A method for predicting influence of sonar barrier on sonar elements based on virtual source method

Abstract

This invention discloses a method for predicting the impact of sonar baffles on sonar array elements based on the virtual source method. The method includes: establishing an equivalent theoretical model; simplifying the scattering problem of the equivalent theoretical model into a multiple scattering problem between two infinitely long rigid cylinders; deriving an analytical expression for the scattered sound pressure on the surface of the infinitely long rigid cylinders; calculating the theoretical analytical solution for the scattered sound pressure on the cylinder surface; establishing a finite element model of the two infinitely long rigid cylinders and using the model to solve for the scattered sound pressure on the cylinder surface; comparing the model solution with the theoretical analytical solution to verify the correctness and effectiveness of the analytical expression; changing the cylinder size and the distance between the cylinder and the baffle, comparing the calculation results with the case without a baffle, and analyzing the effect of the baffle on the scattered sound pressure on the cylinder surface. This invention ensures computational accuracy while possessing a clear physical mechanism and high computational efficiency, thus providing a reliable research basis and theoretical support for evaluating the impact of sonar baffles on sonar array elements in practical engineering.

Description

Technical Field

[0001] This invention relates to underwater acoustic engineering and underwater acoustics technology, specifically a method for predicting the influence of sonar baffles on sonar array elements based on the virtual source method. Background Technology

[0002] In sonar system design, baffles are used to improve the acoustic performance of sonar array elements. Their geometry, size, and relative position to the elements significantly affect the sound pressure distribution on the element surface through complex scattering effects. Accurately predicting this effect is crucial for optimizing the directivity, gain, and interference suppression of the sonar system.

[0003] Traditional methods largely rely on full-scale experimental testing or numerical simulations based on simplified acoustic models. While experimental methods are intuitive and reliable, they are costly, time-consuming, and difficult to use for comparison of multiple solutions in the early design stages. Common numerical simulation methods (such as the finite element method and boundary element method) often face challenges such as high computational cost, complex modeling, or insufficient high-frequency computational accuracy when dealing with "baffle-element" coupling problems with complex multiple scattering characteristics. Therefore, there is an urgent need to develop a theoretical prediction method that can guarantee computational accuracy while possessing clear physical mechanisms and high computational efficiency to guide the optimal design of sonar baffles and the performance evaluation of sonar elements. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a prediction method for the influence of sonar baffles on sonar array elements based on the virtual source method. This method can ensure calculation accuracy, has a clear physical mechanism and high calculation efficiency, and can guide the optimized design of sonar baffles and the performance evaluation of sonar array elements.

[0005] Technical solution: The present invention provides a method for predicting the impact of sonar baffles on sonar array elements based on the virtual source method, comprising:

[0006] Based on the geometric and physical characteristics of actual sonar baffles and sonar array elements, an equivalent theoretical model of an infinitely large rigid plate and an infinitely long rigid cylinder is established.

[0007] Based on the virtual source method, the scattering problem of the equivalent theoretical model is simplified into a multiple scattering problem between two infinitely long rigid cylinders;

[0008] Based on the multiple scattering problem between two infinitely long rigid cylinders, an analytical expression for the scattered sound pressure on the surface of an infinitely long rigid cylinder is derived. Boundary conditions are applied to each infinitely long rigid cylinder, and the total sound field of the two infinitely long rigid cylinders is calculated by combining the scattered sound pressure on the surface of the two infinitely long rigid cylinders in the analytical expression.

[0009] In the COMSOL finite element software, a two-dimensional finite element model of two infinitely long rigid cylinder systems corresponding to the multiple scattering problem between two infinitely long rigid cylinders is established. The two-dimensional finite element model of two infinitely long rigid cylinders is used to solve the sound pressure scattered on the surface of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders.

[0010] The calculated sound pressure scattered from the surfaces of two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders were compared with the sound pressure scattered from the surfaces of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders obtained by the model. The comparison results showed that the calculation results of the analytical expression were consistent with the results obtained by the model, thus verifying the correctness of the analytical expression for the sound pressure scattered from the surfaces of infinitely long rigid cylinders.

[0011] By changing the size parameters of two infinitely long rigid cylinders and the distance parameter between them, the scattered sound pressure on the surface of the infinitely long rigid cylinder is calculated under each parameter with a sonar baffle, based on the verified analytical expression of the scattered sound pressure on the surface of the infinitely long rigid cylinder.

[0012] Calculate the scattered sound pressure on the surface of an infinitely long rigid cylinder under various parameters without a sonar baffle;

[0013] By comparing and analyzing the scattered sound pressure on the surface of an infinitely long rigid cylinder with various parameters under different conditions with and without a sonar baffle, the influence of the sonar baffle on the sound pressure on the surface of the sonar array is revealed.

[0014] Furthermore, the establishment of an equivalent theoretical model of an infinitely large rigid plate and an infinitely long rigid cylinder based on the geometric and physical characteristics of the actual sonar baffle and sonar array elements includes:

[0015] The sonar baffle is simplified into an infinitely large rigid plate, and the sonar array element is simplified into an infinitely long rigid cylinder, thus establishing an equivalent theoretical model of an infinitely large rigid plate and an infinitely long rigid cylinder.

[0016] Furthermore, based on the virtual source method theory, the scattering problem of the equivalent theoretical model is simplified to a multiple scattering problem between two infinitely long rigid cylinders, including:

[0017] According to the virtual source method, an identical infinitely long rigid cylinder is introduced at a symmetrical position on the other side of the infinitely large rigid plate, while the infinitely large rigid plate is removed. This makes the superposition field of the original source and the virtual source satisfy the normal vibration velocity of zero at the plate, thus transforming the scattering problem of the equivalent theoretical model into a multiple scattering problem between two infinitely long rigid cylinders.

[0018] Furthermore, the derivation of the analytical expression for the scattered sound pressure on the surface of an infinitely long rigid cylinder, based on the multiple scattering problem between two infinitely long rigid cylinders, includes:

[0019] Expanding the incident wave in two infinitely long rigid cylindrical coordinate systems yields expressions for the expansion of the incident wave in the upper cylindrical coordinate system and expressions for the expansion of the incident wave in the lower infinitely long rigid cylindrical coordinate system.

[0020] Each infinitely long rigid cylinder generates scattered sound pressure after being subjected to an incident sound wave. The analytical expression for the scattered sound pressure on the surface of a single infinitely long rigid cylinder is as follows:

[0021]

[0022] in, The sound pressure scattered from the surface of an infinitely long rigid cylinder above an infinitely large rigid flat plate; The scattering coefficient is the surface scattering coefficient of an infinitely long rigid cylinder above an infinitely large rigid plate. The sound pressure scattered from the surface of an infinitely long rigid cylinder beneath an infinitely large rigid flat plate; is the scattering coefficient of the infinitely long rigid cylinder surface beneath an infinitely large rigid plate; This is a Hankel function of the first kind.

[0023] Furthermore, the expressions for the expansion of the incident wave in the upper cylindrical coordinate system and the expressions for the expansion of the incident wave in the lower infinitely long rigid cylindrical coordinate system are as follows:

[0024] ;

[0025] in, This is the distance between the sound pressure measurement point and the center of the upper circle; The angle between the line connecting the sound pressure measurement point and the center of the upper circle and the horizontal axis; Let be the expression for the expansion of the incident wave in an infinitely long rigid cylindrical coordinate system above; This is the distance between the sound pressure measurement point and the center of the lower circle; The angle between the line connecting the sound pressure measurement point and the center of the lower circle and the horizontal axis; Let be the expression for the expansion of the incident wave in the infinitely long rigid cylindrical coordinate system below; is the base of the natural logarithm; The imaginary unit; The wave number of the incident wave; The angle between the incident sound wave and the x-axis; First order ; It is a Bessel function of the first kind.

[0026] Furthermore, the step of applying boundary conditions to each infinitely long rigid cylinder, utilizing the orthogonality of the boundary conditions combined with the analytical expression of the scattered sound pressure from the surfaces of the two infinitely long rigid cylinders, calculates the total sound field of the two infinitely long rigid cylinders, including:

[0027] Based on the addition theorem, the scattered waves of a cylindrical sonar array are represented in the imaginary source coordinate system as follows:

[0028] ;

[0029] in, It is the second order; The distance between the two infinitely long rigid cylinders is half the distance between them. The entire sound field is represented in the actual sonar array coordinate system, and corresponding boundary conditions are applied to each infinitely long rigid cylinder.

[0030] By utilizing boundary conditions and the orthogonality of functions, and combining this with the analytical expression for the sound pressure scattered from the surface of an infinitely long rigid cylinder, we can obtain the sound pressure scattered from the surface of the infinitely long rigid cylinder above. The sound pressure scattered by the infinitely long rigid cylinder surface below Calculate the total sound field on the surfaces of two infinitely long rigid cylinders. .

[0031] Furthermore, the expression for the boundary condition is:

[0032] .

[0033] Furthermore, the total sound field on the surfaces of the two infinitely long rigid cylinders The expression is as follows:

[0034] ;

[0035] In the formula, This is the incident sound pressure.

[0036] Furthermore, the step of establishing a two-dimensional finite element model of two infinitely long rigid cylinders in the COMSOL finite element software, corresponding to the multiple scattering problem between two infinitely long rigid cylinders, and using the two-dimensional finite element model of the two infinitely long rigid cylinders to solve for the scattered sound pressure on the surface of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders, includes:

[0037] Two identical infinitely long rigid cylinders were constructed in a two-dimensional plane using COMSOL finite element software. A perfectly matched cylindrical layer was used, and a plane wave was incident in a background pressure field. The incident radio frequency and incident angle were set to establish two-dimensional finite element models of the two infinitely long rigid cylinders. The two-dimensional finite element models of the two infinitely long rigid cylinders and the water area were divided into free triangular meshes according to one-sixth of the wavelength. The scattered sound pressure on the surface of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders were calculated using the two-dimensional finite element models of the two infinitely long rigid cylinders.

[0038] Furthermore, the calculation of the scattered sound pressure on the surface of an infinitely long rigid cylinder under various parameters without a sonar barrier includes:

[0039] Suppose a plane wave is incident perpendicularly on an infinitely long rigid cylinder. The scattered field is axis-independent and symmetric with respect to the azimuth angle. Transforming the three-dimensional infinitely long rigid cylinder into a two-dimensional plane circle for analysis, the incident wave expands as follows:

[0040] ;

[0041] in, Neumann factor; The distance from the point of incidence to the cylinder; The angle between the point of incidence, the center of the cylinder, and the x-axis; Let be the expression for the incident sound pressure. This is the unfolding form of the incident sound pressure; imaginary unit Power; It is the azimuth function; For the first type of Bessel function; similar to the case of a sphere, the scattered wave is represented by the first type of Hankel function, and the scattered sound pressure on the surface of an infinitely long rigid cylinder under various parameters without a sonar barrier is:

[0042] ;

[0043] in, This is the scattered sound pressure; The scattering coefficient is the Hankel function; it is determined by the boundary conditions on the cylindrical surface. For an infinitely long rigid cylinder, it has...

[0044] ;

[0045] ;

[0046] ;

[0047] in, The first derivative of the cylindrical Bessel function; The first derivative of the Hankel function is used; the scattering coefficient is obtained using boundary conditions. Based on the solved scattering coefficient The formula for calculating the scattered sound pressure on the surface of an infinitely long rigid cylinder is used to solve for the scattered sound field on the surface of the infinitely long rigid cylinder.

[0048] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows:

[0049] (1) In step S1 of this invention, an equivalent theoretical model is proposed, which simplifies the actual sonar baffle and array elements into an equivalent theoretical model of "infinitely large rigid plate - infinitely long rigid cylinder", and uses the virtual source method to transform it into a multiple scattering problem of two infinitely long rigid cylinders, which significantly simplifies the theoretical description of complex boundary acoustic coupling.

[0050] (2) In step S3 of the present invention, the analytical expression of the scattered sound pressure on the surface of an infinitely long rigid cylinder is derived. The scattered sound pressure on the surface of an infinitely long rigid cylinder is solved by the analytical expression. While ensuring the calculation accuracy, the calculation efficiency is greatly improved, and the limitations of traditional methods in high-frequency or complex multiple scattering scenarios, such as large amount of calculation and long time consumption, are overcome.

[0051] (3) In step S5 of the present invention, the reliability of the prediction results is ensured by cross-verification of theoretical analysis and finite element simulation, providing an analytical tool with both theoretical depth and engineering practicality for the optimized design of sonar baffles;

[0052] (4) The present invention has good parametric analysis capabilities, which can conveniently study the influence of parameters such as baffle size and distance, facilitate multi-scheme comparison and performance prediction in the early stage of design, and effectively guide engineering practice. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the process of the present invention;

[0054] Figure 2 This is a schematic diagram of the structure of the sonar array element and the sonar baffle in this invention;

[0055] Figure 3 This is a schematic diagram illustrating the basic principle of the virtual source method in this invention;

[0056] Figure 4 This is a schematic diagram of the coordinate system used in this invention to calculate the multiple scattering problem of two infinitely long rigid cylinders;

[0057] Figure 5 A comparison chart showing the results of finite element software calculations and the results of calculations based on theoretical analytical expressions;

[0058] Figure 6 This is a comparison diagram of the scattered sound pressure on the surface of the cylinder after changing the cylinder size according to the present invention;

[0059] Figure 7 This is a comparison of the scattered sound pressure on the cylinder surface after changing the distance between the cylinder and the sonar baffle according to the present invention. Detailed Implementation

[0060] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0061] This invention discloses a method for predicting the impact of sonar baffles on sonar array elements based on the virtual source method. By simplifying the actual sonar baffle and array elements into an "infinitely large rigid plate-infinitely long rigid cylinder" model, and applying the virtual source method to represent it as a multiple scattering problem of two infinitely long rigid cylinders, a theoretical solution for the scattered sound pressure on the cylinder surface is obtained. This method is verified and parametrically analyzed using finite element simulation, and can accurately predict the distribution of sound pressure on the surface of sonar array elements under different sonar array sizes and distances from the baffle, providing a reliable theoretical basis for the design and performance optimization of sonar system baffles. Figure 1 As shown, the forecasting method of the present invention specifically includes the following steps:

[0062] S1. Based on the geometric and physical characteristics of actual sonar baffles and sonar array elements, establish equivalent theoretical models of an infinitely large rigid plate and an infinitely long rigid cylinder. Specifically:

[0063] like Figure 2 As shown, the sonar baffle is simplified to an infinitely large rigid plate 1, and the sonar array element is simplified to an infinitely long rigid cylinder 2, thus establishing an equivalent theoretical model of an infinitely large rigid plate-infinitely long rigid cylinder.

[0064] S2. Based on the virtual source method, the scattering problem of the equivalent theoretical model is simplified to a multiple scattering problem between two infinitely long rigid cylinders. Specifically:

[0065] like Figure 3 As shown, the core concept of the virtual source method is that when studying the acoustic scattering problem of the plate-cylinder combination, an identical mirror cylinder 7 can be introduced on the other side of the sonar baffle 6 at a position symmetrical to the cylinder 3, and the original sonar baffle 6 can be removed, thereby transforming the original "plate-cylinder" scattering problem into an equivalent multiple scattering problem of "two infinitely long rigid cylinders".

[0066] In step S2, according to the virtual source method, an identical infinitely long rigid cylinder is introduced at a symmetrical position on the other side of the infinitely large rigid plate, while the infinitely large rigid plate is removed. This ensures that the superposition field of the original source and the virtual source satisfies zero normal vibration velocity at the plate. The scattering problem of the equivalent theoretical model in step S1 is transformed into a multiple scattering problem between two infinitely long rigid cylinders.

[0067] S3. Based on the multiple scattering problem between the two infinitely long rigid cylinders obtained in step S2, derive the analytical expression for the scattered sound pressure on the surface of the infinitely long rigid cylinder; apply boundary conditions to each infinitely long rigid cylinder, and calculate the total sound field of the two infinitely long rigid cylinders by combining the scattered sound pressure on the surface of the two infinitely long rigid cylinders in the analytical expression for the scattered sound pressure on the surface of the infinitely long rigid cylinders.

[0068] The specific implementation process of step S3 is as follows:

[0069] S3.1 Based on the multiple scattering problem between two infinitely long rigid cylinders obtained in step S2, derive the analytical expression for the scattered sound pressure on the surface of the infinitely long rigid cylinder, as follows:

[0070] Expanding the incident wave in two infinitely long rigid cylindrical coordinate systems yields the expressions for the expansion of the incident wave in the upper cylindrical coordinate system and the expansion of the incident wave in the lower infinitely long rigid cylindrical coordinate system, as shown below:

[0071] ;

[0072] like Figure 4 As shown, the radius of the infinitely long rigid cylinder is The distance between the centers of two infinitely long rigid cylinders is The angle between the line connecting the sound pressure measurement point and the origin and the x-axis is... ; This is the distance between the sound pressure measurement point and the center of the upper cylinder; The angle between the line connecting the sound pressure measurement point and the center of the upper cylinder and the horizontal axis; Let be the expression for the expansion of the incident wave in an infinitely long rigid cylindrical coordinate system above; This is the distance between the sound pressure measurement point and the center of the cylinder below; The angle between the line connecting the sound pressure measurement point and the center of the lower cylinder and the horizontal axis; Let be the expression for the expansion of the incident wave in the infinitely long rigid cylindrical coordinate system below; is the base of the natural logarithm; The imaginary unit; The wave number of the incident wave; The angle between the incident sound wave and the x-axis; First order ; It is a Bessel function of the first kind.

[0073] Each infinitely long rigid cylinder generates scattered sound pressure after being subjected to an incident sound wave. The analytical expression for the scattered sound pressure on the surface of a single infinitely long rigid cylinder is as follows:

[0074]

[0075] in, The sound pressure scattered from the surface of an infinitely long rigid cylinder above an infinitely large rigid flat plate; The scattering coefficient is the surface scattering coefficient of an infinitely long rigid cylinder above an infinitely large rigid plate. The sound pressure scattered from the surface of an infinitely long rigid cylinder beneath an infinitely large rigid flat plate; is the scattering coefficient of the infinitely long rigid cylinder surface beneath an infinitely large rigid plate; This is a Hankel function of the first kind.

[0076] S3.2 Apply boundary conditions to each infinitely long rigid cylinder. Utilize the boundary conditions combined with the orthogonality of the functions, and combine the analytical expression of the scattered sound pressure from the surface of the infinitely long rigid cylinder with the scattered sound pressure from the surface of the two infinitely long rigid cylinders ( and The total sound field of the two infinitely long rigid cylinders was calculated as follows:

[0077] Based on the addition theorem, the scattered waves from a cylindrical sonar array can be represented in the imaginary source coordinate system:

[0078] ;

[0079] in, It is the second order; The distance between the two infinitely long rigid cylinders is half the distance between them. The entire sound field can be represented in the actual sonar array coordinate system, and corresponding boundary conditions can be applied to each infinitely long rigid cylinder. The boundary conditions are as follows:

[0080] ;

[0081] By utilizing boundary conditions and the orthogonality of functions, and combining this with the analytical expression for the sound pressure scattered from the surface of an infinitely long rigid cylinder, we can obtain the sound pressure scattered from the surface of the infinitely long rigid cylinder above. The sound pressure scattered by the infinitely long rigid cylinder surface below Calculate the total sound field on the surfaces of two infinitely long rigid cylinders. Its expression is as follows:

[0082] .

[0083] in, This is the incident sound pressure.

[0084] S4. In the COMSOL finite element software, establish a two-dimensional finite element model of the two infinitely long rigid cylinders corresponding to the multiple scattering problem between them. Use this two-dimensional finite element model to solve for the scattered sound pressure on the surface of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders. Details are as follows:

[0085] Two identical infinitely long rigid cylinders were constructed in a two-dimensional plane using COMSOL finite element software. A perfectly matched cylindrical layer was used. A plane wave was incident in a background pressure field, with the incident radio frequency preset to 10 kHz and the incident angle set to [value missing]. Thus, two-dimensional finite element models of two infinitely long rigid cylindrical systems were established; free triangular meshes were generated for the two-dimensional finite element models of the two infinitely long rigid cylindrical systems and the water area according to one-sixth of the wavelength; and the scattered sound pressure on the surface of the two infinitely long rigid cylindrical systems was calculated using the two-dimensional finite element models of the two infinitely long rigid cylindrical systems respectively. and The total sound field of the two infinitely long rigid cylinders.

[0086] S5. Compare the sound pressure scattered from the surfaces of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders calculated in step S3 with the sound pressure scattered from the surfaces of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders solved by the model in step S4. The comparison results show that the calculation results of the analytical expression are consistent with the solution results of the model, thus verifying the correctness of the analytical expression of the sound pressure scattered from the surfaces of the infinitely long rigid cylinders.

[0087] In step S5, the scattered sound pressure from the surfaces of the two infinitely long rigid cylinders calculated in step S3 is... and The sound pressure scattered from the surfaces of two infinitely long rigid cylinders obtained from the model solution in step S4 () and By comparing the total sound field of two infinitely long rigid cylinders, The total sound field of the two infinitely long rigid cylinders obtained from the model solution in step S4 A comparison was made, and the results are as follows: Figure 5 As shown. From Figure 5 It can be seen that plane waves are all calculated using... When the incident angle is angular, the theoretical solution is completely consistent with the finite element calculation results, thus verifying the correctness of the analytical expression for the scattered sound pressure on the cylindrical surface.

[0088] S6. Change the size parameters of the two infinitely long rigid cylinders and the distance parameter between the two infinitely long rigid cylinders, and calculate the scattered sound pressure on the surface of the infinitely long rigid cylinder under each parameter with a sonar baffle based on the verified analytical expression of the scattered sound pressure on the surface of the infinitely long rigid cylinder.

[0089] Since the equivalent theoretical model has been simplified to a multiple scattering problem between two infinitely long rigid cylinders in step S2, changing the size of a single infinitely long rigid cylinder in the equivalent theoretical model is equivalent to changing the size of the two infinitely long rigid cylinders in the simplified scattering problem. Similarly, changing the distance between a single infinitely long rigid cylinder and an infinitely large rigid plate in the equivalent theoretical model is equivalent to changing the distance between the two infinitely long rigid cylinders in the simplified scattering problem. Based on this, by changing the size parameters of the two infinitely long rigid cylinders and the distance parameters between them, and using the verified analytical expression for the scattered sound pressure on the cylinder surface, the scattered sound pressure on the surface of the infinitely long rigid cylinder under various parameters with a sonar baffle can be calculated.

[0090] Figure 6 The variation of scattered sound pressure values ​​on the surface of cylinders of different sizes is shown. It can be seen that the size of the cylinder has a significant impact on the distribution of scattered sound pressure on its surface, and this impact covers all azimuth angles. In the area directly illuminated by sound waves (azimuth angle approximately...), The sound pressure amplitude fluctuates relatively little with the radius; while... to The azimuth range exhibits the most intense fluctuations. Within this range, the larger the cylinder's radius, the lower the surface-scattered sound pressure. This is primarily because as the radius increases, the cylinder's area increases accordingly, leading to more destructive interference of sound waves during multiple scattering processes, thus reducing the surface-scattered sound pressure.

[0091] By varying the distance between two infinitely long rigid cylinders, the scattered sound pressure on the surface of the infinitely long rigid cylinders under different parameters with a sonar baffle is calculated. Figure 7 As shown.

[0092] S7. Calculate the scattered sound pressure on the surface of the infinitely long rigid cylinder under various parameters when there is no sonar barrier (i.e., only an infinitely long rigid cylinder). Figure 7 As shown, the details are as follows:

[0093] Suppose a plane wave is incident perpendicularly on an infinitely long rigid cylinder. The scattered field is axis-independent and symmetric with respect to the azimuth angle. Transforming the three-dimensional infinitely long rigid cylinder into a two-dimensional plane circle for analysis, the incident wave can be expanded as follows:

[0094] ;

[0095] in, For Neumann factor, when hour ,when hour ; Let be the distance from the point of incidence to the cylinder. Let be the angle between the point of incidence, the center of the cylinder, and the x-axis. Let be the expression for the incident sound pressure. This is the unfolding form of the incident sound pressure; imaginary unit Power; It is the azimuth function; This is a Bessel function of the first kind. Similar to the case of a sphere, the scattered sound pressure of an infinitely long rigid cylinder should be expressed by a Hankel function of the first kind. The scattered sound pressure on the surface of the infinitely long rigid cylinder under various parameters, without a sonar baffle (i.e., only an infinitely long rigid cylinder), is:

[0096] ;

[0097] in, For scattered sound pressure, For Hankel function, scattering coefficient The boundary conditions on the cylindrical surface determine that for an infinitely long rigid cylinder,

[0098] ;

[0099] ;

[0100] ;

[0101] in, The first derivative of the cylindrical Bessel function; The scattering coefficient can be finally obtained by using the first derivative of the Hankel function and the boundary conditions. Based on the solved scattering coefficient Thus, the scattered sound field on the surface of the infinitely long rigid cylinder under various parameters is obtained when there is no sonar baffle (i.e., there is only one infinitely long rigid cylinder).

[0102] S8. Compare and analyze the scattered sound pressure on the surface of an infinitely long rigid cylinder under various parameters when there is a sonar baffle with the scattered sound pressure on the surface of an infinitely long rigid cylinder under various parameters when there is no sonar baffle (i.e. there is only one infinitely long rigid cylinder), so as to reveal the influence law of the sonar baffle on the sound pressure on the surface of the sonar array.

[0103] In step S8, the scattered sound pressure under different parameters with and without a sonar baffle (i.e., only an infinitely long rigid cylinder) is compared and analyzed to reveal the influence of the baffle on the sound pressure on the sonar array surface. The results of the comparative analysis are as follows: Figure 6 and Figure 7 As shown. Figure 6 The comparison results for different cylinder size parameters are shown. It can be seen that the cylinder size has a significant impact on the surface scattered sound pressure distribution, and this impact covers all azimuth angles. In the area directly irradiated by sound waves (azimuth angle approximately...), The sound pressure amplitude fluctuates relatively little with the radius; while... to The azimuth range exhibits the most intense fluctuations. Within this range, the larger the cylinder's radius, the lower the surface-scattered sound pressure. This is primarily because as the radius increases, the cylinder's area increases accordingly, leading to more destructive interference of sound waves during multiple scattering processes, thus reducing the surface-scattered sound pressure. Figure 7 The comparison results of distance parameters between different cylinders and sonar baffles are presented. It can be seen that the sonar baffle has a significant modulating effect on the scattered sound pressure distribution on the cylinder surface. The main area of ​​the cylinder affected by the sonar baffle is located on the side of the cylinder facing away from the baffle (azimuth angle approximately...). ). Among them, in to Within the azimuth range, the sound pressure amplitude varies most significantly with distance. Within this range, the scattered sound pressure from the cylindrical surface is higher than that without a baffle when the distance is 0.6m and 1m, but decreases when the distance is 1.3m. This may be related to the change in the phase of the scattered wave from the sonar baffle caused by the change in distance. Therefore, in practical design, the change in the phase of the scattered wave caused by the distance to the sonar baffle needs to be considered.

[0104] This invention can accurately calculate the scattered sound pressure on a cylindrical surface affected by a baffle. Furthermore, by changing the cylinder size and the distance between the cylinder and the baffle, the calculation results are compared with those without a baffle. The invention systematically analyzes the effect of the baffle on the scattered sound pressure on the cylindrical surface, thus providing a reliable research basis and theoretical support for evaluating the impact of sonar baffles on sonar array elements in practical engineering.

[0105] The technical solution of this invention first simplifies the sonar baffle and array elements in actual engineering as an infinitely large rigid plate and an infinitely long rigid cylinder, respectively, establishing a "plate-cylinder" theoretical model. Then, using the virtual source method, this model is equivalent to a multiple scattering problem between two rigid cylinders, thereby deriving an analytical solution for the scattered sound pressure on the cylinder surface. This method has a clear physical mechanism and significantly higher computational efficiency than purely numerical methods. To further ensure the engineering reliability of the predictions, this invention further utilizes finite element software to establish a corresponding model for verification. Based on this, the influence of parameters such as baffle size and distance is systematically analyzed, ultimately forming a complete technical solution from theoretical modeling and method verification to parametric analysis and engineering guidance. This provides a reliable tool with both theoretical depth and engineering practicality for the optimized design of sonar baffles.

Claims

1. A method for predicting the impact of sonar baffles on sonar array elements based on the virtual source method, characterized in that, include: Based on the geometric and physical characteristics of actual sonar baffles and sonar array elements, an equivalent theoretical model of an infinitely large rigid plate and an infinitely long rigid cylinder is established. Based on the virtual source method, the scattering problem of the equivalent theoretical model is simplified into a multiple scattering problem between two infinitely long rigid cylinders; Based on the multiple scattering problem between two infinitely long rigid cylinders, an analytical expression for the scattered sound pressure on the surface of an infinitely long rigid cylinder is derived. Boundary conditions are applied to each infinitely long rigid cylinder, and the total sound field of the two infinitely long rigid cylinders is calculated by combining the scattered sound pressure on the surface of the two infinitely long rigid cylinders in the analytical expression. In COMSOL finite element software, a two-dimensional finite element model of two infinitely long rigid cylinders is established to correspond to the multiple scattering problem between two infinitely long rigid cylinders. The two-dimensional finite element model of the two infinitely long rigid cylinders is used to solve the scattered sound pressure on the surface of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders. The calculated sound pressure scattered from the surfaces of two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders were compared with the sound pressure scattered from the surfaces of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders obtained by the model. The comparison results showed that the calculation results of the analytical expression were consistent with the results obtained by the model, thus verifying the correctness of the analytical expression for the sound pressure scattered from the surfaces of infinitely long rigid cylinders. By changing the size parameters of two infinitely long rigid cylinders and the distance parameter between them, the scattered sound pressure on the surface of the infinitely long rigid cylinder is calculated under each parameter with a sonar baffle, based on the verified analytical expression of the scattered sound pressure on the surface of the infinitely long rigid cylinder. Calculate the scattered sound pressure on the surface of an infinitely long rigid cylinder under various parameters without a sonar baffle; By comparing and analyzing the scattered sound pressure on the surface of an infinitely long rigid cylinder with various parameters under different conditions with and without a sonar baffle, the influence of the sonar baffle on the sound pressure on the surface of the sonar array is revealed.

2. The method for predicting the influence of sonar baffles on sonar array elements based on the virtual source method according to claim 1, characterized in that, The equivalent theoretical model for an infinitely large rigid plate and an infinitely long rigid cylinder, established based on the geometric and physical characteristics of actual sonar baffles and sonar array elements, includes: The sonar baffle is simplified into an infinitely large rigid plate, and the sonar array element is simplified into an infinitely long rigid cylinder, thus establishing an equivalent theoretical model of an infinitely large rigid plate-infinitely long rigid cylinder.

3. The method for predicting the influence of sonar baffles on sonar array elements based on the virtual source method according to claim 1, characterized in that, The virtual source method theory simplifies the scattering problem of the equivalent theoretical model into a multiple scattering problem between two infinitely long rigid cylinders, including: According to the virtual source method, an identical infinitely long rigid cylinder is introduced at a symmetrical position on the other side of the infinitely large rigid plate, while the infinitely large rigid plate is removed. This makes the superposition field of the original source and the virtual source satisfy the normal vibration velocity of zero at the plate, thus transforming the scattering problem of the equivalent theoretical model into a multiple scattering problem between two infinitely long rigid cylinders.

4. The method for predicting the influence of sonar baffles on sonar array elements based on the virtual source method according to claim 1, characterized in that, The derivation of the analytical expression for the scattered sound pressure on the surface of an infinitely long rigid cylinder, based on the multiple scattering problem between two infinitely long rigid cylinders, includes: Expanding the incident wave in two infinitely long rigid cylindrical coordinate systems yields expressions for the expansion of the incident wave in the upper cylindrical coordinate system and expressions for the expansion of the incident wave in the lower infinitely long rigid cylindrical coordinate system. Each infinitely long rigid cylinder generates scattered sound pressure after being subjected to an incident sound wave. The analytical expression for the scattered sound pressure on the surface of a single infinitely long rigid cylinder is as follows: ； in, The sound pressure scattered from the surface of an infinitely long rigid cylinder above an infinitely large rigid flat plate; The scattering coefficient is the surface scattering coefficient of an infinitely long rigid cylinder above an infinitely large rigid plate. The sound pressure scattered from the surface of an infinitely long rigid cylinder beneath an infinitely large rigid flat plate; is the scattering coefficient of the infinitely long rigid cylinder surface beneath an infinitely large rigid plate; This is a Hankel function of the first kind.

5. The method for predicting the influence of sonar baffles on sonar array elements based on the virtual source method according to claim 4, characterized in that, The expressions for the expansion of the incident wave in the upper cylindrical coordinate system and the expressions for the expansion of the incident wave in the lower infinitely long rigid cylindrical coordinate system are as follows: ； in, This is the distance between the sound pressure measurement point and the center of the upper circle; The angle between the line connecting the sound pressure measurement point and the center of the upper circle and the horizontal axis; Let be the expression for the expansion of the incident wave in an infinitely long rigid cylindrical coordinate system above; This is the distance between the sound pressure measurement point and the center of the lower circle; The angle between the line connecting the sound pressure measurement point and the center of the lower circle and the horizontal axis; Let be the expression for the expansion of the incident wave in the infinitely long rigid cylindrical coordinate system below; is the base of the natural logarithm; The imaginary unit; The wave number of the incident wave; The angle between the incident sound wave and the x-axis; First order ; It is a Bessel function of the first kind.

6. The method for predicting the influence of sonar baffles on sonar array elements based on the virtual source method according to claim 4, characterized in that, The process involves applying boundary conditions to each infinitely long rigid cylinder, utilizing the boundary conditions combined with the orthogonality of the functions, and combining the analytical expression of the scattered sound pressure from the surfaces of the two infinitely long rigid cylinders to calculate the total sound field of the two infinitely long rigid cylinders, including: Based on the addition theorem, the scattered waves of a cylindrical sonar array are represented in the imaginary source coordinate system as follows: ； in, It is the second order; The distance between the two infinitely long rigid cylinders is half the distance between them. The entire sound field is represented in the actual sonar array coordinate system, and corresponding boundary conditions are applied to each infinitely long rigid cylinder. By utilizing boundary conditions and the orthogonality of functions, and combining this with the analytical expression for the sound pressure scattered from the surface of an infinitely long rigid cylinder, we can obtain the sound pressure scattered from the surface of the infinitely long rigid cylinder above. The sound pressure scattered by the infinitely long rigid cylinder surface below Calculate the total sound field on the surfaces of two infinitely long rigid cylinders. .

7. The method for predicting the influence of sonar baffles on sonar array elements based on the virtual source method according to claim 6, characterized in that, The expression for the boundary condition is: 。 8. The method for predicting the influence of sonar baffles on sonar array elements based on the virtual source method according to claim 6, characterized in that, The total sound field of the two infinitely long rigid cylindrical surfaces The expression is as follows: ； In the formula, This is the incident sound pressure.

9. The method for predicting the influence of a sonar baffle on sonar array elements based on the virtual source method according to claim 1, wherein establishing a two-dimensional finite element model of two infinitely long rigid cylinders in COMSOL finite element software corresponding to the multiple scattering problem between two infinitely long rigid cylinders, and using the two-dimensional finite element model of the two infinitely long rigid cylinders to solve for the scattered sound pressure on the surface of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders, includes: Two identical infinitely long rigid cylinders were constructed in a two-dimensional plane using COMSOL finite element software. A perfectly matched cylindrical layer was used, and a plane wave was incident in a background pressure field. The incident radio frequency and incident angle were set to establish two-dimensional finite element models of the two infinitely long rigid cylinders. The two-dimensional finite element models of the two infinitely long rigid cylinders and the water area were divided into free triangular meshes according to one-sixth of the wavelength. The scattered sound pressure on the surface of the two infinitely long rigid cylinders and the total sound field of the two infinitely long rigid cylinders were calculated using the two-dimensional finite element models of the two infinitely long rigid cylinders.

10. The prediction method for the influence of a sonar baffle on sonar array elements based on the virtual source method according to claim 1, wherein calculating the scattered sound pressure on the surface of an infinitely long rigid cylinder under various parameters without a sonar baffle includes: Suppose a plane wave is incident perpendicularly on an infinitely long rigid cylinder. The scattered field is axis-independent and symmetric with respect to the azimuth angle. Transforming the three-dimensional infinitely long rigid cylinder into a two-dimensional plane circle for analysis, the incident wave expands as follows: ； in, Neumann factor; The distance from the point of incidence to the cylinder; The angle between the point of incidence, the center of the cylinder, and the x-axis; Let be the expression for the incident sound pressure. This is the unfolding form of the incident sound pressure; imaginary unit Power of; It is the azimuth function; For the first type of Bessel function; similar to the case of a sphere, the scattered wave is represented by the first type of Hankel function. The scattered sound pressure on the surface of an infinitely long rigid cylinder under various parameters without a sonar barrier is: ； in, This is the scattered sound pressure; Hankel function; scattering coefficient The boundary conditions on the cylindrical surface determine that for an infinitely long rigid cylinder, ； ； ； in, The first derivative of the cylindrical Bessel function; The first derivative of the Hankel function is used; the scattering coefficient is obtained using boundary conditions. Based on the solved scattering coefficient The formula for calculating the scattered sound pressure on the surface of an infinitely long rigid cylinder is used to solve for the scattered sound field on the surface of the infinitely long rigid cylinder.

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