A method for calculating the strength of an arbitrarily arranged infinite long cylindrical group target

Abstract

The application discloses a kind of infinite long cylinder group target strength calculation method of arbitrary arrangement, comprising: establishing cylinder group, the radius and center coordinates of each cylinder are determined;Determine the first-order scattering expression of each cylinder, and carry out local coordinate system conversion, the first-order scattering expression of each cylinder after conversion is superimposed, and the sound field coupling relationship between each cylinder in cylinder group is obtained;Rigid boundary condition is applied to each cylinder surface in cylinder group, and the first-order scattering coefficient of single cylinder is solved;On the basis of considering multiple scattering effect between cylinders, the first-order scattering coefficient of single cylinder is used to recursively obtain the multi-order scattering coefficient of cylinder group;The scattering sound field of each order of cylinder group is calculated;Each order scattering sound field is superimposed, and the total scattering sound field of cylinder group is obtained;The target strength of cylinder group is calculated.The application can solve the problem that the efficiency of underwater cylinder group structure target strength prediction is lower and modeling is complex in the prior art.

Description

Technical Field

[0001] This invention relates to underwater acoustic engineering technology, specifically to a method for calculating the strength of an infinitely long group of arbitrarily arranged cylinders. Background Technology

[0002] The scattered sound field of underwater targets includes not only mirror-reflected waves, angular waves, and various elastic scattered waves, but also multiple scattered waves caused by complex multi-body structures. For example, the torpedo tubes located in the non-pressure hull of the bow of an underwater vehicle and the vertical tubes in the sail are approximately a cylindrical group structure. When sound waves are transmitted into the outer shell and sail of the underwater vehicle, there is obstruction between the tubes, and multiple scattering occurs, i.e., higher-order scattering effects. Therefore, when calculating the sound scattering characteristics of such structures, it is necessary to consider the multiple scattering of sound waves on the target. Currently, the main methods for calculating the intensity of underwater cylindrical target groups are finite element method and boundary element method, which have low computational efficiency and complex modeling. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a method for calculating the strength of an infinitely long group of arbitrarily arranged cylinders, which can solve the problems of low prediction efficiency and complex modeling of underwater cylinder group structure targets in the prior art.

[0004] Technical solution: The present invention provides a method for calculating the target strength of an arbitrarily arranged group of infinitely long cylinders, comprising:

[0005] Construct a group of cylinders containing multiple parallel cylinders, in which the cylinders are arranged arbitrarily in space, and determine the radius and center coordinates of each cylinder.

[0006] Under plane wave incidence conditions, the first-order scattering expression for each cylinder is determined based on its radius and center coordinates, using Gr... The f-addition theorem transforms the first-order scattering expressions of each cylinder in a local coordinate system, and then superimposes the transformed first-order scattering expressions of each cylinder to obtain the acoustic field coupling relationship between each cylinder in the cylinder group.

[0007] Based on the acoustic field coupling relationship between the cylinders in the cylinder group, rigid boundary conditions are applied to the surface of each cylinder in the cylinder group, and the first-order scattering coefficient of a single cylinder is solved using the rigid boundary conditions.

[0008] Considering the multiple scattering effects between cylinders, the multi-order scattering coefficients of the cylinder group are derived from the first-order scattering coefficient of a single cylinder; the scattering sound fields of the cylinder group at each order are calculated using the recursive expression of the multi-order scattering coefficients of the cylinder group.

[0009] The scattered sound fields of the cylinder group are superimposed to obtain the total scattered sound field of the cylinder group; the target intensity of the cylinder group is calculated using the total scattered sound field of the cylinder group.

[0010] Furthermore, the cylinders in the cylinder group are infinitely long underwater cylinders, and the axes of multiple cylinders are parallel to each other, with multiple cylinders perpendicular to the direction of sound wave propagation.

[0011] Furthermore, the first-order scattering expression for each cylinder is as follows:

[0012] ;

[0013] in, This is a first-order scattered sound field; It is the order; The first-order scattering coefficient; For H nkel function; Wave number; Speed ​​of sound; For the field point and the first The distance between the cylinders; For the field point and the first The included angle of the cylinders; For the first The scattered sound field of a cylinder varies with azimuth angle Its periodic distribution characteristics.

[0014] Furthermore, the Gr The expression for the f-addition theorem is as follows:

[0015] ;

[0016] in, For H nkel function; For Bessel functions; Wave number; Speed ​​of sound; For the first The cylinder points to the first The azimuth of a cylinder; For the first The cylinder and the first The distance between the cylinders; For the field point and the first The included angle of the cylinders; For the field point and the first The distance between the cylinders.

[0017] Furthermore, the expression for the first-order scattering coefficient of the single cylinder is as follows:

[0018] ;

[0019] in, For the first The first-order scattering coefficient of a cylinder; The derivative of the first kind of Bessel function; The derivative of the first kind of Hankel function; Wave number; Speed ​​of sound; For the first The radius of a cylinder.

[0020] Furthermore, the expression for the multi-order scattering coefficients of the cylindrical group is as follows:

[0021] ; in, The scattering order; For the first A cylinder First-order scattering coefficient; This serves as an index for each level in the recursive process of the scattering coefficients; For the first The cylinder numbers that participated in the scattering in the secondary scattering; For the first The cylindrical wave expansion mode order corresponding to the secondary scattering; For the first The cylinder corresponds to the first The scattering coefficient of a single cylinder in one mode; This is a Hankel function of the first kind, with order . The process by which the scattered wave propagates from the previous scattering cylinder and couples to the current cylinder; For the first The center of the cylinder and the first The distance between the centers of the cylinders; Let be the phase factor in multiple scattering, where For the first The center of the cylinder points to the first The azimuth angle of the line connecting the centers of the cylinders; The angle of incidence; The incident wave vector.

[0022] Furthermore, the expressions for the scattered sound fields of the cylindrical group at each order are as follows:

[0023] ;

[0024] in, for Step-scattered sound field; The number of cylinders. These are multi-order scattering coefficients; It is a Hankel function of the first kind; For the field point and the first The distance between the cylinders; Wave number; Speed ​​of sound; For the first The scattered sound field of a cylinder varies with azimuth angle Its periodic distribution characteristics.

[0025] Furthermore, the expression for the total scattered sound field is:

[0026] ;

[0027] in, This represents the total scattered sound field; For the first The cylinder in the first First-order scattering coefficient under cylindrical surface waves; Let be the phase factor, where For the first The angular phase term of the first mode characterizes the distribution of the scattered sound field in the azimuth angle. For position and phase terms, characterizing the first... The incident phase difference of each cylinder relative to the reference point; ; .

[0028] Furthermore, the expression for the target intensity is as follows:

[0029] ;

[0030] in, The target strength.

[0031] Furthermore, the rigid boundary condition is that the sound wave acts on the cylindrical surface, and the normal particle velocity on the cylindrical surface is 0.

[0032] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows:

[0033] (1) The recursive method of multi-order scattering coefficients between cylinders is adopted to solve the technical problem of low prediction efficiency of target intensity of cylinder group, and finally the rapid prediction of target intensity of underwater cylinder group can be realized.

[0034] (2) The acoustic scattering characteristics of the cylinder group can be controlled by changing the number, spacing and arrangement of the cylinders, which can provide theoretical support for the prediction of the acoustic scattering characteristics of underwater multi-body targets. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the process of the present invention;

[0036] Figure 2 This is a schematic diagram of the two-dimensional finite element calculation of the cylindrical group in this invention;

[0037] Figure 3 A comparison diagram of the theoretical solution and finite element results for the target strength of multiple cylindrical composite structures under combined receiving and transmitting conditions;

[0038] Figure 4 A comparison of theoretical solutions and finite element results for the intensity of a group of cylindrical targets at different incident angles under separate transmitting and receiving conditions;

[0039] Figure 5 A comparison of target strength results for different numbers of cylinders;

[0040] Figure 6 A comparison of target strength results with different cylinder spacing;

[0041] Figure 7 Schematic diagrams of two configurations for five cylinders;

[0042] Figure 8 The diagram shows the comparison of the target strength of five cylinders under different configurations. Detailed Implementation

[0043] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0044] like Figure 1 As shown, the present invention provides a method for calculating the target strength of an arbitrarily arranged group of infinitely long cylinders, comprising:

[0045] S1. Establish a cylinder group containing multiple parallel cylinders, in which the cylinders are arbitrarily arranged in space, and determine the radius and center coordinates of each cylinder.

[0046] In step S1, the cylinders in the cylinder group are infinitely long underwater cylinders, and the axes of multiple cylinders are parallel to each other, and multiple cylinders are perpendicular to the direction of sound wave propagation.

[0047] S2. Under plane wave incidence conditions, determine the first-order scattering expression for each cylinder based on its radius and center coordinates, using Gr... The f-addition theorem transforms the first-order scattering expressions of each cylinder in a local coordinate system, and then superimposes the transformed first-order scattering expressions of each cylinder to obtain the acoustic field coupling relationship between the cylinders in the cylinder group.

[0048] In this embodiment, the first-order scattering expression for each cylinder is as follows:

[0049]

[0050] in, This is a first-order scattered sound field; It is the order; The first-order scattering coefficient; For H nkel function; Wave number; Speed ​​of sound; For the field point and the first The distance between the cylinders; For the field point and the first The included angle of the cylinders; For the first The scattered sound field of a cylinder varies with azimuth angle Its periodic distribution characteristics.

[0051] In this embodiment, Gr The expression for the f-addition theorem is as follows:

[0052]

[0053] in, For H nkel function; For Bessel functions; For the first The cylinder points to the first The azimuth of a cylinder; For the first The cylinder and the first The distance between the cylinders; For the field point and the first The included angle of the cylinders; For the field point and the first The distance between the cylinders.

[0054] S3. Based on the acoustic field coupling relationship between the cylinders in the cylinder group, apply rigid boundary conditions to the surface of each cylinder in the cylinder group, and use the rigid boundary conditions to solve for the first-order scattering coefficient of a single cylinder.

[0055] In this embodiment, the rigid boundary condition refers to the situation where the sound wave acts on the surface of the cylinder, and the normal particle velocity on the surface of the cylinder is 0.

[0056] In this embodiment, the expression for the first-order scattering coefficient is as follows:

[0057] ;

[0058] in, For the first The first-order scattering coefficient of a cylinder; The derivative of the first kind of Bessel function; The derivative of the first kind of Hankel function; Wave number; Speed ​​of sound; For the first The radius of a cylinder.

[0059] S4. Considering the multiple scattering effects between cylinders, the multi-order scattering coefficients of the cylinder group are derived from the first-order scattering coefficient of a single cylinder; the scattering sound fields of the cylinder group are calculated using the recursive expressions of the multi-order scattering coefficients of the cylinder group.

[0060] In this embodiment, the scattering coefficients of each order are obtained recursively from the previous order scattering coefficient, thus forming a recursive calculation relationship for higher-order scattering coefficients. The expression for the multi-order scattering coefficients of the cylinder group is as follows:

[0061] ;

[0062] in, The scattering order; For the first The m-th order scattering coefficient of a cylinder; This serves as an index for each level in the recursive process of the scattering coefficients; For the first The cylinder numbers that participated in the scattering in the secondary scattering; For the first The cylindrical wave expansion mode order corresponding to the secondary scattering; For the first The cylinder corresponds to the first The scattering coefficient of a single cylinder in one mode; This is a Hankel function of the first kind, with order . The process by which the scattered wave propagates from the previous scattering cylinder and couples to the current cylinder; For the first The center of the cylinder and the first The distance between the centers of the cylinders; Let be the phase factor in multiple scattering, where For the first The center of the cylinder points to the first The azimuth angle of the line connecting the centers of the cylinders; The angle of incidence; The incident wave vector.

[0063] In this embodiment, the expressions for the scattered sound fields of the cylindrical group at each order are as follows:

[0064]

[0065] in, for Step-scattered sound field; The number of cylinders; These are multi-order scattering coefficients; It is a Hankel function of the first kind; For the field point and the first The distance between the cylinders; Wave number; Speed ​​of sound; For the first The scattered sound field of a cylinder varies with azimuth angle Its periodic distribution characteristics.

[0066] S5. Superimpose the scattered sound fields of each order of the cylinder group to obtain the total scattered sound field of the cylinder group; use the total scattered sound field of the cylinder group to calculate the target intensity of the cylinder group.

[0067] In this embodiment, the total scattered sound field is obtained by linearly superimposing the scattered sound fields of each order, and its expression is:

[0068] ;

[0069] in, This represents the total scattered sound field; For the first The cylinder in the first First-order scattering coefficient under cylindrical surface waves; Let be the phase factor, where For the first The angular phase term of the first mode characterizes the distribution of the scattered sound field in the azimuth angle. For position and phase terms, characterizing the first... The incident phase difference of each cylinder relative to the reference point; The scattering order; ; .

[0070] In this embodiment, the expression for the target intensity is as follows:

[0071] ;

[0072] in, The target strength.

[0073] This invention addresses the problems of multiple scattering coupling and complex sound field calculations in multi-cylinder composite structures under arbitrary spatial arrangements. Based on Gr... The f-addition theorem enables the transformation of the sound field between different local coordinate systems of the cylinders, establishes the recursive relationship of the scattering coefficients of each order of the cylinder group, and obtains the target intensity of the cylinder group by superimposing the scattered sound fields of each order. By determining the radius and center coordinates of each cylinder, a rapid prediction of the target intensity of the cylinder group can be achieved. This invention has good computational accuracy and provides theoretical support for the prediction of the acoustic scattering characteristics of complex underwater multi-body targets.

[0074] This invention employs the idea of ​​recursion of higher-order scattering coefficients to determine the center coordinates of each cylinder. Based on the Graf addition theorem, it realizes the sound field transformation between different local coordinate systems of cylinders. Each order scattering coefficient is obtained by recursion of the previous order scattering coefficient, thus deriving the recursive expression of higher-order scattering coefficients. This not only solves the problem of modeling difficulties but also improves the speed of underwater cylinder group target intensity prediction.

[0075] The effectiveness of the present invention will be verified through two examples below.

[0076] Example 1:

[0077] When the frequency of the sound wave is The sound field medium is water, and the sound waves are perpendicular to the axis of each cylinder, such as... Figure 2 As shown. Figure 2 This is a schematic diagram for calculation. Figure 2 It includes a perfectly matched layer 1, a sound field domain 2, and a rigid cylinder 3. The sound field domain is used to calculate the scattered sound field of the rigid cylinder, and the perfectly matched layer absorbs the sound wave reflections at the boundary of the sound field domain. For each cylinder radius; This represents the spacing between the cylinders. The radius of each cylinder is... All are 0.026m; cylinder spacing The angle of incidence of the sound wave is 0.106m. for Step size is The finite element simulation results are compared with the theoretical solutions. Figure 3 The results of combinations of four, five, six, and eight cylinders were compared, and it can be seen that the finite element results and the theoretical solutions are in good agreement. Therefore, the method can quickly predict the target intensity under the condition of combined transmission and reception of cylinder groups. Figure 3 (in) The figure shows a comparison between the theoretical solution and the finite element method results for the target strength of the four cylindrical composite structure under the combined transmitting and receiving configuration. Figure 3 Figure (b) shows a comparison between the theoretical solution and the finite element results for the target strength of the four cylindrical combined structure under the combined receiving and transmitting conditions; Figure 3 Figure (c) shows a comparison between the theoretical solution and the finite element results for the target strength of the four cylindrical combined structure under the combined receiving and transmitting conditions; Figure 3 Figure (d) in the figure shows a comparison between the theoretical solution and the finite element results of the target strength of the four cylindrical combined structure under the combined receiving and transmitting conditions.

[0078] Example 2:

[0079] When the frequency of the sound wave is The sound field medium is water, and the sound waves are perpendicular to the axis of each cylinder, such as... Figure 2 As shown. Figure 2 This is a schematic diagram for calculation. Figure 2It includes a perfectly matched layer 1, a sound field domain 2, and a rigid cylinder 3. The sound field domain is used to calculate the scattered sound field of the rigid cylinder, and the perfectly matched layer absorbs the sound wave reflections at the boundary of the sound field domain. For each cylinder radius; This represents the spacing between the cylinders. The radius of each cylinder is... All are 0.129m; cylinder spacing The angle of incidence of the sound wave is 0.524m. They are respectively , , as well as Receiving angle Step size is The finite element simulation results are compared with the theoretical solutions. Figure 4 The results show a comparison of the target strength of the eight cylindrical composite structures with separate transmitting and receiving points. It can be seen that the finite element results and the theoretical solutions are in good agreement. Therefore, the method described can quickly predict the target strength under the condition of separate transmitting and receiving points for a group of cylinders. Figure 4 (in) The figure shows the incident angle under separate transmitting and receiving configurations. Comparison of theoretical solutions and finite element results for the target strength of a group of cylinders; Figure 4 Figure (b) shows the incident angle under separate transmitting and receiving configurations. Comparison of theoretical solutions and finite element results for the target strength of a group of cylinders; Figure 4 Figure (c) shows the incident angle under separate transmission and reception configuration. Comparison of theoretical solutions and finite element results for the target strength of a group of cylinders; Figure 4 Figure (d) shows the incident angle under separate transmission and reception configuration. Comparison of theoretical solutions and finite element results for the target strength of a group of cylinders.

[0080] Example 3:

[0081] When the frequency of the sound wave is The sound field medium is water, and the sound waves are perpendicular to the axis of each cylinder, such as... Figure 2 As shown. Figure 2 This is a schematic diagram for calculation. Figure 2 It includes a perfectly matched layer 1, a sound field domain 2, and a rigid cylinder 3. The sound field domain is used to calculate the scattered sound field of the rigid cylinder, and the perfectly matched layer absorbs the sound wave reflections at the boundary of the sound field domain. For each cylinder radius; Let be the spacing between the cylinders. Calculate the target strength for four, five, six, and eight cylinders respectively, given the radius of each cylinder. All are 0.026m; cylinder spacing The angle of incidence of the sound wave is 0.106m. for Step size is . Figure 5 The results show the comparison of different numbers of cylinders, thus the method can analyze the acoustic scattering characteristics of cylinders with different numbers of cylinders.

[0082] Example 4:

[0083] When the frequency of the sound wave is The sound field medium is water, and the sound waves are perpendicular to the axis of each cylinder, such as... Figure 2 As shown, Figure 2 This is a schematic diagram for calculation. Figure 2 It includes a perfectly matched layer 1, a sound field domain 2, and a rigid cylinder 3. The sound field domain is used to calculate the scattered sound field of the rigid cylinder, and the perfectly matched layer absorbs the sound wave reflections at the boundary of the sound field domain. For each cylinder radius; The distance between the cylinders is used to calculate the target strength for different numbers of cylinders. Taking five cylinders as an example, the position of the central cylinder remains unchanged, while the distance between the other four cylinders is... The incident angles of the sound waves are 0.106m, 0.125m, 0.144m, and 0.163m, respectively. for Step size is . Figure 6 The results show the target intensity comparison for different cylinder spacings, thus the method described can analyze the acoustic scattering characteristics of different cylinder spacings.

[0084] Example 5:

[0085] When the frequency of the sound wave is The sound field medium is water, and the sound waves are perpendicular to the axis of each cylinder, such as... Figure 2 As shown, Figure 2 This is a schematic diagram for calculation. Figure 2 It includes a perfectly matched layer 1, a sound field domain 2, and a rigid cylinder 3. The sound field domain is used to calculate the scattered sound field of the rigid cylinder, and the perfectly matched layer absorbs the sound wave reflections at the boundary of the sound field domain. Let be the radius of each cylinder; 2b be the spacing between the cylinders. Calculate the target strength for different cylinder configurations. Figure 7 (in) The figure shows configuration one. The value is 0.0528 for 2b and 10.97 for 2b. Figure 7 Figure (b) shows configuration two. It is 10.97. Figure 8 The results show the target intensity comparison for different cylindrical configurations, thus the method described can analyze the acoustic scattering characteristics of different cylindrical configurations.

[0086] As can be seen from Examples 3-5, the present invention can control the acoustic scattering characteristics of a group of cylinders by changing the number, spacing and arrangement of the cylinders, which can provide theoretical support for the prediction of the acoustic scattering characteristics of underwater multi-body targets.

Claims

1. A method for calculating the strength of an infinitely long group of arbitrarily arranged cylinders, characterized in that, include: Construct a group of cylinders containing multiple parallel cylinders, in which the cylinders are arranged arbitrarily in space, and determine the radius and center coordinates of each cylinder. Under plane wave incidence conditions, the first-order scattering expression for each cylinder is determined based on its radius and center coordinates, using Gr... The f-addition theorem transforms the first-order scattering expressions of each cylinder in a local coordinate system, and then superimposes the transformed first-order scattering expressions of each cylinder to obtain the acoustic field coupling relationship between each cylinder in the cylinder group. Based on the acoustic field coupling relationship between the cylinders in the cylinder group, rigid boundary conditions are applied to the surface of each cylinder in the cylinder group, and the first-order scattering coefficient of a single cylinder is solved using the rigid boundary conditions. Considering the multiple scattering effects between cylinders, the multi-order scattering coefficients of the cylinder group are derived from the first-order scattering coefficient of a single cylinder; the scattering sound fields of the cylinder group at each order are calculated using the recursive expression of the multi-order scattering coefficients of the cylinder group. The scattered sound fields of the cylinder group are superimposed to obtain the total scattered sound field of the cylinder group; the target intensity of the cylinder group is calculated using the total scattered sound field of the cylinder group.

2. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that: The cylinders in the group of cylinders are infinitely long underwater cylinders, and the axes of multiple cylinders are parallel to each other, with multiple cylinders perpendicular to the direction of sound wave propagation.

3. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that, The first-order scattering expressions for each cylinder are as follows: ； in, This is a first-order scattered sound field; It is the order; The first-order scattering coefficient; For H nkel function; Wave number; Speed ​​of sound; For the field point and the first The distance between the cylinders; For the field point and the first The included angle of the cylinders; For the first The scattered sound field of a cylinder varies with azimuth angle Its periodic distribution characteristics.

4. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that, The Gr The expression for the f-addition theorem is as follows: ； in, For H nkel function; For Bessel functions; Wave number; Speed ​​of sound; For the first The cylinder points to the first The azimuth of a cylinder; For the first The cylinder and the first The distance between the cylinders; For the field point and the first The included angle of the cylinders; For the field point and the first The distance between the cylinders.

5. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that, The expression for the first-order scattering coefficient of the single cylinder is as follows: ； in, For the first The first-order scattering coefficient of a cylinder; The derivative of the first kind of Bessel function; The derivative of the first kind of Hankel function; Wave number; Speed ​​of sound; For the first The radius of a cylinder.

6. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that, The expression for the multi-order scattering coefficients of the cylindrical group is as follows: ； in, The scattering order; For the first The m-th order scattering coefficient of a cylinder; This serves as an index for each level in the recursive process of the scattering coefficients; For the first The cylinder numbers that participated in the scattering in the secondary scattering; For the first The cylindrical wave expansion mode order corresponding to the secondary scattering; For the first The cylinder corresponds to the first The scattering coefficient of a single cylinder in one mode; This is a Hankel function of the first kind, with order . The process by which the scattered wave propagates from the previous scattering cylinder and couples to the current cylinder; For the first The center of the cylinder and the first The distance between the centers of the cylinders; Let be the phase factor in multiple scattering, where For the first The center of the cylinder points to the first The azimuth angle of the line connecting the centers of the cylinders; The angle of incidence; The incident wave vector.

7. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that, The expressions for the scattered sound fields of the cylindrical group are as follows: ； in, for Step-scattered sound field; The number of cylinders; These are multi-order scattering coefficients; It is a Hankel function of the first kind; For the field point and the first The distance between the cylinders; Wave number; Speed ​​of sound; For the first The scattered sound field of a cylinder varies with azimuth angle Its periodic distribution characteristics.

8. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that, The expression for the total scattered sound field is: ； in, This represents the total scattered sound field; For the first The cylinder in the first First-order scattering coefficient under cylindrical surface waves; Let be the phase factor, where For the first The angular phase term of the first mode characterizes the distribution of the scattered sound field in the azimuth angle. For position and phase terms, characterizing the first... The incident phase difference of each cylinder relative to the reference point; ; .

9. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that, The expression for the target intensity is as follows: ； in, The target strength.

10. The method for calculating the target strength of an infinitely long group of arbitrarily arranged cylinders according to claim 1, characterized in that: The rigid boundary condition is that the sound wave acts on the surface of the cylinder, and the normal particle velocity on the surface of the cylinder is 0.

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