A method and system for analyzing the dynamic characteristics of an acoustic resonance mixing system

Abstract

This invention belongs to the field of fluid-structure interaction dynamics analysis technology, and specifically discloses a method and system for analyzing the dynamic characteristics of an acoustic-frequency resonant hybrid system. The method includes: introducing an external excitation force vector and a fluid feedback force vector into the dynamic control equations of the acoustic-frequency resonant hybrid system to form coupled dynamic equations; numerically characterizing the fluid feedback force using a multi-harmonic fitting method to obtain a fluid force model; based on the fluid force model, obtaining the dominant frequency component of the fluid force and mapping it equivalently to an additional mass parameter and an equivalent damping parameter; then fitting the optimal functional form of the additional mass parameter and the equivalent damping parameter relative to the excitation acceleration; updating the coupled dynamic equations based on the optimal functional form to achieve dynamic characteristic analysis under different excitation acceleration conditions. This invention can accurately analyze the dynamic characteristics of an acoustic-frequency resonant hybrid system under high-acceleration vibration environments to address nonlinear dynamic problems induced by fluid-structure interaction.

Description

Technical Field

[0001] This invention belongs to the field of fluid-structure interaction dynamics analysis technology, and more specifically, relates to a method and system for analyzing the dynamic characteristics of a hybrid acoustic resonant system. Background Technology

[0002] With the increasing demands on the preparation of composite chemical materials, acoustic vibration mixing technology is gradually being applied to the mixing and dispersion processes of high-viscosity, multiphase complex systems. Acoustic resonance mixing systems typically generate large-amplitude vibrations by operating the structure near the resonant frequency, creating macroscopic circulation and local shearing within the fluid, thereby achieving material dispersion and mixing. When handling high-viscosity and multi-component systems, this type of system can effectively avoid the localized temperature rise and material damage caused by traditional mechanical blade shearing, thus achieving uniform dispersion and mixing of sensitive components.

[0003] The study of the dynamic characteristics of acoustic resonant hybrid systems operating under high-acceleration vibration conditions is of great significance. In actual operation, fluid-structure interaction exists between the fluid within the hybrid container and the vibrating structure. The fluid exerts additional mass and damping effects on the structure, thus influencing the system's natural frequencies, mode shapes, and response characteristics. Due to the system's multi-degree-of-freedom structural characteristics, the influence of fluid load is more complex, causing the system's equivalent dynamic parameters to change with vibration conditions, which to some extent affects the system's stable operation. Currently, numerical simulation (such as MBD and CFD co-analysis) is a highly accurate method for characterizing the dynamics of this system, but it requires handling unsteady iterations of large-scale meshes, consuming significant computational resources and time, making it difficult to meet the needs of subsequent frequent global optimization iterations. While simplification methods based on equivalent mechanical models are computationally efficient, existing models mostly focus on equivalent simplification under low-acceleration environments, and the introduced additional degrees of freedom increase the complexity of model solving.

[0004] Therefore, there is an urgent need for a method that can accurately analyze the dynamic characteristics of acoustic-frequency resonant hybrid systems under high-acceleration vibration environments, so as to better handle nonlinear dynamic problems induced by fluid-structure interaction. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method and system for analyzing the dynamic characteristics of an acoustic resonant hybrid system, the purpose of which is to accurately analyze the dynamic characteristics of an acoustic resonant hybrid system under high acceleration vibration environment.

[0006] To achieve the above objectives, according to a first aspect of the present invention, a method for analyzing the dynamic characteristics of a sound frequency resonance hybrid system is proposed, comprising the following steps: In the dynamic control equations of the acoustic resonant hybrid system, external excitation force vector and fluid feedback force vector are introduced to form coupled dynamic equations. For the fluid feedback force vector in the coupled dynamic equations, the multi-harmonic fitting method is used to numerically characterize the fluid feedback force to obtain the fluid force model. Based on the fluid force model, the periodic components of the fluid feedback force at the dominant frequency under different excitation acceleration conditions are obtained, namely the fluid force dominant frequency components. The hydrodynamic dominant frequency component is equivalently mapped to the additional mass parameter and the equivalent damping parameter; thus, based on the additional mass parameter and the equivalent damping parameter under different excitation acceleration conditions, the optimal functional form of the additional mass parameter and the equivalent damping parameter relative to the excitation acceleration is obtained by fitting. The coupled dynamic equations are updated based on the optimal function form to obtain an equivalent parameterized linearized dynamic model; Based on the equivalent parameterized linearized dynamic model, dynamic characteristic analysis under different excitation acceleration conditions is realized.

[0007] As a further preferred embodiment, a multi-harmonic fitting method is used to numerically characterize the fluid feedback force, resulting in a fluid force model, including: Obtain fluid feedback force time history data under steady-state conditions with different excitation accelerations, and then determine the initial estimate of the dominant frequency; Construct a multiharmonic expression model that includes the first three harmonic components; Based on the initial estimate of the dominant frequency, the multiharmonic expression model is transformed into a linear regression form to obtain the linear multiharmonic expression model. The least squares method is then used to estimate the parameters of the linear multiharmonic expression model to obtain the optimal dominant frequency and corresponding harmonic parameters. Based on the parameter estimation results, the linear multiharmonic expression model is reconstructed to obtain the fluid dynamics model.

[0008] As a further preferred embodiment, the method for determining the initial estimate of the main frequency includes: Obtain fluid force time history data under steady-state conditions with different excitation accelerations, select the fluid feedback force time history data corresponding to the time period after the system enters the stable resonance stage, and perform mean-removing preprocessing on it; The preprocessed fluid feedback force time history data were subjected to a fast Fourier transform to obtain its spectral distribution; Based on the spectral distribution, an initial search frequency band is set near the excitation frequency, and the main frequency is initially screened within the initial search frequency band. The frequency corresponding to the spectral peak is selected as the initial estimate of the main frequency.

[0009] As a further preferred embodiment, the linear multiharmonic expression model is specifically as follows:

[0010] in, For linear multiharmonic expression models, t For a specific moment; To truncate the order, and For the first Harmonic coefficients, harmonic parameters ; As a candidate main frequency, , The initial estimate of the main frequency, The radius is the frequency search radius.

[0011] As a further preferred embodiment, the dominant frequency component of the hydrodynamic force is equivalently mapped to an additional mass parameter and an equivalent damping parameter, including: The hydrodynamic frequency component is decomposed into component expressions corresponding to structural displacement, velocity, and acceleration terms by trigonometric expansion. Furthermore, the hydrodynamic frequency component is decomposed into an inertial contribution term proportional to acceleration and an energy dissipation contribution term proportional to velocity, and then equivalently mapped to additional mass parameters and equivalent damping parameters, respectively.

[0012] As a further preferred embodiment, the coupled dynamic equations are as follows:

[0013] in, For the quality matrix, Here is the structural damping matrix. Here is the stiffness matrix; The external excitation force vector, For fluid feedback force vector; , , These are the system displacement vector, velocity vector, and acceleration vector, respectively.

[0014] As a further preferred approach, a linearized dynamic model based on equivalent parameterization is used to analyze the dynamic characteristics under different excitation acceleration conditions, including: Based on the excitation acceleration, the corresponding additional mass parameters and equivalent damping parameters are obtained according to the optimal function form, and the linearized dynamic model is updated. Based on the updated linearized dynamic model, the steady-state response and frequency domain characteristics of the acoustic-frequency resonant hybrid system are calculated, realizing the rapid characterization of nonlinear fluid-structure interaction characteristics.

[0015] According to a second aspect of the present invention, a dynamic characteristic analysis system for an acoustic resonant hybrid system is provided, comprising a processor, the processor being used to execute the above-described method for analyzing the dynamic characteristics of the acoustic resonant hybrid system.

[0016] According to a third aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the above-described method for analyzing the dynamic characteristics of an acoustic resonant hybrid system.

[0017] According to a fourth aspect of the present invention, a computer program product is provided, characterized in that it includes a computer program, which, when executed by a processor, implements the above-described method for analyzing the dynamic characteristics of an acoustic resonant hybrid system.

[0018] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages: 1. This invention overcomes the parameter distortion caused by spectral energy leakage in single-frequency fitting by performing multi-harmonic fitting and extracting the dominant frequency component of the fluid feedback force; the parameterized equivalent model constructed by accurately extracting the dominant frequency component can more accurately characterize the action mechanism of nonlinear fluid force under high acceleration.

[0019] 2. Based on the principle of energy equivalence, this invention transforms the dominant frequency component of fluid force into additional mass parameters and equivalent damping parameters, thereby achieving decoupled solution of fluid force and structural system in the physical domain. This method transforms the complex fluid-structure interaction field calculation into the algebraic solution of structural dynamic equations through parameterized linear substitution, avoiding the unsteady iterative calculation of fluid-structure interaction in traditional methods, and saving computational resources and time costs.

[0020] 3. This invention establishes a functional expression model for the variation of additional mass parameters and equivalent damping parameters with acceleration, enabling the equivalent parameters to be updated according to the excitation conditions. This allows for rapid analysis of the additional fluid effects under different vibration intensities. Compared with existing models that assume a fixed additional mass, this invention can more accurately reflect the evolution of the system's dynamic response under multiple conditions.

[0021] 4. This invention constructs a complete calculation process of "main frequency extraction - equivalent mapping - parameter functionization - decoupling solution", which enables the resonance frequency drift, excitation force requirement and steady-state frequency domain response of the acoustic frequency resonance hybrid system under different excitation conditions to be calculated through a unified equivalent dynamic model, thereby facilitating multi-condition response analysis and system parameter design. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the three-degree-of-freedom dynamic model of the acoustic resonance hybrid system involved in the embodiments of the present invention; Figure 2 This is a time history diagram showing the relationship between fluid feedback force and container velocity under stable resonance conditions in an embodiment of the present invention. Figure 3This is a flowchart illustrating the calculation process for multi-harmonic fitting of fluid feedback force in an embodiment of the present invention. Figure 4 This is a graph showing the relationship between the coefficient of determination and energy coverage as a function of acceleration in an embodiment of the present invention. Figure 5 This is a comparison curve of the excitation force versus acceleration when using an equivalent model and when not using an equivalent model in an embodiment of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0024] The present invention provides a method for analyzing the dynamic characteristics of a sound frequency resonance hybrid system, comprising the following steps: S1. The acoustic resonant hybrid system is abstracted into a three-degree-of-freedom lumped-mass dynamic system consisting of a carrier body, an excitation mass, and a frame mass, and the corresponding dynamic control equations are constructed; an external excitation force vector is introduced into the dynamic control equations. and fluid feedback force vector This forms a coupled dynamics model.

[0025] Taking a typical three-degree-of-freedom acoustic resonant hybrid system as an example for analysis, its mechanical model is as follows: Figure 1 As shown, the system includes a carrier body, an excitation mass, and a support frame. The carrier body carries the fluid medium, the excitation mass is connected to an excitation device (such as a voice coil motor) to provide periodic excitation, and the support frame supports the system structure. Step S1 specifically includes the following steps: S11. Equivalently represent the carrier mass as a first concentrated mass block. The excitation mass is equivalent to a second concentrated mass block. The supporting framework is equivalent to a third concentrated mass block. And define their displacements in the principal vibration direction as . , and .

[0026] Define the system displacement vector as:

[0027] S12. Based on the structural connection relationship of the acoustic resonance hybrid system, establish elastic connection units between each concentrated mass block, and construct the system stiffness matrix. .like Figure 1 As shown, the elastic connection unit includes: a first elastic unit between the load body and the supporting frame, with an equivalent stiffness of... The second elastic element between the excitation mass and the supporting frame has an equivalent stiffness of... The third elastic element between the carrier and the excitation mass has an equivalent stiffness of The fourth elastic element between the support frame and the base has an equivalent stiffness of .

[0028] The system stiffness matrix is ​​expressed as:

[0029] S13, Constructing the System Quality Matrix The mass matrix is ​​in diagonal form, and is expressed as follows:

[0030] S14. Introduce structural damping terms and construct the system damping matrix. .like Figure 1 As shown, the damping unit includes: a first damping unit between the load-bearing component and the support frame component, whose equivalent damping coefficient is... The second damping unit between the excitation assembly and the support frame assembly has an equivalent damping coefficient of... The third damping unit between the load assembly and the excitation assembly has an equivalent damping coefficient of... The fourth damping unit between the support frame assembly and the base has an equivalent damping coefficient of... .

[0031] The system damping matrix is ​​expressed as follows:

[0032] S15. Based on Newton's second law, construct a structure containing a mass matrix. Structural damping matrix and stiffness matrix The dynamic control equations are derived, and an external excitation force vector is introduced into the dynamic control equations. and fluid feedback force vector This leads to a coupled dynamic model that incorporates the nonlinear additional forces of high-viscosity fluids:

[0033] External excitation force vector Represents the excited mass With the carrier body The interaction force between them, based on their relative motion, can be represented as a vector:

[0034] in, The amplitude of the force applied by the exciter. The excitation frequency is denoted as .

[0035] The fluid feedback force term mainly acts on the first degree of freedom, and it is expressed as:

[0036] in, This refers to the fluid feedback force acting on the payload component. This force exhibits significant nonlinear characteristics as the payload component's motion state changes, and is processed in subsequent steps using frequency domain dominant frequency extraction and equivalent mapping methods.

[0037] S2. For the fluid feedback force vector in the coupled dynamic equation, the nonlinear fluid feedback force is extracted from the complex coupled system and analyzed as an independent subsystem. The multi-harmonic fitting method is used to numerically characterize the fluid feedback force to obtain the fluid force model.

[0038] S21. Obtain fluid force time history data under steady-state conditions with different excitation accelerations, and preprocess the data.

[0039] To obtain high-quality fluid dynamics data under controllable operating conditions, this embodiment employs Fluent CFD simulation technology to acquire fluid dynamics time history data under different acceleration amplitudes. The simulation uses a pre-defined ideal sinusoidal motion law of the container to eliminate the feedback influence of fluid reaction force on the container trajectory, the expression of which is as follows:

[0040] After obtaining the fluid force time history data under different acceleration conditions, the fluid force data is first preprocessed, including: extracting the time segment after the system reaches a stable resonance state from the complete time history, and performing mean removal processing on the fluid force signal to eliminate the influence of the initial transition stage and static bias on the spectrum analysis.

[0041] S22. Perform a Fast Fourier Transform (FFT) on the preprocessed fluid dynamics time history data to obtain the spectral distribution; based on the expected excitation frequency, set an initial search frequency band near the excitation frequency, and perform initial screening of the dominant frequency within the frequency band, selecting the frequency corresponding to the spectral peak as the initial estimate of the dominant frequency. The dominant frequency corresponds to the dominant component in the distribution of fluid dynamic energy.

[0042] S23. Construct a multi-harmonic expression model that includes the first three harmonic components.

[0043] Figure 2 The figure shows the time history signal of the fluid feedback force experienced by the component under a vibration acceleration of 90g (g is the gravitational acceleration). It can be seen that under stable resonance conditions, the fluid feedback force on the load-carrying component and the velocity of the mixing container exhibit periodic fluctuations over time. Both have the same vibration frequency at the dominant frequency. Moreover, the fluid feedback force as a whole presents a quasi-sinusoidal wave pattern with the same frequency as the container velocity, with occasional local waveform distortion and amplitude abrupt changes only occurring at the peak of the fluid force wave under high acceleration conditions. The local distortion at the peak exhibits obvious nonlinear impact characteristics, which are not composed of a single frequency component, but rather a complex nonlinear waveform formed by the superposition of the dominant frequency component, multiple harmonic components, and random impact components.

[0044] Further observation revealed that the motion state of the fluid within the container changed with varying excitation intensity under different excitation acceleration conditions. When the excitation acceleration was low, the fluid force mainly exhibited a quasi-sinusoidal periodic oscillation with the same frequency as the container's motion. As the excitation acceleration increased, the fluid force waveform was superimposed with higher-order harmonic components and impact disturbance components on top of the dominant frequency component, exhibiting non-pure sine characteristics.

[0045] Therefore, under different acceleration conditions, the fluid force acting on the container can be uniformly expressed as:

[0046] in, This refers to the impact disturbance term in fluid dynamics.

[0047] To accurately remove higher-order energy interference and extract pure dominant frequency components during the modeling process, this embodiment uses the first three harmonic components to truncate the hydrodynamic characteristics, ignoring higher-order components with small energy contributions and random disturbances, and constructs a multi-harmonic expression model:

[0048] S24. The multiharmonic expression model is transformed into a linear regression form, and the least squares method is used to estimate the parameters of the linear multiharmonic expression model based on the refined dominant frequency search interval.

[0049] like Figure 3 As shown, at the initial estimated value of the main frequency Based on this, a more refined main frequency search range is constructed:

[0050] For candidate main frequency Perform a traversal search, and for each candidate frequency Constructing a multi-harmonic basis function matrix The above multiharmonic expression model is then transformed into a linear regression form, resulting in a linear multiharmonic expression model:

[0051] in, and For the first First harmonic coefficient, This is the truncation order.

[0052] The multiharmonic basis function matrix for:

[0053] in This represents the number of sampling points.

[0054] Harmonic parameters are solved using the least squares method. Candidate main frequency obtained Fitting results .

[0055]

[0056] Calculate candidate clock frequency The sum of squared residuals:

[0057] in, The vector of fluid force data to be fitted. To fit the fluid force vector.

[0058] Determine the current Is it less than the historical best value? Current When the value is less than the optimal value, update the optimal clock frequency. and corresponding harmonic parameters .

[0059] The completion of the candidate dominant frequency traversal is determined by whether the goodness-of-fit index meets the requirements; if not, the matrix is ​​reconstructed for the next candidate dominant frequency. The process involves least squares calculation; if the traversal is complete, the optimal main frequency is output. and corresponding harmonic parameters .

[0060] S25. Based on the optimal clock frequency Based on the corresponding harmonic parameters, the linear multiharmonic expression model is reconstructed to obtain the hydrodynamic model, which serves as the input for subsequent equivalent mapping and system decoupling solutions.

[0061] Furthermore, the goodness-of-fit index includes: a coefficient of determination is introduced to evaluate the ability of the multi-harmonic expression model to characterize the periodic characteristics of fluid feedback force. This is used to measure the degree of consistency between the fitted result and the original fluid feedback force.

[0062]

[0063] in, The periodic fluid force obtained by fitting the multi-harmonic expression model. This is the original fluid feedback force.

[0064] Simultaneously define the energy proportion of periodic forces. This is used to measure the contribution ratio of the periodic component to the total hydrodynamic response, and its expression is:

[0065] like Figure 4 As shown, under different excitation acceleration conditions, the goodness-of-fit index and the proportion of periodic force energy remain at a high level overall. In the low to medium acceleration range, the multi-harmonic expression model can fully characterize the periodic characteristics of fluid feedback force; under high acceleration conditions, although the nonlinear impact component is enhanced, the periodic component still dominates.

[0066] S3. Based on the fluid force model, obtain the dominant frequency component of the fluid force and map it equivalently to the additional mass parameter and the equivalent damping parameter; according to the additional mass parameter and the equivalent damping parameter under different excitation acceleration conditions, fit the optimal functional form of the additional mass parameter and the equivalent damping parameter relative to the excitation acceleration.

[0067] S31. Under stable resonance conditions, the displacement, velocity, and acceleration responses of the carrier body in the principal vibration direction can be expressed as follows:

[0068]

[0069]

[0070] in, The steady-state displacement amplitude, Let ω be the system excitation angular frequency.

[0071] S32. Based on the fluid dynamics model, extract the periodic component of the fluid feedback force at the dominant frequency, i.e., the dominant frequency component of the fluid dynamics, and expand it using the formula in S31 as follows:

[0072] in, and These are the amplitude parameters of the dominant frequency cosine and sine terms, respectively. This represents the amplitude of the dominant frequency of the fluid force. This represents the phase difference between the dominant frequency component of the fluid force and the displacement response.

[0073] Here, only the dominant frequency component that plays a decisive role in the steady-state response of the system is extracted and retained from the fluid dynamic model for equivalent modeling. Based on the energy transfer characteristics of the acoustic resonance system in steady state, the second and third harmonics and other higher-order frequency components are regarded as disturbance terms with zero average power during the dominant oscillation period and are reduced in order to remove the interference of non-functional components on the identification of equivalent parameters.

[0074] S33. The dominant frequency component of the fluid force is trigonometrically expanded and decomposed into component expressions corresponding to the structural displacement, velocity, and acceleration terms. Based on the principle of energy conservation, the inertial contribution and viscous dissipation contribution in the dominant frequency component are equivalently divided. The inertial contribution term proportional to acceleration is equivalent to an additional mass parameter, and the energy dissipation contribution term proportional to velocity is equivalent to an equivalent damping parameter. The restoring force term is merged to avoid the coupling uncertainty of additional stiffness and additional mass in parameter identification. The result is:

[0075] in, To add quality parameters, This is the equivalent damping parameter.

[0076] S34. Substituting the formula constructed in S31 into the formula in S33, we get:

[0077] Match the coefficients of like terms in the above formula with those in formula S32, that is, let Item and With the coefficients of each term being equal, the solutions for the additional mass parameter and the equivalent damping parameter can be obtained:

[0078]

[0079] S35. Under different excitation acceleration conditions, the main frequency parameters obtained based on S2 and And combined with the response amplitude under the corresponding operating conditions and excitation angular frequency Repeat steps S31 to S34 to calculate the corresponding working conditions. and .

[0080] The additional mass parameters and equivalent damping parameters obtained under different working conditions are combined to form a discrete equivalent parameter dataset:

[0081] in, This represents the amplitude of the excitation acceleration.

[0082] S36. Based on the additional mass parameters and equivalent damping parameters under different excitation acceleration conditions, the optimal functional forms of the additional mass parameters and equivalent damping parameters relative to the excitation acceleration are fitted, thereby forming a parameterized expression model for subsequent replacement of dynamic equations.

[0083] The model expressing the additional mass parameter function can be represented as:

[0084] The equivalent damping parameter function expression model can be represented as:

[0085] in, This is the function expression obtained through fitting.

[0086] To cover the various possible variations of the equivalent parameters, a candidate function set is constructed, including polynomial function models, exponential function models, and saturated function models. The candidate models are then screened using fitting error evaluation criteria to determine the optimal function expression.

[0087] The fitting error evaluation criterion is a multi-criteria scoring function, excluding the coefficient of determination. In addition, the Bayesian Information Criterion (BIC) is introduced as a complexity penalty term, and a smoothness index defined by the root mean square of the second derivative is combined. To ensure the stability of the formula, the scoring function is defined as follows:

[0088] in, These are the weighting factors for each evaluation indicator.

[0089] This yields a functional expression model of the variation of the additional mass parameter and the equivalent damping parameter with the excitation acceleration, which is used for dynamic equation replacement and decoupling solution in subsequent steps.

[0090] S4. The coupled dynamic equations are updated based on the optimal function form to obtain an equivalent parameterized linearized dynamic model. Based on the equivalent parameterized linearized dynamic model, the steady-state response of the system is calculated using the modal decoupling and frequency domain response function method, thereby realizing the dynamic characteristic analysis under different excitation acceleration conditions.

[0091] S41. Under the current excitation acceleration conditions, determine the corresponding additional mass parameters based on the optimal function form established in S3. and equivalent damping parameters .

[0092] By adding the additional mass parameters to the mass term of the first degree of freedom, an updated equivalent mass matrix is ​​constructed:

[0093] S42, Based on the updated equivalent mass matrix and the stiffness matrix established in S1 Establish the generalized characteristic equation of the system:

[0094] in, The system mode shape matrix, The diagonal frequency matrix is ​​composed of eigenvalues.

[0095] The mode shape vectors of each order are mass normalized to satisfy the orthogonality constraint:

[0096] in, It is an identity matrix.

[0097] S43. Using the modal transformation matrix to convert the external excitation force vector in physical space Projecting onto the modal coordinate system, we obtain the equivalent excitation components for each mode:

[0098] Combining the intrinsic damping parameters of the system structure and the equivalent damping parameters of the fluid The damping ratio of the target resonance mode is corrected to determine the first... Equivalent damping ratio of first mode Thus, a modal dynamics model incorporating fluid energy dissipation effects is constructed.

[0099] S44. Establish the frequency response functions of each mode in the frequency domain. steady-state response amplitude of the first mode Represented as:

[0100] in, , For the first The natural circular frequency of the first order.

[0101] Based on the principle of modal superposition, the steady-state displacement response amplitude of the load component in the physical coordinate system is obtained by linearly combining the modal responses of each order. :

[0102] in, For the mode shape matrix First row The elements of the column.

[0103] Further calculation of the velocity amplitude of the cargo-carrying components With acceleration amplitude :

[0104]

[0105] In engineering practice, if the target acceleration amplitude needs to be met... Based on the following acceleration response and excitation force amplitude The linear mapping relationship between them is used to calculate the required excitation force input:

[0106] like Figure 5 As shown, under different excitation acceleration conditions, the excitation force curves calculated using the linearized dynamic model with equivalent parameterization of this invention differ significantly from those of the traditional model that does not consider fluid energy dissipation effects (only adds mass). The results indicate that when using the linearized dynamic model with equivalent parameterization of this invention, the excitation force exhibits a nonlinear continuous evolution trend with acceleration, accurately capturing the system response changes caused by parameter drift under high acceleration, thus avoiding the calculation distortion caused by the traditional fixed-parameter model. Furthermore, it can quickly and accurately obtain the global dynamic response of the acoustic resonant hybrid system under loaded conditions without requiring real-time coupling iteration of the flow field and structure.

[0107] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of analyzing the dynamic characteristics of an acoustic resonance mixing system, characterized by, Includes the following steps: In the dynamic control equations of the acoustic resonant hybrid system, external excitation force vector and fluid feedback force vector are introduced to form coupled dynamic equations. For the fluid feedback force vector in the coupled dynamic equations, the multi-harmonic fitting method is used to numerically characterize the fluid feedback force to obtain the fluid force model. Based on the fluid force model, the periodic components of the fluid feedback force at the dominant frequency under different excitation acceleration conditions are obtained, namely the fluid force dominant frequency components. The hydrodynamic dominant frequency component is equivalently mapped to the additional mass parameter and the equivalent damping parameter; thus, based on the additional mass parameter and the equivalent damping parameter under different excitation acceleration conditions, the optimal functional form of the additional mass parameter and the equivalent damping parameter relative to the excitation acceleration is obtained by fitting. The coupled dynamic equations are updated based on the optimal function form to obtain an equivalent parameterized linearized dynamic model; Based on the equivalent parameterized linearized dynamic model, dynamic characteristic analysis under different excitation acceleration conditions is realized.

2. The method of claim 1, wherein the audio resonance mixing system is a system of a plurality of audio resonance mixing devices. The fluid feedback force is numerically characterized using a multi-harmonic fitting method, resulting in a fluid force model, including: Obtain fluid feedback force time history data under steady-state conditions with different excitation accelerations, and then determine the initial estimate of the dominant frequency; Construct a multiharmonic expression model that includes the first three harmonic components; Based on the initial estimate of the dominant frequency, the multiharmonic expression model is transformed into a linear regression form to obtain the linear multiharmonic expression model. The least squares method is then used to estimate the parameters of the linear multiharmonic expression model to obtain the optimal dominant frequency and corresponding harmonic parameters. Based on the parameter estimation results, the linear multiharmonic expression model is reconstructed to obtain the fluid dynamics model.

3. The method for analyzing the dynamic characteristics of a hybrid acoustic resonance system as described in claim 2, characterized in that, The method for determining the initial estimate of the main frequency includes: Obtain fluid force time history data under steady-state conditions with different excitation accelerations, select the fluid feedback force time history data corresponding to the time period after the system enters the stable resonance stage, and perform mean-removing preprocessing on it; The preprocessed fluid feedback force time history data were subjected to a fast Fourier transform to obtain its spectral distribution; Based on the spectral distribution, an initial search frequency band is set near the excitation frequency, and the main frequency is initially screened within the initial search frequency band. The frequency corresponding to the spectral peak is selected as the initial estimate of the main frequency.

4. The method for analyzing the dynamic characteristics of a hybrid acoustic resonant system as described in claim 2, characterized in that, The linear multiharmonic expression model is specifically as follows: in, For linear multiharmonic expression models, t For a specific moment; To truncate the order, and For the first Harmonic coefficients, harmonic parameters ; As a candidate main frequency, , The initial estimate of the main frequency, The radius is the frequency search radius.

5. The method for analyzing the dynamic characteristics of a hybrid acoustic resonance system as described in claim 1, characterized in that, The dominant frequency component of the hydrodynamic force is equivalently mapped to additional mass parameters and equivalent damping parameters, including: The hydrodynamic frequency component is decomposed into component expressions corresponding to structural displacement, velocity, and acceleration terms by trigonometric expansion. Furthermore, the hydrodynamic frequency component is decomposed into an inertial contribution term proportional to acceleration and an energy dissipation contribution term proportional to velocity, and then equivalently mapped to additional mass parameters and equivalent damping parameters, respectively.

6. The method for analyzing the dynamic characteristics of a hybrid acoustic resonant system as described in claim 1, characterized in that, The specific coupled dynamic equations are as follows: in, For the quality matrix, Here is the structural damping matrix. Here is the stiffness matrix; The external excitation force vector, For fluid feedback force vector; , , These are the system displacement vector, velocity vector, and acceleration vector, respectively.

7. The method for analyzing the dynamic characteristics of a hybrid acoustic resonant system as described in any one of claims 1-6, characterized in that, Based on the equivalent parameterized linear dynamic model, dynamic characteristic analysis under different excitation acceleration conditions is achieved, including: Based on the excitation acceleration, the corresponding additional mass parameters and equivalent damping parameters are obtained according to the optimal function form, and the linearized dynamic model is updated. Based on the updated linearized dynamic model, the steady-state response and frequency domain characteristics of the acoustic-frequency resonant hybrid system are calculated, realizing the rapid characterization of nonlinear fluid-structure interaction characteristics.

8. A dynamic characteristic analysis system for an acoustic frequency resonance hybrid system, characterized in that, Includes a processor, said processor being configured to execute the method for analyzing the dynamic characteristics of an acoustic resonant hybrid system as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for analyzing the dynamic characteristics of the acoustic resonance hybrid system as described in any one of claims 1-7.

10. A computer program product, characterized in that, The system includes a computer program that, when executed by a processor, implements the method for analyzing the dynamic characteristics of an acoustic resonant hybrid system as described in any one of claims 1-7.

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