Modeling and calculation method and system for coupled vibration of cylindrical shell structure with liquid tank inside

Abstract

The present invention belongs to the technical field related to ships and underwater vehicles, and discloses a modeling and calculation method and system for coupled vibration of a cylindrical shell structure containing a liquid tank inside. The method includes the following steps: S1 For a cylindrical shell structure with a liquid tank inside a ship, the cylindrical shell section where the liquid tank is located is selected as a research object, and the structure of the research object is simplified to a partially liquid-filled cylindrical shell containing a horizontal plate inside; S2 Constructing the motion control equation of the coupling of the cylindrical shell, the flat plate and the internal fluid; S3 Solving the motion control equation of the coupling of the cylindrical shell, the flat plate and the internal fluid, respectively obtaining the natural frequency of the cylindrical shell structure under free vibration and the vibration response of the cylindrical shell structure under external excitation. Through the present invention, the problem of rapid prediction of the natural frequency and vibration response of a cylindrical shell structure with a liquid tank inside a ship is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to ships and underwater vehicles, and more specifically, relates to a modeling and calculation method and system for coupled vibration of a cylindrical shell structure containing a liquid tank inside. Background Art

[0002] Cylindrical shell structures are widely used in the field of shipbuilding and marine engineering. The main structure of underwater vehicles often adopts shell structures such as cylindrical shells. In addition to ensuring the requirements of structural strength, stiffness and stability, the requirements for its vibration are also becoming increasingly stringent.

[0003] However, underwater vehicles often have many types of liquid tanks or ballast tanks inside the structure. For the shell structure with liquid tanks inside, on the one hand, the vibration energy of the internal structure will not only be transmitted to the external flow field through the cylindrical shell, but also be transmitted to the shell through the liquid in the tank and then to the external flow field; more importantly, the sloshing of the liquid with free liquid surface inside after external excitation will couple with the shell structure to form complex fluid-solid coupling vibration. For this complex coupling form of cylindrical shell structure, if the finite element method and other methods are used for modeling and calculation, there are disadvantages such as low efficiency and poor economy.

[0004] Therefore, for this cylindrical shell structure with a liquid tank inside, it is urgent to propose an equivalent and reasonable acoustic vibration theoretical model and an efficient calculation method to quickly predict the natural frequency and vibration response of the coupled system, and further improve the theoretical system of acoustic vibration research on the cylindrical shell coupled system, so as to provide theoretical support for the design and evaluation stage of underwater vehicles with liquid tanks inside. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a modeling and calculation method and system for the coupled vibration of a cylindrical shell structure containing a liquid tank inside, which solves the problem of rapid prediction of the natural frequency and vibration response of a cylindrical shell structure with a liquid tank inside a ship.

[0006] To achieve the above object, according to one aspect of the present invention, a modeling and calculation method for coupled vibration of a cylindrical shell structure containing a liquid tank is provided, the method comprising the following steps:

[0007] S1 For a cylindrical shell structure with a liquid tank inside a ship, the cylindrical shell section where the liquid tank is located is selected as the research object, and the structure of the research object is simplified to a partially liquid-filled cylindrical shell with a horizontal plate inside;

[0008] S2 considers the linear sloshing of the internal fluid in the cylindrical shell, as well as the force and displacement continuity characteristics between the cylindrical shell and the horizontal plate, and between the cylindrical shell and the internal fluid, and constructs the motion control equations of the coupling of the cylindrical shell, the flat plate and the internal fluid;

[0009] S3 solves the motion control equations of the coupling among the cylindrical shell, the flat plate and the internal fluid, and obtains the natural frequency of the cylindrical shell structure under free vibration and the vibration response of the cylindrical shell structure under external excitation.

[0010] Further preferably, in step S2, the motion control equations of the coupling of the flat plate, the internal fluid and the cylindrical shell are performed according to the following steps:

[0011] S21 constructs motion control equations of the cylindrical shell and the flat plate respectively, describes the force and displacement of the cylindrical shell and the flat plate according to the wave propagation principle in the flat plate, and combines the displacement and force continuity characteristics of the cylindrical shell and the flat plate at the coupling position to couple the motion control equations of the cylindrical shell and the flat plate to obtain the motion control equations of the coupling of the cylindrical shell and the flat plate;

[0012] S22 considers the linear sloshing of the internal fluid in the cylindrical shell, constructs the velocity potential function of the internal fluid, uses the velocity potential function to solve and obtains the load force of the internal fluid acting on the cylindrical shell, and adds the load force to the motion control equation of the coupling between the cylindrical shell and the flat plate in combination with the force and displacement continuity characteristics between the cylindrical shell and the internal fluid, thereby coupling the internal fluid into the motion control equation of the coupling between the cylindrical shell and the flat plate to obtain the motion control equation of the coupling of the cylindrical shell, the flat plate and the internal fluid.

[0013] Further preferably, in step S21, the motion control equation of the cylindrical shell is performed as follows:

[0014]

[0015] Where u, v and w are the axial, circumferential and radial displacement functions respectively, R0 is the radius of the cylindrical shell, μ is the Poisson's ratio, E is the elastic modulus, h is the thickness of the cylindrical shell, and q z , and q r are the axial, circumferential and radial excitation functions applied to the cylindrical shell, respectively, H 3×3 is the transfer matrix between the displacement amplitude and load amplitude of the cylindrical shell.

[0016] Further preferably, in step S21, the motion control equation of the plate is performed as follows:

[0017] Bending vibration:

[0018] In-plane vibration:

[0019] Where I is the lateral displacement of the plate, U a is the in-plane displacement in the y direction, Ub is the in-plane displacement in the z direction, D is the bending stiffness of the plate, K is the in-plane membrane stiffness of the plate, ρ s is the density of the plate, h p is the thickness of the plate, μ is the Poisson's ratio, is the Laplace operator, ω is the circular frequency, y is the plane where the plate is located and perpendicular to the axial direction of the cylindrical shell, and z is along the axial direction of the cylindrical shell.

[0020] Further preferably, in step S21, the motion control equation of the cylindrical shell and the flat plate coupling is performed according to the following relationship:

[0021]

[0022] Among them, SM1, SM2, SM3, and SM4 are the displacement function matrix amplitudes of the cylindrical shell in the axial, circumferential, radial, and rotational directions, respectively, and GK is the coefficient matrix of the cylindrical shell displacement function in the coupling control equation of the cylindrical shell and the flat plate.

[0023] Further preferably, in step S22, the velocity potential function of the internal fluid is performed according to the following relationship:

[0024]

[0025] Among them, Ф A (r,θ,z) is the antisymmetric velocity potential function of the internal fluid, Ф S (r, θ, z) is the symmetric velocity potential function of the internal fluid, (r, θ) represents the polar coordinates of the liquid cross section, r represents the distance of the polar coordinates, θ represents the angle of the polar coordinates, z represents the direction along the axial direction of the cylindrical shell, and k m is the axial wave number, n is the circumferential mode number, a 2n 、b 2n+1 is the unknown coefficient, I 2n-1 (k m r), I 2n (k m r), I 2n+1 (k m r), I 2n+2 (k m r) are all Bessel functions, K * =ω *2 / g,ω * is the circular frequency of liquid sloshing, g is the acceleration due to gravity, K * is an intermediate variable.

[0026] Further preferably, in step S22, the motion control equation of the coupling among the cylindrical shell, the flat plate and the internal fluid is performed according to the following relationship:

[0027]

[0028] Among them, SM1, SM2, SM3, and SM4 are the displacement function matrix amplitudes of the cylindrical shell in the axial, circumferential, radial, and angular directions, respectively, and GBC is the coefficient matrix of the cylindrical shell displacement function in the coupling control equation of the cylindrical shell, the flat plate, and the internal fluid.

[0029] Further preferably, in step S2, the characteristics of the force and displacement continuity between the cylindrical shell and the horizontal plate are that at the coupling position of the cylindrical shell and the flat plate, the displacements and forces of the cylindrical shell and the flat plate in all directions are equal, and the characteristics of the force and displacement continuity between the cylindrical shell and the internal fluid are that on the wet surface where the cylindrical shell and the internal fluid are in contact, the radial velocities of the cylindrical shell and the internal fluid remain equal.

[0030] Further preferably, in step S3, the natural frequency is solved by setting the determinant of the coefficient matrix of the motion control equation for the coupling of the cylindrical shell, the flat plate and the liquid to zero; the vibration response of the cylindrical shell structure under external excitation is solved by applying the external excitation to the cylindrical shell structure to update the motion control equation for the coupling of the cylindrical shell, the flat plate and the liquid, and then setting the determinant of the coefficient matrix of the updated motion control equation to zero.

[0031] According to another aspect of the present invention, a modeling and calculation system for coupled vibration of a cylindrical shell structure containing liquid inside is provided, the system comprising a processor, and the processor is used for the above-mentioned modeling and calculation method for coupled vibration of a cylindrical shell structure containing liquid inside.

[0032] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0033] 1. In the present invention, the cylindrical shell structure with a liquid tank inside is firstly equivalent to a partially liquid-filled cylindrical shell with a horizontal plate inside; then the motion control equations of the coupling of the cylindrical shell, the flat plate and the internal fluid are constructed; finally, the natural frequency and vibration response of the coupling system are solved; the vibration characteristics of the cylindrical shell structure with a liquid tank inside can be effectively solved, providing theoretical support for the design and evaluation stage of underwater vehicles with liquid tanks inside, and having better efficiency and economic benefits compared with the existing numerical methods;

[0034] 2. The present invention utilizes the continuity characteristics of force and displacement between the cylindrical shell and the horizontal plate, and between the cylindrical shell and the internal fluid, respectively, to couple the characteristics of the horizontal plate and the internal fluid into the motion control equation of the cylindrical shell, and finally obtains the motion control equation of the three couplings, which fully considers the influence of the horizontal plate and the internal fluid on the vibration characteristics of the cylindrical shell, and is more in line with the actual application scenario and in accordance with the actual application situation;

[0035] 3. The present invention conducts theoretical modeling and computational analysis on the cylindrical shell structure with liquid tank inside. The vibration characteristics of the cylindrical shell structure with different liquid tank inside can be obtained by simply changing the parameters of the cylindrical shell and the liquid tank. Compared with the numerical method, the modeling efficiency and computational efficiency are significantly improved, and it also has better economic benefits.

[0036] 4. The present invention obtains the natural frequency of the coupling system and the vibration response under different excitations, and the results are in good agreement with the calculation results of the finite element software; by quickly predicting the vibration characteristics of the coupling system, the theoretical system of vibration research on the cylindrical shell coupling system is further improved, providing theoretical support for the design and evaluation stage of underwater vehicles containing liquid tanks inside. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of a modeling and calculation method for coupled vibration of a cylindrical shell structure containing liquid inside constructed according to a preferred embodiment of the present invention;

[0038] Figure 2 It is a schematic diagram of an equivalent partially liquid-filled cylindrical shell model with a horizontal floor plate inside constructed according to a preferred embodiment of the present invention;

[0039] Figure 3 It is a coordinate system and parameter diagram of an equivalent partially liquid-filled cylindrical shell with a horizontal floor plate inside constructed according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0041] like Figure 1 As shown, the present invention provides a modeling and calculation method for coupled vibration of a cylindrical shell structure containing a liquid tank inside, which includes the following steps:

[0042] S1 For the cylindrical shell structure containing liquid tanks inside the ship, a simplified model is performed on it, which is equivalent to a partially liquid-filled cylindrical shell with a horizontal plate inside. The simplified structure includes a cylindrical shell, an internal fluid and a horizontal plate, wherein the internal fluid and the horizontal plate are arranged in the cylindrical shell, and the horizontal plate is laid flat on the internal fluid. The equivalent model is as follows Figure 2 As shown, the structural coordinate system and fluid coordinate system are established on the equivalent model. The coordinate system and structural parameters are shown in Figure 3 As shown; L is the length of the cylindrical shell, h is the thickness of the cylindrical shell, R0 is the average radius of the cylindrical shell, h pis the thickness of the horizontal plate. The coupled system model defines two cylindrical coordinate systems: the structural coordinate system and the liquid coordinate system. Located at the geometric center O1 of the cylindrical shell, where the coordinate z represents the longitudinal direction of the cylindrical shell, The liquid coordinate system (r, θ, z) is located at the center of the free liquid surface, O2. The coordinate z represents the longitudinal direction of the free liquid surface, and (r, θ) represents the polar coordinate of the liquid cross section. b is the height of the horizontal plate, H b >0 means that the horizontal plate is higher than the shell mid-plate; H represents the distance between the free surface and the shell mid-surface, and H>0 means that the free surface is lower than the shell mid-surface.

[0043] S2 Based on Flügge shell theory and thin plate theory, the motion control equations of the cylindrical shell and the flat plate are established, and combined with the continuity characteristics of the displacement and force of the cylindrical shell and the flat plate at the coupling position, the motion control equations of the cylindrical shell and the flat plate are coupled to obtain the motion control equations of the coupled cylindrical shell and the flat plate; considering the linear sloshing of the internal liquid, the velocity potential function of the internal fluid is solved based on the Laplace equation; through the continuity conditions of the displacement and force on the wet surface of the cylindrical shell, the motion control equations of the coupling of the cylindrical shell, the flat plate and the internal fluid are obtained.

[0044] S21 Based on Flügge shell theory and thin plate theory, the motion control equations of cylindrical shell and flat plate are established respectively. The displacement function and force function of the cylindrical shell are described based on the wave propagation method.

[0045] According to Flügge shell theory, the governing equations of motion for a cylindrical shell with horizontal decking can be written as:

[0046]

[0047] Where u, v and w are the axial, circumferential and radial displacement functions respectively. μ is Poisson's ratio; E is the elastic modulus. z ,q φ and q r are the axial, circumferential and radial excitation functions applied to the cylindrical shell respectively. 3×3 is the transfer matrix between the displacement amplitude and load amplitude of the cylindrical shell.

[0048] The theoretical model of a cylindrical shell with a flat plate inside can be written as follows:

[0049]

[0050]

[0051] Among them, the delta function is the Dirac function. and They represent the axial, circumferential and radial forces acting on the cylindrical shell due to the coupling between the flat plate and the cylindrical shell. When j = 1, it represents the force and moment generated on the right side of the plate, that is, φ1 = φ0; when j = 2, it represents the force and moment generated on the left side of the plate, that is, φ2 = π-φ0.

[0052] Under simply supported boundary conditions, the displacement function and generalized force function can be written as follows:

[0053]

[0054] Among them, U mn 、V mn and W mn are the axial, circumferential and radial displacement amplitudes, respectively, and Fz mn , Fr mn , and MBr mn is the force and moment amplitude, k m is the axial half-wave number, m is the axial mode number, n is the circumferential mode number, k m =mπ / L.

[0055] The equation of motion for the cylindrical shell can finally be written as:

[0056]

[0057] Among them, G is the transfer matrix between the displacement amplitude and force amplitude of the cylindrical shell.

[0058] Based on the thin plate theory, the bending vibration and in-plane vibration of the plate are considered separately:

[0059] The bending vibration equation of the plate is:

[0060]

[0061] Where Ι is the lateral displacement of the plate, ρ s is the density of the plate; μ is Poisson’s ratio; is the Laplace operator; ω is the circular frequency, and the bending stiffness D = Eh p 3 / [12(1-μ 2 )]. For a flat plate, it can be regarded as a flat plate with two simply supported sides and two free sides. The solution of equation (14) is:

[0062]

[0063] Where A, B, C, and D are the coefficients of the plate bending vibration displacement function; k m =mπ / L,

[0064] The relationship between the lateral shear force and bending moment and the lateral displacement and rotation angle can be obtained as follows:

[0065]

[0066] Among them, n t and m z represent the lateral shear force and bending moment on the coupling edge, η and η′ represent the lateral displacement and rotation angle on the coupling edge, S 4×4 is the coefficient matrix.

[0067] The in-plane vibration equation of the plate is:

[0068]

[0069] Among them, U a is the in-plane displacement in the y direction, U b is the in-plane displacement in the z direction. K is the film stiffness, K = Ehp / (1-μ2). According to the propagation of waves on the plate, the solution for the in-plane displacement can be obtained:

[0070]

[0071] Among them, u a (y) and u b (y) are:

[0072] u a (y) = [pcos(py)A1 + k m cos(qy)B2]+[-psin(py)A2+k m sin(qy)B1]

[0073] u b (y) = [k m sin(py)A1-qsin(qy)B2]+[k m cos(py)A2+qcos(qy)B1]

[0074] in,

[0075] The relationship between the internal force and displacement of the plate can be obtained as follows:

[0076]

[0077] Among them, n z and n y are the membrane forces in the z and y directions at the coupling position, respectively. a and u brepresents the in-plane displacement in the z and y directions on the coupled edge of the cylindrical shell and the plate, T 4×4 is the coefficient matrix.

[0078] Through the continuity conditions of displacement and force at the coupling position of the cylindrical shell and the plate, the cylindrical shell-plate coupling vibration equation is obtained.

[0079] The continuity condition for the existence of force and displacement at the connection between the plate and the cylindrical shell is that the displacement and force of the cylindrical shell and the plate in all directions are equal; as follows:

[0080]

[0081] Where C is the coefficient matrix, and They are:

[0082]

[0083] Among them, α is the rotation angle.

[0084] according to Rewrite the above formula into the following form:

[0085]

[0086] The continuity condition of displacement (22) can be written as:

[0087]

[0088] Wherein, j = 1, 2. k (j) , S.M. k (k=1, 2, 3, 4) are:

[0089]

[0090] SM1=[U m1 ,U m2 ,U m3 ,…,U mn ] T ,n=1,2,…,N

[0091] SM2=[V m1 ,V m2 ,V m3 ,…,V mn ] T ,n=1,2,…,N

[0092] SM3=[W m1 ,W m2 ,W m3 ,…,W mn ] T,n=1,2,…,N

[0093] SM4=[V m1 -iW m1 ,V m2 -2iW m2 ,V m3 -3iW m3 ,…,V mn -inW mn ] T ,n=1,2,…,N

[0094] SI=[SI (1) ,SI (2) ] -1

[0095] Then the transfer matrix F between the external generalized force of the shell and the shell displacement amplitude coefficient is tr for:

[0096] F tr =C -1 ·TS·C·SI

[0097] The coupled vibration equation of the cylindrical shell and the flat plate can be rewritten as:

[0098]

[0099] Among them, F tr (1:4,:) and F tr (5:8,:) represent the matrix F tr 1st to 4th and 5th to 8th rows.

[0100] Substituting -N to N into n in equation (25), we can get the equation:

[0101]

[0102] According to formula (26), the coefficient matrix I-GK can be obtained. The natural frequency can be obtained by setting the determinant of the coefficient matrix to zero.

[0103] S22 considers the internal fluid to be linear sloshing, and solves the velocity potential function of the internal fluid based on the Laplace equation. The internal fluid load force is obtained by integrating the velocity potential function and the wet surface.

[0104] Assume that the liquid velocity potential function is Φ(r,θ,z), which should satisfy the Laplace equation. In the cylindrical coordinate system, the Laplace equation is:

[0105]

[0106] Using the separation of variables method, the velocity potential function Φ(r,θ,z) can be written as:

[0107] Φ(r,θ,z)=φ(r,θ)cos(kz) (28)

[0108] Considering that the free surface sloshing of the internal liquid is linear sloshing, the liquid velocity potential function should satisfy the dynamic boundary conditions of the free surface according to the linear wave theory:

[0109]

[0110] Where g is the acceleration due to gravity and η is the sloshing amplitude of the free surface.

[0111] The internal liquid velocity potential function should also satisfy the kinematic boundary conditions on the free surface and is written in the cylindrical coordinate system as:

[0112]

[0113] Substituting equations (28-30) into equation (27), we can obtain the velocity potential function of the internal fluid:

[0114]

[0115] Among them, k m is the axial wave number; n is the circumferential mode number; I n (k m r) is the Bessel function; K * =ω *2 / g.

[0116] Since it is a partially liquid-filled cylindrical shell, the internal liquid load F p Written as a piecewise function:

[0117]

[0118] in is the maximum circumferential coordinate of the free liquid surface in the shell coordinate system. P| R＝R0 is the dynamic pressure of the liquid at the coupling surface.

[0119] According to the Bernoulli equation, the fluid dynamic pressure can be expressed by the velocity potential function as:

[0120]

[0121] Among them, ρ f is the density of the internal fluid.

[0122] The expression for the magnitude of the internal liquid load term can be found as follows:

[0123]

[0124] Through the continuity conditions of displacement and force on the wet surface of the cylindrical shell and the internal fluid, the radial velocities of the cylindrical shell and the internal fluid remain equal on the wet surface where the cylindrical shell and the internal fluid are in contact. The equation of motion of the partially liquid-filled cylindrical shell with a horizontal plate inside is obtained.

[0125] Since the internal fluid acts on the radial direction of the cylindrical shell, the vibration equation of the cylindrical shell with internal plate under the action of the internal fluid is as follows:

[0126]

[0127] Substituting the internal fluid load amplitude expression obtained in step S22 into equation (35), the motion equation of the partially liquid-filled cylindrical shell with an internal horizontal floor plate can be obtained:

[0128]

[0129] Similarly, by setting the coefficient matrix determinant det(I-GBC)=0, the natural frequency and modal vibration shape of the partially liquid-filled cylindrical shell with a horizontal floor plate inside can be obtained.

[0130] S3 obtains the natural frequency of the coupling system based on the obtained dynamic equation of the coupling system; and obtains the vibration response of the cylindrical shell under different excitations.

[0131] (1) Under free vibration, according to the obtained dynamic equation of the coupled system, the natural frequency of the coupled system is obtained by changing the matrix so that the determinant of the coefficient matrix GBC is zero.

[0132] (2) When the cylindrical shell is subjected to external radial excitation, the external excitation load is described based on the wave propagation method. Combined with the dynamic equation of the coupled system, the displacement amplitude coefficient in the coupling equation is obtained, and then the dynamic response of the cylindrical shell is obtained.

[0133] When the cylindrical shell is subjected to external radial point excitation, the external excitation load expression can be written as:

[0134]

[0135] The external excitation amplitude can be written as follows:

[0136]

[0137] Then the forced vibration equation of a partially liquid-filled cylindrical shell with a horizontal plate inside can be written as:

[0138]

[0139] The forced motion equation of a partially liquid-filled cylindrical shell with an internal horizontal plate is obtained as follows:

[0140]

[0141] Where I is the unit matrix, the matrix GBC is consistent with equation (36), and JL is a (8n+4)×1-order matrix related to the external excitation amplitude. Given the specific position coordinates (z0, φ0) of the excitation force and the excitation frequency f0, the displacement amplitude coefficient in the coupling equation can be obtained, and then the vibration response of the cylindrical shell can be obtained.

[0142] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A modeling and calculation method for coupled vibration of a cylindrical shell structure containing a liquid tank inside, characterized in that: The method comprises the following steps: S1 For a cylindrical shell structure with a liquid tank inside a ship, the cylindrical shell section where the liquid tank is located is selected as the research object, and the structure of the research object is simplified to a partially liquid-filled cylindrical shell with a horizontal plate inside; S2 considers the linear sloshing of the internal fluid in the cylindrical shell, as well as the force and displacement continuity characteristics between the cylindrical shell and the horizontal plate, and between the cylindrical shell and the internal fluid, and constructs the motion control equations of the coupling of the cylindrical shell, the flat plate and the internal fluid; S3 solves the motion control equations of the cylindrical shell, the flat plate and the internal fluid coupled to obtain the natural frequency of the cylindrical shell structure under free vibration and the vibration response of the cylindrical shell structure under external excitation; Among them, the vibration equation of the cylindrical shell with internal plate under the action of internal fluid is as follows: The forced vibration equation of a partially liquid-filled cylindrical shell with a horizontal plate inside is as follows: Among them, U mn 、V mn and W mn are the axial, circumferential and radial displacement amplitudes, n is the circumferential mode number, G is the transfer matrix between the displacement amplitude and force amplitude of the cylindrical shell, f mn is the internal liquid load term amplitude, fe mn is the external excitation amplitude.

2. A modeling and calculation method for coupled vibration of a cylindrical shell structure containing a liquid tank inside as claimed in claim 1, characterized in that: In step S2, the motion control equations of the coupling of the plate, the internal fluid and the cylindrical shell are carried out according to the following steps: S21 constructs motion control equations of the cylindrical shell and the flat plate respectively, describes the force and displacement of the cylindrical shell and the flat plate according to the wave propagation principle in the flat plate, and combines the displacement and force continuity characteristics of the cylindrical shell and the flat plate at the coupling position to couple the motion control equations of the cylindrical shell and the flat plate to obtain the motion control equations of the coupling of the cylindrical shell and the flat plate; S22 considers the linear sloshing of the internal fluid in the cylindrical shell, constructs the velocity potential function of the internal fluid, uses the velocity potential function to solve and obtains the load force of the internal fluid acting on the cylindrical shell, and adds the load force to the motion control equation of the coupling between the cylindrical shell and the flat plate in combination with the characteristics of force and displacement continuity between the cylindrical shell and the internal fluid, thereby coupling the internal fluid into the motion control equation of the coupling between the cylindrical shell and the flat plate to obtain the motion control equation of the coupling of the cylindrical shell, the flat plate and the internal fluid.

3. A modeling and calculation method for coupled vibration of a cylindrical shell structure containing a liquid tank inside as claimed in claim 2, characterized in that: In step S21, the motion control equation of the cylindrical shell is performed as follows: Where u, v and w are the axial, circumferential and radial displacement functions respectively, R0 is the radius of the cylindrical shell, μ is the Poisson's ratio, E is the elastic modulus, h is the thickness of the cylindrical shell, and q z , and q r are the axial, circumferential and radial excitation functions applied to the cylindrical shell, respectively, H 3×3 is the transfer matrix between the displacement amplitude and load amplitude of the cylindrical shell.

4. A modeling and calculation method for coupled vibration of a cylindrical shell structure containing a liquid tank inside as claimed in claim 2 or 3, characterized in that: In step S21, the motion control equation of the plate is performed as follows: Bending vibration: In-plane vibration: Where I is the lateral displacement of the plate, U a is the in-plane displacement in the y direction, U b is the in-plane displacement in the z direction, D is the bending stiffness of the plate, K is the in-plane membrane stiffness of the plate, ρ s is the density of the plate, h p is the thickness of the plate, μ is the Poisson's ratio, is the Laplace operator, ω is the circular frequency, y is the plane where the plate is located and perpendicular to the axial direction of the cylindrical shell, and z is along the axial direction of the cylindrical shell.

5. The modeling and calculation method for coupled vibration of a cylindrical shell structure containing a liquid tank inside as claimed in claim 2, characterized in that: In step S21, the motion control equation of the cylindrical shell and the flat plate coupling is performed according to the following relationship: Among them, SM1, SM2, SM3, and SM4 are the displacement function matrix amplitudes of the cylindrical shell in the axial, circumferential, radial, and rotational directions, respectively, and GK is the coefficient matrix of the cylindrical shell displacement function in the coupling control equation of the cylindrical shell and the flat plate.

6. A method for modeling and calculating coupled vibration of a cylindrical shell structure containing a liquid tank as claimed in claim 2, characterized in that: In step S22, the velocity potential function of the internal fluid is performed according to the following relationship: Among them, Ф A (r,θ,z) is the antisymmetric velocity potential function of the internal fluid, Ф S (r,θ,z) is the symmetric velocity potential function of the internal fluid, (r,θ) is the polar coordinate of the liquid cross section, r is the distance of the polar coordinate, θ is the angle of the polar coordinate, z is the axial direction of the cylindrical shell, k m is the axial wave number, n is the circumferential mode number, a 2n 、b 2n+1 is the unknown coefficient, I 2n-1 (k m r), I 2n (k m r), I 2n+1 (k m r), I 2n+2 (k m r) are all Bessel functions, K * =ω *2 / g,ω * is the circular frequency of liquid sloshing, g is the acceleration due to gravity, K * is an intermediate variable.

7. A method for modeling and calculating coupled vibration of a cylindrical shell structure containing a liquid tank as claimed in claim 2, characterized in that: In step S22, the motion control equation of the coupling of the cylindrical shell, the flat plate and the internal fluid is carried out according to the following relationship: Among them, SM1, SM2, SM3, and SM4 are the displacement function matrix amplitudes of the cylindrical shell in the axial, circumferential, radial, and angular directions, respectively, and GBC is the coefficient matrix of the cylindrical shell displacement function in the coupling control equation of the cylindrical shell, the flat plate, and the internal fluid.

8. A method for modeling and calculating coupled vibration of a cylindrical shell structure containing a liquid tank inside as claimed in claim 1 or 2, characterized in that: In step S2, the characteristics of the force and displacement continuity between the cylindrical shell and the horizontal plate are that at the coupling position of the cylindrical shell and the flat plate, the displacements and forces of the cylindrical shell and the flat plate in all directions are equal, and the characteristics of the force and displacement continuity between the cylindrical shell and the internal fluid are that on the wet surface where the cylindrical shell and the internal fluid are in contact, the radial velocities of the cylindrical shell and the internal fluid remain equal.

9. A method for modeling and calculating coupled vibration of a cylindrical shell structure containing a liquid tank inside as claimed in claim 1 or 2, characterized in that: In step S3, the natural frequency is solved by setting the determinant of the coefficient matrix of the motion control equation for coupling the cylindrical shell, the flat plate and the liquid to zero; the vibration response of the cylindrical shell structure under external excitation is solved by applying the external excitation to the cylindrical shell structure to update the motion control equation for coupling the cylindrical shell, the flat plate and the liquid, and then setting the determinant of the coefficient matrix of the updated motion control equation to zero.

10. A modeling and calculation system for coupled vibration of a cylindrical shell structure containing a liquid tank inside, characterized in that: The system includes a processor, which is used to execute the modeling and calculation method for coupled vibration of a cylindrical shell structure containing liquid inside as described in any one of claims 1-9.

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