Multi-layer structure separated and integrated underwater target vibration sound radiation calculation method
By dividing the underwater target into the main hull and multi-layer subsystems, using multiple methods to construct dynamic equations and integrate coupling, the accuracy and efficiency problems of vibration and acoustic radiation calculations of complex underwater targets are solved, and efficient calculation and accurate simulation in a wide frequency band are achieved.
Patent Information
- Application Number
- CN202510945538.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-09
- Publication Date
- 2025-10-10
AI Technical Summary
Existing technologies have difficulty in accurately calculating the vibration and acoustic radiation of underwater targets containing complex vibration isolators, resulting in low calculation accuracy, which affects the accuracy and reliability of the assessment.
The underwater target is divided into the main hull and multi-layer subsystems. The dynamic equations are constructed using analytical methods, numerical methods and experimental testing methods respectively. The overall structural dynamic equations are obtained through integrated coupling, and the calculations are performed in combination with virtual modes and matrix rearrangement technology.
It improves the accuracy and efficiency of vibration and acoustic radiation calculations of underwater targets with complex structures, supports wide-band calculations, achieves accurate simulation of vibration isolators, and enhances the practical value of engineering.
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Abstract
Description
Technical Field
[0001] The present application relates to the field of underwater target vibration and acoustic radiation calculation, and in particular to a method for calculating underwater target vibration and acoustic radiation with multi-layer structure separation and integration. Background Art
[0002] Vibration acoustic radiation is an important performance indicator of underwater targets, which directly determines their concealment and safety. At the same time, its radiation noise will also interfere with the operating accuracy of underwater target detection and navigation systems. Therefore, it is of great significance to conduct research on the vibration acoustic radiation characteristics of underwater targets.
[0003] In 2002, Marsick began to study the vibration and acoustic radiation problem of underwater targets using analytical methods. However, due to the limitations of analytical methods, it is generally only used for cylindrical shells, spherical shells, conical shells and composite structures. However, the underwater target structure in actual engineering applications is complex, usually including the main hull and a large number of internal structures, and the internal structures are assembled through vibration isolators. When using numerical methods to calculate the vibration and acoustic radiation of underwater targets containing vibration isolation structures, there are problems that large-scale structures and complex small-scale structures are difficult to model and calculate: (1) The main hull of the underwater target is the most representative large-scale structure, and its geometric form is relatively simple. However, since its size is much larger than that of the internal structure, if the main hull and the internal structure have the same grid size, the number of units required for convergence of calculation accuracy will be too large. (2) The vibration isolator in the underwater target is a typical complex small-scale structure. In particular, the optimization design research of new vibration isolators has produced a lot of results in recent years, such as filling the vibration isolator with solid-liquid mixed materials, using nonlinear vibration isolators, and using the vibration isolator in parallel with the vibration absorber. These innovative vibration isolator designs have further increased the difficulty of modeling and calculation. When calculating the vibration isolation effectiveness of new isolators, the complex design and densely packed units make it difficult to accurately reflect the physical properties of the isolators. These limitations result in low numerical accuracy for calculating the vibration and acoustic radiation of underwater targets, impacting the accuracy and reliability of the assessment of their performance. Summary of the Invention
[0004] In response to the above-mentioned problems and technical requirements, this application proposes a method for calculating the vibration and acoustic radiation of underwater targets with a multi-layer structure separation and integration. The technical solution of this application is as follows:
[0005] A method for calculating the vibration and acoustic radiation of an underwater target with a multi-layer structure separation and integration, the method comprising:
[0006] Based on the vibration transmission path, the underwater target is divided into the main hull and n-layer subsystems. Each subsystem consists of several non-connected structures inside the hull. The first subsystem is directly connected to the main hull, and the j-th subsystem is connected to the j+1-th subsystem through the j-th vibration isolator. Among them, the integer parameter n ≥ 2, the integer parameter 1 ≤ j ≤ n-1;
[0007] The dynamic equations of the main hull are constructed based on analytical methods, the dynamic equations of each subsystem are constructed based on numerical methods, and the dynamic equations of each layer of vibration isolators are constructed based on experimental test methods.
[0008] The dynamic equations of the main hull, the dynamic equations of each layer of subsystems, and the dynamic equations of each layer of vibration isolators are integrated and coupled to obtain the overall structural dynamic equations. The vibration and acoustic radiation calculation results of the underwater target are obtained by solving the overall structural dynamic equations.
[0009] Its further technical solution obtains the overall structural dynamic equation including:
[0010] For any two directly connected structures among the main hull, each layer of subsystems, and each layer of vibration isolators, the dynamic equations of the main hull, the dynamic equations of each layer of subsystems, and the dynamic equations of each layer of vibration isolators are integrated and coupled in combination with matrix rearrangement transformation technology based on the displacement continuity conditions of the connection point between the two structures and the relationship between the excitation force and the reaction force to obtain the dynamic equation of the overall structure.
[0011] Its further technical solution is to construct the main hull dynamic equation based on analytical method, including:
[0012] The analytical method is used to construct the coupled vibration equations of the main hull and water and the virtual modes of the main hull are introduced to obtain the expanded dynamic equations of the main hull.
[0013] Its further technical solution, the expanded main hull dynamic equation is:
[0014]
[0015] Among them, Z A represents the generalized dynamic stiffness matrix and Z A =-ω 2 M A +K A , M A is the generalized mass matrix of the main hull considering the attached water mass, K A is the generalized stiffness matrix of the main hull, ω represents the excitation frequency; F A1 is the column vector of the external excitation force applied to the cylindrical shell, F A2 is the force column vector of the connection point between the main hull and the first layer subsystem, It is H A The transposed matrix, H A Represents the vibration mode matrix corresponding to the main hull excitation point and connection point H A1 Corresponding to the point of action of the excitation force outside the main ship, H A2Corresponding to the connection point between the main hull and the first layer subsystem; η is the generalized coordinate of the main hull, η v is the virtual modal generalized coordinate, Z V =I.
[0016] A further technical solution thereof is to construct the dynamic equation of the i-th layer subsystem based on a numerical method for any integer parameter 1≤i≤n, including:
[0017] The modal condensation dynamic stiffness matrix of the i-th layer subsystem is obtained by using finite element modal analysis and modal synthesis super-element method, and the dynamic equation of the i-th layer subsystem is constructed to characterize the relationship between the modal condensation dynamic stiffness matrix, displacement matrix and excitation matrix of the i-th layer subsystem.
[0018] Among them, the displacement matrix of the i-th layer subsystem includes the displacement of the calculation point of the i-th layer subsystem and the displacement of the connection point between the i-th layer subsystem and the adjacent structure, and the excitation matrix of the i-th layer subsystem includes the excitation of the calculation point of the i-th layer subsystem and the excitation of the connection point between the i-th layer subsystem and the adjacent structure.
[0019] Its further technical solution, based on the experimental test method, constructs the dynamic equations of each layer of vibration isolators including:
[0020] Based on the experimental test method, the impedance test results of the j-th layer vibration isolator are obtained, and based on the impedance test results, the dynamic stiffness matrix of the j-th layer vibration isolator is obtained by using the four-terminal network parameter method through the degree of freedom change. The dynamic equation of the j-th layer vibration isolator is constructed to characterize the relationship between the dynamic stiffness matrix, displacement matrix and excitation matrix of the j-th layer vibration isolator;
[0021] The displacement matrix of the j-th vibration isolator includes the displacements of the connection points between the j-th vibration isolator and the j-th subsystem and the j+1-th subsystem, and the excitation matrix of the j-th vibration isolator includes the excitations of the connection points between the j-th vibration isolator and the j-th subsystem and the j+1-th subsystem.
[0022] Its further technical solution,
[0023] (1) When 1≤i≤n-1, the dynamic equation of the constructed i-th layer subsystem is:
[0024]
[0025] Among them, when i=1, and They represent the displacement and excitation of the connection point between the first layer subsystem and the main hull, respectively. When i≥2, and denote the displacement and excitation of the connection point between the i-th layer subsystem and the i-1-th layer isolator, respectively; and denote the displacement and excitation of the calculation point of the i-th layer subsystem, respectively. and denote the displacement and excitation of the connection point between the ith layer subsystem and the ith layer isolator, respectively; is the modal condensed dynamic stiffness matrix of the i-th layer subsystem;
[0026] (2) When i = n, the dynamic equation of the constructed n-th layer subsystem is:
[0027]
[0028] in, and denote the displacement and excitation of the connection point between the nth layer subsystem and the n-1th layer isolator, respectively. and represent the displacement and excitation of the calculation point of the n-th layer subsystem, is the modal condensed dynamic stiffness matrix of the n-th layer subsystem.
[0029] In a further technical solution, the dynamic equation of the j-th layer vibration isolator is:
[0030]
[0031] in, and denote the displacement and excitation of the connection point between the j-th layer isolator and the j-th layer subsystem respectively; and denote the displacement and excitation of the connection point between the jth layer isolator and the j+1th layer subsystem respectively; represents the dynamic stiffness matrix of the j-th layer of vibration isolators.
[0032] Its further technical solution, the underwater target vibration acoustic radiation calculation method includes:
[0033] Determine the connection point between the j-th layer isolator and the j-th layer subsystem to meet the displacement continuity condition: And the relationship between force and reaction force Determine that the connection point between the jth layer isolator and the j+1th layer subsystem satisfies the displacement continuity condition: And the relationship between force and reaction force Determine the relationship between the force and reaction force at the connection between the main hull and the first layer subsystem
[0034] Its further technical solution, the overall structural dynamic equation obtained is:
[0035]
[0036] in, is the identity matrix; H A represents the displacement mode matrix of the selected point on the main hull in the cylindrical shell coordinate system and H A1 Corresponding to the point of action of the excitation force outside the main ship, H A2 Each point corresponds to the connection point between the main hull and the foundation, and has five degrees of freedom.
[0037] The beneficial technical effects of this application are:
[0038] The present application discloses a method for calculating the vibration and acoustic radiation of underwater targets with multi-layer structure separation and integration. The method divides underwater targets with complex structures into multiple layers according to the position of the vibration transmission path, and solves the main hull using an analytical method according to the structural characteristics of the main hull, sub-layers and vibration isolators. The virtual modal method is used to couple the "water-hull" analytical results and the internal structure numerical solution. The modal synthesis super element method is used to numerically solve the non-connected structures inside the main hull (such as rafts, bases, etc.), and a rearrangement transformation is performed on this basis to facilitate the integrated coupling with the analytical solution and experimental test results. The vibration isolator adopts a four-terminal parameter method to convert impedance-dynamic stiffness to facilitate the coupling of the analytical solution and the numerical solution. Finally, the vibration and acoustic radiation results of the underwater target are obtained through the multi-layer structure integration method. This method solves the problem of the difficulty in matching calculation accuracy and calculation efficiency for the modeling and calculation of underwater targets with complex structures, realizes the efficient calculation of the acoustic radiation of underwater targets with vibration isolation systems, and improves the calculation accuracy of the vibration and acoustic radiation of underwater targets with complex structures.
[0039] This method is highly flexible in terms of spatial location and installation, based on the vibration transmission path, and supports the integrated coupling of multiple methods. The calculation frequency range can cover several thousand hertz, significantly improving the applicability of wide-band calculations compared to the bottleneck of purely numerical methods, which often limit the calculation frequency range. Furthermore, this method eliminates the need to simplify the isolator to an ideal spring model during calculations. Instead, it can use dynamic stiffness matrix data obtained from experimental testing as input for accurate simulation, significantly enhancing the method's practical engineering value. BRIEF DESCRIPTION OF THE DRAWINGS
[0040] Figure 1 It is a flowchart of a method for calculating underwater target vibration acoustic radiation according to an embodiment of the present application.
[0041] Figure 2 This is a schematic diagram of the structural division of underwater targets in an example.
[0042] Figure 3 This is a comparison chart of the line spectrum calculation results using the integrated method of the present application and the traditional numerical method in an example.
[0043] Figure 4 yes Figure 3 The 1 / 3 octave spectrum calculation results of the integrated method and the conventional numerical method in the example are compared respectively. DETAILED DESCRIPTION
[0044] The specific embodiments of the present application are further described below with reference to the accompanying drawings.
[0045] The present application discloses a multi-layer structure separation integrated underwater target vibration sound radiation calculation method. The underwater target to which the present application is directed contains a complex structure, which includes a main hull and its internal structure. The main hull structure is relatively simple but has large-scale characteristics, and the internal structure of the main hull can be divided into two types: non-connected structure and connected structure. The non-connected structure is the main structure of the underwater target used for optimizing vibration sound radiation design, and common examples include pontoons and pedestals. The connected structure is relatively complex but small in size, and is mainly a vibration isolator.
[0046] The underwater target vibration sound radiation calculation method includes the following steps, please refer to Figure 1 the flowchart shown in the figure:
[0047] Step 110, according to the vibration transmission path, the underwater target containing a complex structure is divided into three different types of structures: a main hull, n-layer subsystems, and vibration isolators between the subsystems. Each layer of the subsystem includes several non-connected structures inside the hull. The first layer of the subsystem is directly connected to the main hull, and the jth layer of the subsystem is connected to the j+1th layer of the subsystem through the jth layer of the vibration isolator. Wherein, the integer parameter n≥2, and the integer parameter 1≤j≤n-1.
[0048] For example, in one example, the underwater target is as shown in Figure 2 According to the vibration transmission path, the underwater target is divided into a main hull 200, a first layer of subsystem 211, a first layer of vibration isolator 221, a second layer of subsystem 212, a second layer of vibration isolator 222, a third layer of subsystem 213, a third layer of vibration isolator 223, and a fourth layer of subsystem 214.
[0049] The division method adopted by the present application is based on the vibration transmission path, so the equipment directly installed on the pontoon or suspended on the intermediate pontoon connected to the pontoon is allowed to participate in the modeling calculation, and the spatial position and installation method are very flexible.
[0050] Step 120, based on the analytical method, the dynamic equation of the main hull is constructed, based on the numerical method, the dynamic equation of each layer of the subsystem is constructed, and based on the test method, the dynamic equation of each layer of the vibration isolator is constructed;
[0051] The above step 110 has separated the underwater target into three different types of structures according to their different structural forms. These three different types of structures have their own characteristics. In order to improve the calculation accuracy, each structure is first solved independently using different methods according to its own characteristics.
[0052] Each subsystem can be directly solved using numerical methods, so the dynamic equations for each subsystem are constructed directly based on numerical methods. However, the main hull is a large-scale structure that is difficult to model and calculate. This application uses analytical methods to calculate the main hull's structural characteristics. The vibration isolator is a complex small-scale structure that is also difficult to model and calculate. This application uses experimental testing methods to calculate the vibration isolator's structural characteristics.
[0053] (1) Main hull
[0054] The analytical method is used to construct the coupled vibration equations of the main hull and water and introduce the virtual mode of the main hull to obtain the expanded dynamic equations of the main hull. This makes it possible to use the virtual mode method to couple the "water-hull" analytical results and the internal structure numerical solution. The expanded dynamic equations of the main hull are:
[0055]
[0056] Among them, Z A represents the generalized dynamic stiffness matrix and Z A =-ω 2 M A +K A , M A is the generalized mass matrix of the main hull considering the attached water mass, K A is the generalized stiffness matrix of the main hull, and ω represents the excitation frequency. A1 is the column vector of the external excitation force applied to the cylindrical shell, F A2 is the column vector of the force acting on the connection point between the main hull and the first layer subsystem. It is H A The transposed matrix, H A Represents the vibration mode matrix corresponding to the main hull excitation point and connection point H A1 Corresponding to the point of action of the excitation force outside the main ship, H A2 Corresponds to the connection point between the main hull and the first layer subsystem. η is the generalized coordinate of the main hull, η v is the generalized coordinate of the virtual mode. The virtual mode itself can be defined, taking Z V =I, so we can get the virtual modal generalized coordinate η v and the relationship between the generalized coordinates η of the main hull.
[0057] In this paper, the analytical calculation model of the main hull is established by thin shell theory. There are only five effective degrees of freedom at each point on the cylindrical shell, and there is no in-plane rotation freedom. When the subsystem is modeled by shell elements, each node has six degrees of freedom (in theory, the node of the shell element has only five degrees of freedom, but the shell element in the finite element software often expands an in-plane rotation freedom, which has little effect on the stiffness matrix and mass matrix of the element).
[0058] (2) Each layer subsystem
[0059] For any integer parameter 1≤i≤n, the dynamic equation of the i-th layer subsystem is constructed based on numerical methods, including: obtaining the modal condensed dynamic stiffness matrix of the i-th layer subsystem by using the finite element modal analysis and modal synthesis super-element method. Then the dynamic equation of the i-th layer subsystem can be constructed, which represents the relationship between the modal condensed dynamic stiffness matrix, displacement matrix and excitation matrix of the i-th layer subsystem. Among them, the displacement matrix of the i-th layer subsystem includes the displacement of the calculation points of the i-th layer subsystem and the displacement of the connecting points between the i-th layer subsystem and the adjacent structure, and the excitation matrix of the i-th layer subsystem includes the excitation of the calculation points of the i-th layer subsystem and the excitation of the connecting points between the i-th layer subsystem and the adjacent structure.
[0060] When 1≤i≤n-1, the dynamic equation of the i-th layer subsystem constructed can be expressed as:
[0061]
[0062] When i=1, and respectively represent the displacement and excitation of the connecting points between the first layer subsystem and the main hull, and when i≥2, and respectively represent the displacement and excitation of the connecting points between the i-th layer subsystem and the i-1-th layer isolator. and respectively represent the displacement and excitation of the calculation points of the i-th layer subsystem. and respectively represent the displacement and excitation of the connecting points between the i-th layer subsystem and the i-th layer isolator. is the modal condensed dynamic stiffness matrix of the i-th layer subsystem;
[0063] When i=n, the dynamic equation of the n-th layer subsystem constructed is:
[0064]
[0065] Among them, and They represent the displacement and excitation of the connection point between the nth layer subsystem and the n-1th layer isolator, respectively. and They represent the displacement and excitation of the calculation point of the n-th layer subsystem respectively. is the modal condensed dynamic stiffness matrix of the n-th layer subsystem.
[0066] (3) Vibration isolators on each layer
[0067] In addition to the main structure of the hull, accurate modeling and calculation of vibration isolators are also crucial for evaluating and calculating the structural vibration and acoustic radiation. However, due to the complex structure of vibration isolators, numerical methods are not easily applicable. Therefore, based on experimental testing methods, the impedance test results of the j-th layer vibration isolator are obtained. Based on these impedance test results, the dynamic stiffness matrix of the j-th layer vibration isolator is calculated by varying the degrees of freedom using a four-terminal network parameter method. The dynamic equations for the j-th layer vibration isolator are then constructed. These dynamic equations characterize the relationship between the dynamic stiffness matrix, displacement matrix, and excitation matrix of the j-th layer vibration isolator. The displacement matrix of the j-th layer vibration isolator includes the displacements at the connection points between the j-th layer vibration isolator and the j-th layer subsystem and the j+1-th layer subsystem, respectively. The excitation matrix of the j-th layer vibration isolator includes the excitations at the connection points between the j-th layer vibration isolator and the j-th layer subsystem and the j+1-th layer subsystem, respectively.
[0068] For integer parameters 1≤j≤n-1, the dynamic equation of the j-th layer isolator is expressed as:
[0069]
[0070] in, and denote the displacement and excitation of the connection point between the j-th layer isolator and the j-th layer subsystem, respectively. and denote the displacement and excitation of the connection point between the jth layer isolator and the j+1th layer subsystem, respectively. represents the dynamic stiffness matrix of the j-th layer of vibration isolators.
[0071] Step 130, the above step 120 separates the structure of the underwater target and solves it separately. This step requires the integration and assembly of various structures, that is, the dynamic equations of the main hull, the dynamic equations of each layer of subsystems, and the dynamic equations of each layer of vibration isolators are integrated and coupled to obtain the overall structural dynamic equation. Finally, the overall structural dynamic equation is solved to obtain the vibration and acoustic radiation calculation results of the underwater target.
[0072] During collective coupling, for any two directly connected structures among the main hull, each layer of subsystems, and each layer of vibration isolators, the dynamic equations of the main hull, the dynamic equations of each layer of subsystems, and the dynamic equations of each layer of vibration isolators are integrated and coupled based on the displacement continuity conditions of the connection point between the two structures and the relationship between the excitation force and the reaction force, combined with the matrix rearrangement transformation technology.
[0073] If any j-th layer vibration isolator is directly connected to the j-th layer subsystem and the j+1-th layer subsystem respectively, then the connection point between the j-th layer vibration isolator and the j-th layer subsystem satisfies the displacement continuity condition as follows: and the relationship between force and reaction force The connection point between the jth layer isolator and the j+1th layer subsystem satisfies the displacement continuity condition as follows: and the relationship between force and reaction force
[0074] In addition, the relationship between the force and reaction force at the connection between the main hull and the first layer subsystem is {F A2}=-{F B2}, substituting into (1) we have Among them, I1 and I2 are both unit matrices.
[0075] From this, the overall structural dynamic equation can be obtained by combining formulas (1) to (4):
[0076]
[0077] in, is the identity matrix; H A represents the displacement mode matrix of the selected point in the cylindrical shell coordinate system and H A1 Corresponding to the point of action of the excitation force outside the main ship, H A2 Each point corresponds to the connection point between the main hull and the foundation, and has five degrees of freedom.
[0078] Solving the above overall structural dynamic equation (5) can obtain the generalized coordinates of the main hull, and thus obtain the calculation results of the vibration and acoustic radiation of the underwater target.
[0079] This method achieves efficient calculation of underwater target acoustic radiation with built-in vibration isolation system. In one example, the line spectrum comparison of the vibration acoustic radiation calculation results obtained by the integrated method of the present application and the vibration acoustic radiation calculation results calculated by numerical software using numerical methods is shown in the figure below. Figure 3 The 1 / 3 octave spectrum comparison of the vibration sound radiation calculation results obtained by the integrated method of this application and the vibration sound radiation calculation results obtained by numerical calculation using numerical software is shown in the figure below. Figure 4As shown in the figure, the accuracy of this method is consistent with that of the numerical software, while the number of computing units required by this method is one order of magnitude smaller than that of the numerical software, so the calculation time is significantly shorter than that of the numerical software.
[0080] The above description is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and variations directly derived or imagined by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the scope of protection of the present application.
Claims
1. A method for calculating the vibration and acoustic radiation of underwater targets with multi-layer structure separation and integration, characterized in that: The underwater target vibration acoustic radiation calculation method includes: Based on the vibration transmission path, the underwater target is divided into the main hull and n-layer subsystems. Each subsystem consists of several non-connected structures inside the hull. The first subsystem is directly connected to the main hull, and the j-th subsystem is connected to the j+1-th subsystem through the j-th vibration isolator. Among them, the integer parameter n ≥ 2, the integer parameter 1 ≤ j ≤ n-1; The dynamic equations of the main hull are constructed based on analytical methods, the dynamic equations of each subsystem are constructed based on numerical methods, and the dynamic equations of each layer of vibration isolators are constructed based on experimental test methods. The dynamic equations of the main hull, the dynamic equations of each layer of subsystems, and the dynamic equations of each layer of vibration isolators are integrated and coupled to obtain the overall structural dynamic equations. The vibration and acoustic radiation calculation results of the underwater target are obtained by solving the overall structural dynamic equations.
2. The underwater target vibration acoustic radiation calculation method according to claim 1, characterized in that: The overall structural dynamic equations include: For any two directly connected structures among the main hull, each layer of subsystems, and each layer of vibration isolators, the dynamic equations of the main hull, the dynamic equations of each layer of subsystems, and the dynamic equations of each layer of vibration isolators are integrated and coupled in combination with matrix rearrangement transformation technology based on the displacement continuity conditions of the connection point between the two structures and the relationship between the excitation force and the reaction force to obtain the dynamic equation of the overall structure.
3. The underwater target vibration acoustic radiation calculation method according to claim 2, characterized in that: The main hull dynamic equations based on analytical methods include: The analytical method is used to construct the coupled vibration equations of the main hull and water and the virtual modes of the main hull are introduced to obtain the expanded dynamic equations of the main hull.
4. The underwater target vibration acoustic radiation calculation method according to claim 3, characterized in that: The expanded main hull dynamic equation is obtained as follows: Among them, Z A represents the generalized dynamic stiffness matrix and Z A =-ω 2 M A +K A , M A is the generalized mass matrix of the main hull considering the attached water mass, K A is the generalized stiffness matrix of the main hull, ω represents the excitation frequency; F A1 is the column vector of the external excitation force applied to the cylindrical shell, F A2 is the force column vector of the connection point between the main hull and the first layer subsystem, It is H A The transposed matrix, H A Represents the vibration mode matrix corresponding to the main hull excitation point and connection point H A1 Corresponding to the point of action of the excitation force outside the main ship, H A2 Corresponding to the connection point between the main hull and the first layer subsystem; η is the generalized coordinate of the main hull, η v is the virtual modal generalized coordinate, Z V =I.
5. The underwater target vibration acoustic radiation calculation method according to claim 4, characterized in that: For any integer parameter 1≤i≤n, the dynamic equations of the i-th layer subsystem constructed based on the numerical method include: The modal condensation dynamic stiffness matrix of the i-th layer subsystem is obtained by using finite element modal analysis and modal synthesis super-element method, and the dynamic equation of the i-th layer subsystem is constructed to characterize the relationship between the modal condensation dynamic stiffness matrix, displacement matrix and excitation matrix of the i-th layer subsystem. Among them, the displacement matrix of the i-th layer subsystem includes the displacement of the calculation point of the i-th layer subsystem and the displacement of the connection point between the i-th layer subsystem and the adjacent structure, and the excitation matrix of the i-th layer subsystem includes the excitation of the calculation point of the i-th layer subsystem and the excitation of the connection point between the i-th layer subsystem and the adjacent structure.
6. The underwater target vibration acoustic radiation calculation method according to claim 5, characterized in that: The dynamic equations of each layer of vibration isolators constructed based on the experimental test method include: Based on the experimental test method, the impedance test results of the j-th layer vibration isolator are obtained, and based on the impedance test results, the dynamic stiffness matrix of the j-th layer vibration isolator is obtained by using the four-terminal network parameter method through the degree of freedom change. The dynamic equation of the j-th layer vibration isolator is constructed to characterize the relationship between the dynamic stiffness matrix, displacement matrix and excitation matrix of the j-th layer vibration isolator; The displacement matrix of the j-th vibration isolator includes the displacements of the connection points between the j-th vibration isolator and the j-th subsystem and the j+1-th subsystem, and the excitation matrix of the j-th vibration isolator includes the excitations of the connection points between the j-th vibration isolator and the j-th subsystem and the j+1-th subsystem.
7. The underwater target vibration acoustic radiation calculation method according to claim 6, characterized in that: (1) When 1≤i≤n-1, the dynamic equation of the constructed i-th layer subsystem is: Among them, when i=1, and They represent the displacement and excitation of the connection point between the first layer subsystem and the main hull, respectively. When i≥2, and denote the displacement and excitation of the connection point between the i-th layer subsystem and the i-1-th layer isolator, respectively; and denote the displacement and excitation of the calculation point of the i-th layer subsystem, respectively. and denote the displacement and excitation of the connection point between the ith layer subsystem and the ith layer isolator, respectively; is the modal condensed dynamic stiffness matrix of the i-th layer subsystem; (2) When i = n, the dynamic equation of the constructed n-th layer subsystem is: in, and denote the displacement and excitation of the connection point between the nth layer subsystem and the n-1th layer isolator, respectively. and represent the displacement and excitation of the calculation point of the n-th layer subsystem, is the modal condensed dynamic stiffness matrix of the n-th layer subsystem.
8. The underwater target vibration acoustic radiation calculation method according to claim 7, characterized in that: The dynamic equation of the j-th layer vibration isolator is: in, and denote the displacement and excitation of the connection point between the j-th layer isolator and the j-th layer subsystem respectively; and denote the displacement and excitation of the connection point between the jth layer isolator and the j+1th layer subsystem respectively; represents the dynamic stiffness matrix of the j-th layer of vibration isolators.
9. The underwater target vibration acoustic radiation calculation method according to claim 8, characterized in that: The underwater target vibration acoustic radiation calculation method includes: Determine the connection point between the j-th layer isolator and the j-th layer subsystem to meet the displacement continuity condition: And the relationship between force and reaction force Determine that the connection point between the jth layer isolator and the j+1th layer subsystem satisfies the displacement continuity condition: And the relationship between force and reaction force Determine the relationship between the force and reaction force at the connection between the main hull and the first layer subsystem 10. The underwater target vibration acoustic radiation calculation method according to claim 9, characterized in that: The overall structural dynamic equation obtained is: in, is the identity matrix; H A represents the displacement mode matrix of the selected point on the main hull in the cylindrical shell coordinate system and H A1 Corresponding to the excitation force acting point outside the main ship, H A2 Each point corresponds to the connection point between the main hull and the foundation, and has five degrees of freedom.