A unified reflection modeling method for vertical plate structures in waveguides

Abstract

The application provides a unified reflection modeling method of a vertical plate structure in a waveguide, comprising the following steps: establishing a model comprising an upper boundary plate, a lower boundary plate, a middle fluid region and a vertical elastic structure plate; determining a tangential wave number; a tangential wave number expression under a plane wave excitation; a continuous spectrum expression under a point sound source excitation; a discrete spectrum expression under a waveguide mode excitation; a local three-layer scattering unit under a fixed tangential wave number; a unified solution process; a combination with numerical simulation and an extensible mode; and using translational invariance of the vertical structure along a plate surface direction to uniformly express phase changes along the direction as a tangential wave number, so that three types of problems, i.e., an oblique incidence plane wave, a point sound source near field continuous angular spectrum and a waveguide discrete mode, are uniformly described in a same parameter space.

Description

Technical Field

[0001] This invention relates to the intersection of underwater acoustics engineering, structural acoustics, waveguide acoustics and sound scattering theory, and specifically to a unified reflection modeling method for vertical plate structures in waveguides. Background Technology

[0002] In ship structural acoustics, underwater target scattering control, underwater acoustic experimental model design, and research on sound propagation in confined waters, there are often local fluid cavities enclosed by upper and lower boundary plates, or vertical structures such as partitions, reinforcing plates, and functional plates arranged perpendicular to the propagation direction. These structures significantly affect the propagation path of incident sound waves, local standing wave distribution, energy reflection ratio, and modal composition. Therefore, accurately describing the reflection characteristics of vertical structures has always been an important issue in this field.

[0003] Current research on the reflection problem of vertical plates typically employs two main approaches. The first approach approximates the incident sound wave as a far-field obliquely incident plane wave, establishing a transmission and reflection model of the vertical plate structure with the incident angle as the independent variable. This approach offers good physical clarity and facilitates the explanation of reflection peaks and valleys, phase delay within the plate, and normal impedance matching, but it is generally only applicable to ideal cases involving the far field, a single angle, and a single spectral component. The second approach directly uses finite element method, boundary element method, or other numerical techniques to perform full-field solutions for systems with complex boundary conditions and geometry. This approach has a wider range of applications, but it is computationally expensive, has low parameter scanning efficiency, and does not directly reveal the physical laws reflected in the results.

[0004] The problem becomes further complicated when the sound source is a point source, a local transducer, or spherical wave excitation. In this case, the vertical structure receives not a plane wave with a single incident angle, but a superposition of a series of different spatial frequency components—a continuous angular spectrum excitation. Furthermore, under near-field conditions, in addition to the propagation spectrum, there may be significant evanescent spectrum components, which can have a non-negligible impact on local pressure enhancement, near-field notch filtering, phase abrupt changes, and the formation of standing waves within the cavity. Therefore, the traditional method of describing the structural reflection characteristics solely using the "incident angle-reflection coefficient" relationship has significant limitations in point source and near-field problems.

[0005] On the other hand, when the upper and lower boundaries are finite-thickness metal plates or elastic plates, the system exhibits typical waveguide characteristics. In this case, sound propagation is no longer determined solely by the geometric angle of incidence in free water, but by a set of discrete modes constrained by the upper and lower boundary conditions. Different modes have different propagation constants, cutoff characteristics, and spatial distributions, and their reflection results after interacting with the vertical structure also differ. Therefore, in a waveguide environment, simply using a plane wave oblique incidence frame is insufficient to fully describe the structural reflection phenomenon.

[0006] In summary, existing methods have the following shortcomings: First, the plane wave model, point source model, and waveguide mode model are separate and lack a unified parameter organization; second, the traditional definition of the reflection coefficient depends on the incident angle, which is difficult to directly generalize in the near-field and waveguide cases; third, although the fully numerical method can obtain results, it is not conducive to summarizing parameter regularities and rapid analysis. Therefore, it is necessary to propose a new unified theoretical method to incorporate the reflection problem of vertical structures under different excitation conditions and different boundary conditions into the same mathematical framework for processing.

[0007] This invention, based on the translational invariance of the system extending along the vertical structural direction, introduces the "tangential wavenumber" as a unified parameter. As long as the geometry and material distribution of the system remain unchanged in this direction, the phase factor of the sound field in each medium region along this direction will necessarily be consistent, thus conserving the tangential wavenumber. Using this property, the two-dimensional problem can be decomposed into a combination of an exponential factor along the tangential direction and a one-dimensional scattering problem along the normal direction. Therefore, obliquely incident plane waves, continuous angular spectra of point sources, and discrete waveguide modes can all be mapped to a single-spectral problem with a "fixed tangential wavenumber," thereby forming a unified framework for reflection calculation. Summary of the Invention

[0008] The purpose of this invention is to solve the above-mentioned problems and provide a unified reflection modeling method for vertical plate structures in waveguides. By utilizing the translation invariance of the vertical structure along the plate surface, the phase change along this direction is uniformly represented as the tangential wave number, thereby enabling three types of problems—obliquely incident plane waves, near-field continuous angular spectra of point sources, and discrete modes of waveguides—to be uniformly described in the same parameter space.

[0009] To achieve the above objectives, the present invention adopts the following technical solution.

[0010] A unified reflection modeling method for vertical plate structures in waveguides includes the following steps: establishing a model including an upper boundary plate, a lower boundary plate, an intermediate fluid region, and a vertical elastic structural plate; determining the tangential wavenumber; expressing the tangential wavenumber under plane wave excitation; expressing the continuous spectrum under point source excitation; expressing the discrete spectrum under waveguide modal excitation; establishing a local three-layer scattering unit with a fixed tangential wavenumber; a unified solution process; and integration with numerical simulation and scalability.

[0011] Furthermore, one end of the vertical elastic plate is in contact with the upper boundary plate, and the other end is in contact with the lower boundary plate, thereby forming a vertical plate-like structure that runs through the upper and lower boundaries inside the waveguide.

[0012] Furthermore, based on the fluid acoustic propagation control equation and combined with the translational invariance of the model along the plate extension direction, the tangential wavenumber is determined as the unified parameter, and the normal control equation and normal wavenumber are derived, with the continuity of sound pressure and normal velocity as the interface matching conditions.

[0013] Furthermore, the form of the tangential wavenumber value is determined according to the excitation type: plane wave excitation corresponds to a single tangential wavenumber, point source line source excitation corresponds to a continuous set of tangential wavenumbers, and waveguide mode excitation corresponds to a discrete set of tangential wavenumbers.

[0014] Furthermore, for any given tangential wavenumber, the surrounding area of ​​the vertical elastic structure is abstracted into a three-layer scattering unit consisting of water, plate, and water. Based on the relationship between the total wavenumber and the tangential wavenumber of each layer of medium, the normal wavenumber is determined to be real, imaginary, or complex, corresponding to the propagation component and the evanescent component, respectively.

[0015] Furthermore, a single-spectrum scattering solution relationship is established under a fixed tangential wavenumber. The solution relationship may include a transfer matrix form, an equivalent impedance form, or a state-space form.

[0016] Furthermore, depending on the excitation type, continuous spectrum integration or discrete spectrum summation is performed on the single-spectrum reflection response to obtain the overall reflection result.

[0017] Furthermore, the influence of each parameter on the reflection results was analyzed by changing at least one of the following parameters: waveguide height, vertical elastic structure thickness, boundary plate parameters, excitation frequency, and sound source distance.

[0018] Furthermore, this method is used to perform a coarse screening of multi-parameter operating conditions, and the key operating conditions obtained from the screening are imported into numerical simulation software for precise calculation.

[0019] The positive effects of the unified reflection modeling method for vertical plate structures in waveguides proposed in this invention are: (1) It has strong uniformity, incorporating plane waves, point sound sources and waveguide modes into the same parameter framework.

[0020] (2) The physical meaning is clear and can directly explain the relationship between the change of incident angle, near-field spectrum expansion and waveguide mode discretization.

[0021] (3) It has high computational efficiency and is suitable for rapid scanning and pre-simulation screening of large parameter spaces.

[0022] (4) It has strong scalability and is suitable not only for free fluid environments, but also for waveguide environments with finite thickness elastic plates or impedance boundaries at the top and bottom. (5) It is convenient for engineering applications and can directly serve experimental structure design, parameter optimization and numerical simulation prediction. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the overall physical model of the vertical structure in the confined water area described in this invention; Figure 2 A schematic diagram of a local water-plate-water three-layer scattering unit under a fixed tangential wavenumber condition; Figure 3A schematic diagram showing the relationship between plane wave excitation, point source angular spectrum excitation, and waveguide discrete modes uniformly mapped to the tangential wavenumber parameter space; Figure 4 A schematic diagram showing the geometric relationship between the incident angle, tangential wave number, and normal wave number of an obliquely incident plane wave; Figure 5 A schematic diagram of a point sound source or spherical wave unfolding into a continuous tangential wavenumber angular spectrum near a vertical structure; Figure 6 A schematic diagram showing how the upper and lower boundary conditions determine the transverse eigenvalues ​​and discrete tangential wavenumbers of the waveguide. Figure 7 This invention provides a unified reflection solution flowchart; Figure 8 A block diagram showing the influence of parameters such as boundary thickness, structural thickness, frequency, source distance, and waveguide height on the reflection results. Detailed Implementation The following describes a specific implementation of a unified reflection modeling method for a vertical plate structure in a waveguide according to the present invention, with reference to the accompanying drawings. However, it should be noted that the specific implementation is not intended to limit the specific implementation of the present invention. Any similar structures or variations employing the present invention should be included within the scope of protection of the present invention. The following description of the embodiments refers to the accompanying drawings to illustrate specific embodiments in which the present invention can be implemented. Directional terms mentioned in the embodiments, such as "up," "down," "front," "back," "left," "right," "top," and "bottom," are only for reference to the accompanying drawings. Therefore, the directional terms used are for illustrating and understanding the present invention, and not for limiting the present invention.

[0024] See Figures 1-8 .like Figure 1 As shown, the research object is a confined water system consisting of an upper boundary plate, a lower boundary plate, and an intermediate fluid region. A vertical elastic structure is placed in the fluid region. Let the normal direction of the vertical structure be the x-direction, the extension direction of the vertical structure be the z-direction, the net height between the upper and lower boundaries be H, and the thickness of the vertical structure be d. In the fluid region, the sound pressure field satisfies the two-dimensional governing equations: Where p is the sound pressure, k = ω / c is the total wavenumber of the fluid region, ω is the angular frequency, and c is the fluid sound velocity. Since the system processed in this invention satisfies translation invariance in the z-direction, the sound pressure field can be expressed as a separated variable expression, i.e., the product of the phase factor along the z-direction and the function to be determined along the x-direction: Where, k zLet be the tangential wavenumber, and φ(x) be the normal function to be determined. Substituting the above separated variable expression into the above two-dimensional control equation, we can obtain the normal control equation for φ(x): Where, k x Let be the normal wavenumber, and satisfy the normal wavenumber relation: ; The above relationship between normal wavenumbers shows that the original two-dimensional propagation problem can be simplified to a one-dimensional normal scattering problem under a fixed tangential wavenumber. This relationship is also the fundamental reason why this invention achieves unified modeling.

[0025] For plane wave excitation, such as Figure 4 As shown, if the incident angle is defined as the angle θ between the direction of propagation of the incident sound wave and the normal to the vertical structure, then the tangential wave number satisfies the plane wave tangential wave number relationship: Therefore, the conventional angle-of-incidence scanning can be completely equivalently rewritten as tangential wavenumber scanning in this invention. In other words, the plane wave problem is not a special case outside of this invention, but rather a subset within the unified tangential wavenumber framework.

[0026] For point sound sources or spherical wave excitation, such as Figure 5 As shown, the incident field no longer corresponds to a single incident angle, but should be written as a superposition of tangential wavenumber continuous spectra. Its incident field can be expressed using the point source continuous spectrum expression: Where A(k) z Let be the spectral weighting function. From the continuous spectrum expression of the point source, it can be seen that the point source problem is not separate from the plane wave problem, but rather consists of infinitely many plane wave mode components with fixed tangential wavenumbers. For each tangential wavenumber component, the total reflection field can be reconstructed by first obtaining the corresponding single-spectral reflection response and then integrating it according to the aforementioned continuous spectrum weights. Therefore, the point source problem is actually the result of the integral superposition of the fixed tangential wavenumber scatterer problem on the continuous spectrum.

[0027] For waveguide mode excitation, such as Figure 6 As shown, when the upper and lower boundaries are not free boundaries but have rigid, impedance, or finite-thickness equivalent boundary characteristics, the transverse sound field of the system will consist of a set of discrete modes. Its discrete tangential wavenumbers are obtained from the transverse eigenvalue problem, thus forming a discrete root set {k... zn This means that the waveguide mode problem is essentially a discretized special case of the tangential wavenumber continuous spectrum problem. In other words, a plane wave corresponds to a single point, a point source corresponds to a continuous spectrum, and a waveguide mode corresponds to a discrete spectrum, all of which uniformly obey a one-dimensional normal scattering description under a fixed tangential wavenumber condition.

[0028] like Figure 2 As shown, under any fixed tangential wavenumber condition, the local region near the vertical structure can be abstracted as a three-layer scattering unit consisting of water, plate, and water. The fluid region on the left is medium 1, the vertical elastic structure in the middle is medium 2, and the fluid region on the right is medium 3. Let the total wavenumbers of the three media be k1, k2, and k3, respectively. Then the corresponding normal wavenumbers satisfy: ; Where i = 1, 2, 3. If |k z If |k| is less than the corresponding total wavenumber, then the normal wavenumber is a real number, corresponding to the propagation spectrum; if |k| is less than the corresponding total wavenumber, then the normal wavenumber is a real number, corresponding to the propagation spectrum. z If the normal wavenumber is greater than the corresponding total wavenumber, then the normal wavenumber is a purely imaginary or complex number, corresponding to the evanescent spectrum. Therefore, this invention is applicable not only to propagation components but also naturally compatible with evanescent spectrum components in the near field.

[0029] Under a fixed tangential wavenumber, the total field in the fluid region on the left can be written as a superposition of incident and reflected waves, the total field in the fluid region on the right can be written as a transmitted wave, and the total field in the middle vertical structural layer can be written as a superposition of forward and backward waves. Furthermore, a normal characteristic impedance can be defined. For fluid media, the normal characteristic impedance can be: ; Where ρ i Let be the density of the i-th layer of medium. By applying pressure continuity and normal velocity continuity conditions at the left and right interfaces, the interface coupling relationship in the single-spectrum scatterer problem can be established, and the single-spectrum complex reflection response can be obtained. If the vertical structural layer is approximated as an equivalent fluid plate, only longitudinal compressive propagation is considered within the plate; if a higher-order elastic theory is used, it can be further extended to displacement-stress state variables, but without changing the unified framework of this invention.

[0030] To further demonstrate the impact of waveguide boundaries on the results, such as Figure 8 As shown, this invention also allows the upper and lower boundaries to be introduced into the transverse eigenvalue problem through equivalent impedance. For low-to-mid-frequency cases dominated by inertial control, the mass law approximation can be used to construct the boundary impedance, thereby explicitly introducing the influence of boundary thickness, material density, and frequency on the discrete spectrum distribution into the method of this invention. Thus, changes in structural parameters and changes in boundary parameters can be analyzed uniformly within the same framework.

[0031] The technical approach of this invention can be summarized as follows: First, a waveguide and vertical structure model is established; then, using the tangential wavenumber as a unified parameter, different excitation scenarios are mapped to a fixed tangential wavenumber scatterer problem; subsequently, the single-spectrum reflection response is obtained; finally, the continuous spectrum or discrete spectrum is superimposed according to the specific excitation type, such as... Figure 7As shown, this process can output single-spectrum reflection curves under plane wave conditions, equivalent reflection results at observation points under point source conditions, and total amplitude reflection results, total power reflection ratio, or mode redistribution results under waveguide mode conditions.

[0032] Step 1: Establishing the overall model. For example... Figure 1 As shown, a two-dimensional or quasi-two-dimensional underwater acoustic waveguide model is established. The model includes an upper boundary plate, a lower boundary plate, an intermediate fluid region, and a vertical elastic structure located within the intermediate fluid region. The upper end of the vertical elastic structure contacts the upper boundary plate, and the lower end contacts the lower boundary plate, thereby forming a vertical plate-like structure that runs through the upper and lower boundaries inside the waveguide.

[0033] Let H be the net height between the upper and lower boundaries, and d be the thickness of the vertical elastic structure. Take the direction perpendicular to the vertical structure's surface as the x-direction, and the direction extending along the vertical structure's surface as the z-direction. The medium within the fluid region is water, with a density of ρ. w The speed of sound is c w The vertical elastic structure can be a steel plate, a composite material plate, or other elastic plate-like structure, with a density of ρ. s The equivalent wave velocity is c s .

[0034] In this model, the upper and lower boundary plates and the vertical elastic structure together constitute a typical plate-waveguide coupling structure in confined waters. Since the vertical elastic structure extends along the z-direction, and the basic model studied in this invention satisfies translation invariance in the z-direction, the wavenumber component in the z-direction can be used as a unified descriptive parameter.

[0035] Step 2: Obtain the unified tangential wavenumber parameters from the two-dimensional governing equations. For example... Figure 3 As shown, the unified starting point of this invention is the tangential wavenumber. The sound pressure p in the fluid region satisfies the two-dimensional governing equation: Where k = ω / c is the total wave number in the fluid medium, ω is the angular frequency, and c is the speed of sound. Since the model satisfies translation invariance in the z-direction, the sound pressure can be expressed using a separated-variables expression as follows: Where, k z Let be the tangential wavenumber, and φ(x) be the function to be determined along the normal direction. Substituting this separated variable expression into the two-dimensional control equations, we obtain the normal control equations: Therefore, the normal wave number is defined as follows: Therefore, the normal governing equation can be further written as: .

[0036] The above derivation shows that, given the tangential wavenumber k, zTherefore, the original two-dimensional sound propagation problem can be transformed into a one-dimensional normal problem along the x-direction. Thus, the differences between different excitation forms mainly lie in the different sources of the tangential wavenumber set, while the solution form for local scattering under a fixed tangential wavenumber can remain unified.

[0037] Furthermore, the relationship between normal velocity and sound pressure can be obtained from the frequency domain Euler equations: Therefore, at the interfaces of various media, the continuity of sound pressure and normal velocity can be uniformly used as the basic matching conditions. This relationship provides a unified boundary condition basis for the subsequent establishment of local water-plate-water scattering units.

[0038] Step 3: Tangential wavenumber expression under plane wave excitation. For example... Figure 4 As shown, when the incident sound field is an obliquely incident plane wave, let the incident angle θ be the angle between the sound wave propagation direction and the normal to the vertical structure, then the tangential wave number satisfies: Therefore, traditional reflection analysis using the incident angle θ as the independent variable can be transformed in this invention into analysis using the tangential wavenumber k. z Single-spectral analysis with independent variables.

[0039] Assuming the incident wave in medium 1 has a unit amplitude, the sound field in the fluid region on the left can be expressed as the sum of the incident wave and the reflected wave: Where R is the complex reflection coefficient, k x1 Let be the normal wave number in medium 1. The sound field inside the vertical plate layer can be expressed as the sum of the forward and backward waves: Where A and B are the amplitudes of the forward and backward waves inside the plate, respectively, and kx2 is the normal wave number in the plate. The sound field in the fluid region on the right can be represented as a transmitted wave: Where T is the complex transmission coefficient, and k x3 Let be the normal wavenumber in medium 3. As can be seen from the above expression, although the three layers have different normal wavenumbers, they all have the same phase factor along the z-direction. This indicates that maintaining a consistent tangential wavenumber across all regions is crucial for unified modeling.

[0040] Step 4: Continuous spectrum representation under point source excitation. For example... Figure 5 As shown, when the excitation is a point source, a line source, or a local spherical wave, the incident sound field no longer corresponds to a single incident angle, but should be expressed as a superposition of tangential wavenumber continuous spectra. The incident field of a point source can be expressed using a continuous spectrum expression as follows: Where A(k) z Let k be the tangential wavenumber spectrum weighting function. For each tangential wavenumber component, it can be considered as a fixed k. z The single-spectral incident problem is solved, and the corresponding single-spectral reflection response R(k) is obtained from the local scattering unit.z Therefore, the reflected field can be expressed using the superposition expression of continuous spectrum reflection as follows: If it is necessary to construct the equivalent reflection result of the system at a given observation point r, the definition of equivalent reflection at the observation point can be used: It should be noted that the above-mentioned continuous spectrum relationship of point sound sources is used in this patent to illustrate how the point sound source case is incorporated into the unified framework of tangential wavenumber; its more detailed integration path, spectrum truncation strategy, source distance influence and near-field reconstruction method can be further elaborated in the near-field patent of point sound sources.

[0041] Step 5: Discrete spectral representation under waveguide mode excitation. For example... Figure 6 As shown, when the upper and lower boundary plates form waveguide constraints on the fluid region, the system's acoustic field can be represented as a discrete mode superposition. The acoustic field in the waveguide can be summarized as follows: The discrete tangential wavenumber k_{t,n} can be determined by the transverse eigenvalue problem of the waveguide. If the impedance boundary form is adopted, its eigenvalue equation can be summarized as: Where H is the waveguide height, and Z_top and Z_bottom represent the equivalent impedances of the upper and lower boundaries, respectively. Solving this eigenvalue equation yields the discrete tangential wavenumber set {k zn Each discrete tangential wavenumber can be substituted into the local scatterer problem under a fixed tangential wavenumber to obtain the corresponding modal reflection response. It should be noted that the in-depth derivation of eigenvalue solving, modal weight construction, and modal power superposition is the main content of the waveguide mode patent, and this patent only retains the necessary relationships as components of the unified framework.

[0042] Step Six: Local three-layer scattering unit at a fixed tangential wavenumber. For example... Figure 2 As shown, for any fixed tangential wavenumber kz, the local region near the vertical plate can be abstracted as a three-layer scattering unit consisting of water, plate, and water. The fluid region on the left is medium 1, the middle vertical plate layer is medium 2, and the fluid region on the right is medium 3. The normal wavenumbers in the three media uniformly satisfy: , where k i Let k be the total wavenumber in the i-th layer of the medium. z If the wavenumber is less than the total wavenumber of the corresponding medium, then the normal wavenumber of that layer is a real number, representing the propagation component; if k z If the wavenumber is greater than the total wavenumber of the corresponding medium, then the normal wavenumber of that layer is an imaginary or complex number, representing the evanescent component.

[0043] The normal characteristic impedance in a fluid medium can be expressed as: For the case of propagating waves, this impedance can also be written in a form related to the equivalent propagation angle: , where θi is the equivalent propagation angle in the i-th layer of medium.

[0044] At the interfaces x = 0 and x = d, the sound pressure and normal velocity should satisfy the continuity condition: Since all three regions have the same tangential phase factor. Therefore, when matching interfaces, the common tangential phase can be canceled, and only the amplitude relationship in the normal direction is retained.

[0045] If sound pressure and normal velocity are used as state variables, a state vector can be defined as follows: Then the propagation relationship of the plate layer from x = 0 to x = d can be written as: Where M2 is the plate transfer matrix. If an equivalent fluid plate approximation is used, it can be written as... .

[0046] It should be noted that the above transfer matrix relationship is only used in this patent to illustrate the basic solvable form of the local scatterer problem under a fixed tangential wavenumber; the detailed derivation, matrix element processing, and numerical implementation of the transfer matrix are the focus of the transfer matrix patent. This patent only retains the levels necessary to support the unified framework. Under the unified framework, the results of the local three-layer scattering unit can be summarized as follows: , where R(k z T(k,ω) is the single-spectral reflection response at a fixed tangential wavenumber. z ,ω) represents the corresponding transmission response. Different external excitation conditions only determine k. z The way or set of values ​​that k can take does not change the fixed k. z The basic form of the local scatterer problem.

[0047] Step 7: Standardize the solution process. For example... Figure 7 As shown, the overall solution process of this invention follows the following order: (1) Establish an overall physical model based on structural geometry and material parameters, such as Figure 1 As shown; (2) Determine the source of tangential wavenumber according to the excitation type: plane wave corresponds to a single tangential wavenumber, point source corresponds to a continuous tangential wavenumber set, waveguide mode corresponds to a discrete tangential wavenumber set, such as Figure 3 , Figure 5 and Figure 6 As shown; (3) For each tangential wavenumber, establish a local water-plate-water three-layer scattering unit, such as Figure 2 As shown; (4) The monospectral reflection response R(k) is obtained by using the normal wavenumber relationship, normal characteristic impedance and interface continuity condition. z,ω); (5) Perform continuous spectrum integration or discrete spectrum summation according to the excitation type and output the system reflection result. This process shows that the present invention does not separate plane wave, point source and waveguide mode into three unrelated methods, but organizes the three into the same solution chain of "tangential wavenumber determination - fixed tangential wavenumber scattering - spectrum superposition output".

[0048] Step 8: Influence of boundary parameters and structural parameters. For example... Figure 8 As shown, this invention can also be used to analyze the influence of parameters such as boundary thickness, vertical plate thickness, frequency, waveguide height, and source distance on reflection results. Boundary parameters mainly affect the tangential wavenumber set by changing the waveguide discrete spectrum or boundary impedance, while structural parameters mainly affect the single-spectrum reflection response by changing the normal wavenumber, impedance, and phase delay in local scattering units. Therefore, the overall reflection result can be understood as the result of the combined effect of "tangential spectrum distribution" and "single-spectrum reflection response." This understanding helps to distinguish the different contributions of boundary design, structural design, and excitation arrangement to the reflection result in engineering.

[0049] Step Nine: Integration with Numerical Simulation and Scalability. This invention can initially be used for multi-parameter coarse screening. By rapidly scanning parameters such as frequency, plate thickness, boundary thickness, waveguide height, and source distance, regions where strong reflection, reflection valleys, near-field enhancement, or modal coupling enhancement may occur can be identified in advance. Subsequently, a small number of key operating conditions are input into finite element software for precise calculation. This not only reduces the overall simulation workload but also improves the physical interpretation of the results.

[0050] This invention is not limited to single-layer uniform plates. When the vertical structure is a composite material plate, a multilayer plate, a plate with a damping layer, or other structures that can be equivalent to local layered scattering units, as long as its upper and lower ends are in contact with the upper and lower boundary plates respectively, and a corresponding local scattering problem can be established under a fixed tangential wavenumber, the method of this invention can be used for unified analysis. For those skilled in the art, any equivalent changes or improvements made to the implementation steps, parameter settings, and application scenarios without departing from the core idea of ​​this invention should be considered to fall within the protection scope of this invention.

Claims

1. A unified reflection modeling method for vertical plate structures in waveguides, characterized in that, Includes the following steps: Establish a model that includes an upper boundary plate, a lower boundary plate, an intermediate fluid region, and a vertical elastic structural plate; Determine the tangential wavenumber; Tangential wavenumber expression under plane wave excitation; Continuous spectrum representation under point source excitation; Discrete spectral representation under waveguide modal excitation; Local three-layer scattering unit at a fixed tangential wavenumber; Unified solution process; Integration with numerical simulation and its scalability.

2. The unified reflection modeling method for vertical plate structures in waveguides according to claim 1, characterized in that, One end of the vertical elastic plate is in contact with the upper boundary plate, and the other end is in contact with the lower boundary plate, thereby forming a vertical plate-like structure that runs through the upper and lower boundaries inside the waveguide.

3. The unified reflection modeling method for vertical plate structures in waveguides according to claim 1, characterized in that, Based on the fluid acoustic propagation control equation and the translational invariance of the model along the plate extension direction, the tangential wavenumber is determined as the unified parameter, and the normal control equation and normal wavenumber are derived. The continuity of sound pressure and normal velocity are used as interface matching conditions.

4. The unified reflection modeling method for vertical plate structures in waveguides according to claim 1, characterized in that, The form of the tangential wavenumber is determined according to the excitation type. Plane wave excitation corresponds to a single tangential wavenumber, point source line source excitation corresponds to a continuous set of tangential wavenumbers, and waveguide mode excitation corresponds to a discrete set of tangential wavenumbers.

5. The unified reflection modeling method for vertical plate structures in waveguides according to claim 1, characterized in that, For any given tangential wavenumber, the surrounding area of ​​the vertical elastic structure is abstracted into a three-layer scattering unit consisting of water, plate, and water. Based on the relationship between the total wavenumber and the tangential wavenumber of each layer, the normal wavenumber is determined to be real, imaginary, or complex, corresponding to the propagation component and the evanescent component, respectively.

6. The unified reflection modeling method for vertical plate structures in waveguides according to claim 1, characterized in that, A solution relationship for single-spectral scattering is established under a fixed tangential wavenumber. The solution relationship may include transfer matrix form, equivalent impedance form, or state-space form.

7. The unified reflection modeling method for vertical plate structures in waveguides according to claim 1, characterized in that, Depending on the excitation type, perform continuous spectrum integration or discrete spectrum summation on the single-spectrum reflection response to obtain the overall reflection result.

8. The unified reflection modeling method for vertical plate structures in waveguides according to claim 1, characterized in that, By changing at least one of the following parameters—waveguide height, vertical elastic structure thickness, boundary plate parameters, excitation frequency, and sound source distance—analyze the impact of each parameter on the reflection results.

9. The unified reflection modeling method for vertical plate structures in waveguides according to claim 1, characterized in that, This method is used to perform a coarse screening of multi-parameter working conditions, and the key working conditions obtained from the screening are imported into numerical simulation software for precise calculation.

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