed vibration absorber (DVA), an objective function is constructed to minimize the vibration energy within the target frequency band (100-2000Hz);

[0096] The parameters of the acoustic black hole (ABH) and the distributed vibration absorber (DVA) are collaboratively optimized using a collaborative tuning strategy based on the gradient descent method. The strategy includes the following steps:

[0097] S3.1. Map the parameters of the acoustic black hole (ABH) and the distributed vibration absorber (DVA) into real vectors;

[0098] S3.2. Set the initial parameter combination (based on empirical values ​​or random initialization. The initial parameter combination refers to a set of initial values ​​set for these parameters before co-optimizing the acoustic black hole (ABH) and distributed vibration absorber (DVA) parameters);

[0099] S3.3. Construct the finite element model of acoustic black hole (ABH) and distributed vibration absorber (DVA) based on the current parameter combination, perform harmonic response analysis, and obtain the transfer function within the entire target frequency band. , transfer function Indicates the frequency The relationship between the input excitation and the output vibration response amplitude;

[0100] 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;

[0101] According to the transfer function , and superimpose the lightweight penalty term To calculate the objective function value is:

[0102] ;

[0103] in, Represents the objective function, by optimizing the parameters make Minimize to achieve a balance between low-frequency vibration suppression and structural lightweight; Represents all the acoustic black hole (ABH) and distributed vibration absorber (DVA) parameter sets to be optimized, adjust Make the transfer function and target mass reach the optimal value; denotes the starting frequency of target optimization; denotes the ending frequency of target optimization; denotes the lightweight penalty term; denotes the total mass of the structure, including the mass of the ABH structure substrate, the mass of the DVA mass block, and the total mass of the additional damping layer; denotes the set of all acoustic black hole and distributed absorber parameters to be optimized;

[0104] Dynamic frequency band weight The introduction of dynamic frequency band weight is to differentiate the optimization control according to the degree of harm of vibration energy at different frequencies. In practical applications, the impact of vibration energy at different frequency bands on system performance is significantly different: some frequency bands (such as the structural resonance frequency or the key operating frequency band) may cause serious fatigue damage or noise problems, while other frequency bands have lower harm. By dynamically allocating weights (for example, giving higher weights to resonance frequency bands), the optimization process can preferentially suppress vibration energy in high-harm frequency bands while considering overall broadband performance;

[0105] Determine the impact of vibration energy at each frequency band on system performance through experiments or simulations (use a laser vibration meter / acceleration sensor to collect system vibration responses and obtain natural frequencies and modes of vibration through FFT analysis);

[0106] Based on the impact of vibration energy at each frequency band on system performance, construct dynamic frequency band weight (determined by the proportion of energy at each frequency band and the harm level) :

[0107] ;

[0108] where, denotes the input vibration energy spectrum, reflecting the distribution of vibration energy at different frequency bands; denotes the key frequency band indicator function (set to 1 for resonance frequency bands and 0.2 for others); denotes the adjustment parameter, used to amplify the importance of key frequency bands;

[0109] Define the damping coefficient as a function of strain rate In fact, defining the damping coefficient as a function of strain rate is to adjust the damping coefficient based on the actual performance of the material at different strain rates. Specifically, a mathematical model is established that considers the impact of 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 size of the strain rate and its square (i.e., the terms and ), which more accurately reflects the nonlinear energy dissipation characteristics of materials in actual applications, thereby improving the design accuracy of vibration suppression. In the dynamic equation of the vibration system, the damping coefficient directly affects the energy dissipation characteristics of the system, thereby changing the amplitude and phase of the transfer function and in turn affecting the vibration energy term in the objective function . Defining the damping coefficient as a function of the strain rate , the main purpose is to accurately depict the nonlinear energy dissipation characteristics of materials under dynamic load. The traditional linear damping model assumes that the damping coefficient is a fixed value, but in actual engineering, the energy dissipation capacity of damping materials often has a nonlinear relationship with the strain rate: at high strain rates (mechanical impact or high-frequency vibration), the response of the internal microstructure of the material (molecular chain friction, interface slip) will increase, causing the damping coefficient to change significantly as increases. 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 vibration suppression, noise control, and other scenarios; this modeling method can also optimize the structural design parameters (damper layout) to maintain high energy absorption capacity in complex environments such as wideband vibration and temperature changes:

[0110] ;

[0111] wherein represents the linear viscous damping coefficient, which reflects the basic energy dissipation capacity of the material under low strain rate or static conditions (i.e., when the strain rate is close to zero); represents the first-order nonlinear viscous damping coefficient, which reflects the energy dissipation characteristics of the material under moderate strain rates (i.e., when the strain rate starts to increase but is not extremely high), and as the strain rate increases, the damping coefficient will increase linearly; represents the second-order nonlinear viscous damping coefficient, which reflects the energy dissipation characteristics of the material under high strain rates (e.g., high-frequency vibration or impact load), and when the strain rate further increases, the damping coefficient will rapidly increase in a quadratic relationship; and , , are included in the parameter set (which directly affects the amplitude of the transfer function);

[0112] Finite element simulations are performed at different temperatures to generate a data set ;

[0113] The data in the data set is used to train a deep neural network (DNN), which outputs a predicted frequency response function wherein, is the prediction of DNN to ;

[0114] The trained DNN as a surrogate model can quickly predict the frequency response of the system under any given parameter combination, thereby replacing the time-consuming finite element simulation, efficiently evaluating the effects of different design schemes in the optimization process, and realizing the rapid design and optimization of the broadband vibration control system. The introduction of the surrogate model prediction transfer function aims to solve the high computational cost and low efficiency problem caused by the dependence on finite element simulation in traditional optimization. Through machine learning (such as neural network) training, the surrogate model can predict the system vibration response under different parameter combinations (G) ) and environmental conditions with extremely low time consumption, replacing the complex physical simulation. The surrogate model has the following advantages: the surrogate model completes parameter evaluation within seconds, while finite element simulation usually takes several hours; the explicit inclusion of temperature effects on material properties (such as damping loss factor) makes the optimization results environmentally robust; the surrogate model can capture the nonlinear coupling effects between parameters, avoiding the dependence of traditional gradient methods on local solutions; by embedding the surrogate model into the objective function, the optimization accuracy can be guaranteed, and the computational resource demand can be greatly reduced, providing a feasible path for complex multi-objective optimization;

[0115] In summary, the dynamic frequency band weight and the predicted transfer function are introduced into the objective function to optimize the objective function, and the optimized objective function is:

[0116] ;

[0117] wherein, represents the optimized objective function;

[0118] S3.5, the objective function value is optimized by gradient descent method: the gradient of the objective function with respect to the parameters (i.e. the rate of change of the function) is calculated, and the parameters are updated in the opposite direction of the gradient to gradually reduce the objective function value, and the update step is controlled by the learning rate; repeat this process until the objective function converges to the minimum value or meets the preset stopping condition (such as the number of iterations or error threshold).

[0119] S4, based on the finite element analysis results, the mathematical model for analyzing vibration energy transmission and dissipation is used to analyze the transmission path and efficiency of energy between acoustic black hole (ABH) and distributed vibration absorber (DVA);

[0120] In this embodiment, based on the finite element analysis results, the mathematical model for analyzing vibration energy transmission and dissipation is used to analyze the transmission path and efficiency of energy between acoustic black hole (ABH) and distributed vibration absorber (DVA), including the following steps:

[0121] S4.1. Export vibration response data from ANSYS finite element software, including displacement field, velocity field, stress tensor, etc. of each node;

[0122] 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 resonant frequency, mode shape, etc.;

[0123] 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, and obtain the energy distribution in the system;

[0124] Kinetic energy density for: ;

[0125] Potential energy density for: ;

[0126] in, represents the velocity field; Indicates the material density; represents the stress tensor; represents the strain tensor;

[0127] 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, and obtain a frequency domain input power spectrum;

[0128] Input power for: ;

[0129] in, For motivation, is the complex conjugate of velocity; It means taking the real part of a complex number;

[0130] S4.5. Analyze energy transfer paths based on power flow;

[0131] The energy transfer path is analyzed based on the power flow, including the following steps:

[0132] S4.51. Perform Fourier transform on the input power to obtain the frequency domain input power spectrum;

[0133] S4.52. Define the power flow vector and integrate the power flow vector along the structural propagation direction (radial or axial) , The velocity vector components, and obtain the energy transfer path;

[0134] S4.53, the difference of power flow density between acoustic black hole (ABH) region and distributed vibration absorber (DVA) region, analyze the energy distribution proportion;

[0135] S4.54, calculate the acoustic black hole (ABH) dissipation power and the power of the kinetic energy of the distributed vibration absorber (DVA) unit converted into heat energy.

[0136] Acoustic black hole (ABH) dissipation power is:

[0137] ;

[0138] wherein, is the loss factor of damping material; represents a volume element;

[0139] The power of the kinetic energy of the distributed vibration absorber (DVA) unit converted into heat energy :

[0140] ;

[0141] wherein, is the DVA damping coefficient, is the mass block speed; represents the number of DVA units; represents the index of the DVA unit.

[0142] S4.6, divide the structure into acoustic black hole (ABH) area (mainly responsible for the aggregation of high-frequency vibration energy), distributed vibration absorber (DVA) area (mainly responsible for the absorption of low-frequency vibration energy) and transmission path area (transition area connecting ABH and DVA), establish segmented energy balance equation;

[0143] The segmented energy balance equation is:

[0144] ;

[0145] ;

[0146] wherein, represents the power transmitted from ABH to DVA; represents the energy of acoustic black hole (ABH) area; represents the energy of distributed vibration absorber (DVA) area; represents the energy loss of acoustic black hole (ABH) area; represents the energy loss of distributed vibration absorber (DVA) area;

[0147] S4.7, Discretize the energy transfer equation and solve it using finite difference method: divide the continuous physical domain into a series of discrete grid points, then replace 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 solved independently at each grid point. Then, set appropriate boundary conditions according to the actual situation, and update the values at each grid point step by step through iterative algorithm until the solution converges, i.e. the change between adjacent iteration steps is less than a pre-set threshold, to simulate and analyze how energy is transferred and dissipated in the system over time and space.

[0148] S5, Verify the broadband vibration control effect by collecting the vibration signals of acoustic black hole (ABH) through acceleration sensors;

[0149] In this embodiment, the vibration signals of acoustic black hole (ABH) are collected through acceleration sensors to verify the broadband vibration control effect, including the following steps:

[0150] S5.1, Obtain the original data of the vibration signal and perform preprocessing and analysis;

[0151] S5.2, Perform fast Fourier transform on the preprocessed vibration signal to convert it into a frequency domain signal, and based on the frequency domain signal, calculate the power spectral density for evaluating the energy distribution of each frequency component;

[0152] Convert the time domain signal to the frequency domain power spectral density is:

[0153] ;

[0154] wherein, is the number of sampling points; is the sampling frequency; represents the fast Fourier transform operation;

[0155] S5.3, Compare the vibration responses with and without acoustic black hole (ABH) region + distributed vibration absorber (DVA) to calculate the attenuation of vibration energy at each frequency point, i.e. the difference in power spectral density between the initial state and the optimized state;

[0156] S5.4, Based on the input excitation and output response, calculate the transfer function of the system, and use the transfer function to integrate the power flow vector along the propagation direction of the structure to identify the main energy transfer path;

[0157] S5.5, Use an impact hammer to apply transient excitation and collect the vibration attenuation process, and record the acceleration time domain signal located in the acoustic black hole (ABH) region;

[0158] S5.6, Extract the initial vibration amplitude from the collected time-domain signal, track the change of vibration amplitude with time, find the time when the amplitude decays to a% of the initial value, compare the decay times under different conditions (such as only ABH, only DVA, ABH+DVA combination), and evaluate the energy dissipation efficiency of the system;

[0159] S5.7, Hilbert transform of 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);

[0160] Wherein, the Hilbert transform of the acceleration time-domain signal, the extraction of the envelope, the analysis of the envelope decay rate, and the verification of the broadband dissipation characteristics of the acoustic black hole (ABH) region + distributed vibration absorber (DVA) combination include the following steps:

[0161] S5.71, use variational mode decomposition (VMD) to decompose the collected acceleration time-domain signal into K intrinsic mode functions (IMF), which separates the vibration components of different frequency bands: , wherein, represents the index of the intrinsic mode function, represents the total number of IMFs obtained by decomposition;

[0162] S5.72, Hilbert transform is performed on each intrinsic mode function component to generate an analytic signal : , wherein, represents the imaginary unit, and represents the imaginary direction, represents the Hilbert transform, which converts the real signal into the imaginary part, constructs the complex signal to eliminate the negative frequency component, and extracts the instantaneous envelope of each component, and the modulus of the analytic signal is the instantaneous amplitude envelope;

[0163] S5.73, based on the linear viscoelastic theory, an initial decay model is established, and a nonlinear correction term is introduced in the model to adjust and build a segmented decay model, which distinguishes the decay rates of different frequency bands. The traditional linear viscoelastic model assumes that the damping coefficient is a fixed value, but in actual application, the energy dissipation capacity (i.e. damping) of the material often changes with frequency. Especially under high frequency and low frequency conditions, the differences in the response mechanisms of the material's internal microstructure (such as molecular chain friction, interface slip, etc.) will lead to different energy dissipation efficiencies. In actual vibration process, not only there are steady-state vibrations (continuous and stable vibrations), but also there may be transient processes (short-term vibrations during impact or rapid loading). The energy dissipation characteristics of the system will also be different under these different types of vibration modes, and a more accurate model is needed to describe this dynamic behavior;

[0164] The segmented decay model is:

[0165]

[0166] wherein, denotes the critical time; denotes the time variable; denotes the initial amplitude; denotes the transient decay coefficient, controls the exponential decay rate, and reflects the material damping, structural energy dissipation, and other characteristics; denotes the nonlinear correction coefficient, representing the amplitude correction term caused by nonlinear effects (friction hysteresis, material plastic deformation) in the transient stage; denotes the steady-state decay coefficient, reflecting the decay rate dominated by linear damping after the system enters the steady state;

[0167] S5.74, by comparing the decay rates of the envelope lines under different frequency components, verify the energy dissipation capability of the acoustic black hole (ABH) region + distributed vibration absorber (DVA) combination in a wide frequency range.

[0168] The present embodiment provides experimental verification: the same mass of conventional ABH and ABH+DVA structure are respectively pasted on a 1mm aluminum plate for vibration test, under the same excitation, the vibration speed of ABH+damping ring+DVA scheme is significantly smaller than that of conventional ABH scheme, as shown in Figure 2 .

[0169] Embodiment 2: The present embodiment provides a wide-frequency vibration control device based on acoustic black hole and distributed vibration absorber, comprising a sensor, a storage, a processor and a computer program stored in the storage and executable on the processor, wherein the processor executes the computer program to realize the steps of the wide-frequency vibration control method based on acoustic black hole and distributed vibration absorber as described in any one of the above embodiments.

[0170] The basic principles, main features and advantages of the present application are shown and described above. It should be understood by those skilled in the art that the present application is not limited by the above embodiments, and the above embodiments and descriptions in the specification are only preferred examples of the present application and are not intended to limit the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection of the present application is defined by the appended claims and their equivalents.​

Claims

1. A broadband vibration control method based on acoustic black holes and distributed vibration absorbers, characterized in that: The following steps are involved: S1. Construct a three-dimensional model of the acoustic black hole and import the three-dimensional model into the 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: A collaborative tuning strategy based on the gradient descent method is used to collaboratively optimize the parameters of the acoustic black hole and the distributed vibration absorber to achieve broadband vibration control. Dynamic frequency band weights and predicted transfer functions are introduced into the collaborative optimization process. The collaborative tuning strategy based on the gradient descent method is used to collaboratively 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 vectors; S3.

2. Set the initial parameter combination; S3.

3. Construct a finite element model of the acoustic black hole and distributed vibration absorber based on the current parameter combination to 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, the dynamic frequency band weight and the predicted transfer function Introduce it into the objective function to optimize the objective function; S3.

5. Optimize the objective function value by gradient descent method; In S3.4, according to the transfer function , and superimpose the lightweight penalty term To calculate the objective function value is: ； in, represents the objective function; represents all the acoustic black hole and distributed vibration absorber parameter sets to be optimized; Indicates the starting frequency of target optimization; Indicates the termination frequency of target optimization; represents the lightweight penalty term; represents the total mass of the structure; represents the set of all acoustic black holes and distributed vibration absorber parameters to be optimized; Construct dynamic frequency band weights based on the impact of vibration energy in each frequency band on system performance ; Define the damping coefficient as the strain rate Function : ； in, represents the linear viscous damping coefficient; represents the first-order nonlinear viscous damping coefficient; represents the quadratic nonlinear viscous damping coefficient; and 、 、 Include parameter set ; At different temperatures Perform finite element simulation and generate data sets ; Use the data in the dataset to train the deep neural network so that the deep neural network outputs the predicted frequency response function ; In summary, the dynamic frequency band weight and the predicted transfer function Introduce it into the objective function to optimize the objective function; S4. Based on the finite element analysis results, the mathematical model for analyzing vibration energy transfer and dissipation is used to analyze the energy transfer path and efficiency between the acoustic black hole and the distributed vibration absorber; Based on the finite element analysis results, a mathematical model for analyzing vibration energy transfer and dissipation is used to analyze the energy transfer path and efficiency 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 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, and obtain the energy distribution in 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, and obtain a frequency domain input power spectrum; S4.

5. Analyze energy transfer paths based on power flow; S4.

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

7. Discretize the energy transfer equation and solve it using the finite difference method; S5. Collect the vibration signal of the acoustic black hole through the 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 S1, constructing a three-dimensional model of an 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 core shape of the acoustic black hole and set the central thickness; S1.

2. Design the thickness to decrease exponentially along the radial direction and establish a thickness distribution function; S1.

3. Based on wave theory, use the bending wave equation to analyze how vibration waves propagate within an acoustic black hole region with decreasing thickness. S1.

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

5. Use ANSYS finite element analysis software to perform 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 S1.3, based on wave theory, the bending wave equation is used to analyze how vibration waves propagate in an acoustic black hole region with gradually decreasing thickness, including the following steps: S1.

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

32. Based on the thin plate wave theory, construct the governing equations for bending waves; S1.

33. Analyze the changes in wave velocity and wavelength based on the relationship between the wave velocity of flexural waves and the thickness of the acoustic black hole structure; S1.

34. Use the separation of variables method to solve the bending wave governing equations and obtain the displacement field of the vibration wave.

4. The broadband vibration control method based on acoustic black holes and distributed vibration absorbers according to claim 3 is characterized in that: In S2, the design parameters of the distributed vibration absorber are defined, and a spring-mass-damper system model of the distributed vibration absorber unit is established, including the following steps: S2.

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

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

3. Perform modal analysis on the main structure to obtain the natural frequency and mode shape of the main structure; S2.

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

5. The broadband vibration control method based on acoustic black holes and distributed vibration absorbers according to claim 4, characterized in that: In S5, the vibration signal of the acoustic black hole is collected by an acceleration sensor to verify the broadband vibration control effect, which includes 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 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 propagation direction of the structure and identify the main energy transfer paths. 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 acquired 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 time 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 attenuation rate, and verify the broadband dissipation characteristics of the acoustic black hole region + distributed vibration absorber.

6. The broadband vibration control method based on acoustic black holes and distributed vibration absorbers according to claim 5, characterized in that: 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 acoustic black hole region + distributed vibration absorber combination includes the following steps: S5.

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

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

73. Establish an initial attenuation model based on linear viscoelasticity theory, and introduce nonlinear correction terms into the model to adjust and construct a segmented attenuation model to distinguish the attenuation rates in different frequency bands; S5.

74. By comparing the attenuation rates of the envelope at different frequency components, the energy dissipation capability of the acoustic black hole region + distributed vibration absorber combination over a wide frequency range is verified.

7. A broadband vibration control device based on an acoustic black hole and a distributed vibration absorber, comprising a sensor, a memory, 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, the steps of the broadband vibration control method based on acoustic black holes and distributed vibration absorbers as described in any one of claims 1 to 6 are implemented.

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