Method, program and equipment for calculating modal dispersion characteristic and energy distribution of liquid-filled elastic pipe and storage medium

Abstract

The invention belongs to the technical field of liquid-filled pipeline vibration and sound propagation, and particularly relates to a method, a program and equipment for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic pipe and a storage medium. On the basis of a three-dimensional linear elasticity theory and a wave equation, a control equation and boundary conditions of a propagation mode of an infinitely long, uniform and isotropic liquid-filled elastic tube are obtained, differential matrixes are constructed and solved respectively, after a frequency dispersion curve, displacement distribution and stress distribution of the mode are obtained, power flows of the mode in fluid and a tube wall are calculated respectively, and the power flow of the fluid in the tube wall is calculated. And finally obtaining modal energy distribution. According to the invention, the frequency dispersion curve and modal energy distribution of the infinitely long liquid-filled elastic tube can be obtained only by providing the inner diameter, the wall thickness, the density of the tube wall material, the Young modulus, the Poisson's ratio and the density of the liquid in the elastic tube, and the vibration and sound propagation characteristics of the liquid-filled elastic tube can be accurately, conveniently and quickly obtained; and guidance is provided for selecting a proper pipeline system.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration and sound propagation of liquid-filled pipelines, and specifically relates to a method, program, device and storage medium for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube. Background Art

[0002] Pipeline systems have been widely used in engineering practice. Components such as water pumps and valves generate vibrations during operation. The vibration energy propagates in the liquid and pipe wall in the form of waves, which can have adverse effects on system performance and the surrounding environment. Water-filled pipes of the same size but different wall materials have different vibration and sound propagation characteristics, which are manifested in different dispersion characteristics of the modes propagating along the axial direction with frequency changes, and different energy distribution of the modes in the liquid and pipe wall. In order to make the liquid-filled pipe have better vibration reduction and noise reduction effects in the frequency band where the pipeline system generates vibrations, it is necessary to analyze the dispersion characteristics and energy distribution of the propagation modes in water-filled elastic pipes of different materials.

[0003] The commonly used process for calculating the dispersion characteristics of the axial propagation mode in a liquid-filled elastic tube is: (1) Selecting an appropriate physical theory to establish the dispersion relationship expressed by the characteristic equation; (2) Using a numerical algorithm to find the roots of the characteristic equation and obtain the dispersion curve; (3) Substituting these roots into the control equation to calculate the displacement and stress distribution of the mode. This calculation process is called the root-finding method. The numerical algorithms for implementing the root-finding method are mainly divided into two categories: the transfer matrix method and the global matrix method. With the development of computer technology, commercial finite element software such as COMSOL and Actran can also be used to model and calculate the dispersion characteristics of the propagation mode in a liquid-filled elastic tube. At present, there is no software or numerical algorithm on the market that can directly calculate the modal energy distribution in a liquid-filled elastic tube. Summary of the invention

[0004] The purpose of the present invention is to provide a method, program, device and storage medium for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube. The dispersion curve and modal energy distribution of the infinitely long liquid-filled elastic tube can be obtained by simply providing the inner diameter, wall thickness, density of the tube wall material, Young's modulus, Poisson's ratio and density of the liquid in the elastic tube.

[0005] A method for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube comprises the following steps:

[0006] Step 1: Obtain the inner diameter, wall thickness, density of the wall material, Young's modulus, Poisson's ratio and density of the liquid in the elastic tube, and set boundary conditions according to the calculation conditions;

[0007] Step 2: Establish a cylindrical coordinate system with the center of the front end of the elastic tube as the origin, the radius of the elastic tube as the r axis, and the length of the elastic tube as the z axis; construct a set of governing equations for wave propagation in the fluid and tube wall of an infinitely long, uniform, isotropic liquid-filled elastic tube;

[0008]

[0009] Among them, Θ is the potential function vector to be solved, including the potential function of liquid propagation in the elastic tube and the potential function of wave propagation in the tube wall of the elastic tube; the differential matrices of the first-order differential and the second-order differential of each potential function to be solved are constructed in the form of discrete points, and then the matrix L in the control equation group is obtained;

[0010] Step 3: Add boundary conditions to matrix L to form matrix Introduce the matrix Q to solve the generalized eigenvalue problem: By changing the value of frequency ω, different (ω, k z ), according to (ω,k z ) relationship to draw the mode dispersion curve (f,c p ), f = ω / (2π), c p =ω / k z , and according to the obtained potential function φ fl 、φ、 h 3 Obtain the displacement and stress distribution in the radial direction of the axial propagation mode in the liquid-filled elastic tube when the frequency is ω;

[0011] Step 4: Calculate the power flow of the mode in the liquid in the elastic tube and the power flow of the mode in the tube wall of the elastic tube respectively to obtain the energy distribution of the mode in the liquid-filled elastic tube.

[0012] Furthermore, the step 2 is specifically as follows:

[0013] Step 2.1: Displacement Field Function By scalar potential function Φ and vector potential function describe, set up

[0014]

[0015] Where n represents the circumferential order of the mode, which is a natural number. When n is 0, it represents an axisymmetric mode, and when n is not equal to 0, it represents a non-axisymmetric mode.

[0016] Step 2.2: Let the outer diameter of the elastic tube be r 2 , according to the inner diameter r of the elastic tube obtained in step 1 1 , in (0,r 1 ) Take N in the interval1 discrete points, in (r 1 ,r 2 ) Take N in the interval 2 discrete points; for the unknown potential function of the liquid in the elastic tube, φ fl , N 1 The vector corresponding to the discrete point is Constructing the differentiation matrix and satisfy The superscripts (1) and (2) represent the first-order differential and the second-order differential, respectively;

[0017] For the unknown potential function φ of the wave in the tube wall, N 2 The vector corresponding to the discrete point is Constructing the differentiation matrix and satisfy Similarly, for h 3 , respectively construct the differential matrix and

[0018] Step 2.3: Construct the differential matrix L f , L 1 , L 2 , L 3 , L 4 , and then get the matrix L;

[0019]

[0020] Among them, c fl is the sound velocity of the liquid in the elastic tube; c 1 With c 2 are the longitudinal wave velocity and shear wave velocity of the pipe wall material respectively; I 1 N 1 ×N 1 The identity matrix of 2 N 2 ×N 2 The identity matrix of .

[0021] Furthermore, the matrix Q in step 3 is:

[0022]

[0023] in,

[0024] Furthermore, in step 3, according to the potential function φ obtained fl 、φ、 h 3The displacement and stress distribution in the radial direction of the axial propagation mode in the liquid-filled elastic tube when the frequency is ω are obtained as follows:

[0025] Differentiation matrix of the displacement vector components of the wall of an elastic tube:

[0026]

[0027] in,

[0028] Differentiation matrix of the stress tensor components of the wall of an elastic tube:

[0029]

[0030] in, λ and μ are Lamé constants,

[0031] Differentiation matrix of the displacement vector components of a liquid in an elastic tube:

[0032]

[0033] in, ufd3=-L f ;

[0034] The component τ of the stress tensor of the liquid in the elastic tube rrf The differential matrix of: τ rrf =(rs1)φ fl ,

[0035] Furthermore, the power flow P of the modal in the liquid in the elastic tube is calculated in step 4. fluid The specific method is:

[0036]

[0037] in, r iα is the value in step 2 at (0,r 1 ) is the distance from the αth discrete point in the interval to the axis of the elastic tube; ρ fl is the density of the liquid in the elastic tube.

[0038] Furthermore, in step 4, the power flow P of the modal in the wall of the elastic tube is calculated. shell The specific method is:

[0039] If n is 0, that is, axisymmetric mode, then P shell =Pflexure +P extension ;

[0040] If n is not equal to 0, that is, non-axisymmetric mode, then P shell =P flexure +P extension +P torsion ;

[0041] Among them, P flexure is the power of the radial bending wave of the elastic tube wall, P extension is the power of the longitudinal tensile wave of the elastic tube wall, P torsion is the power of the circumferential torsional wave of the elastic tube wall, according to the axial wave number k of the mode (n, m) nm and its displacement component amplitude U at the center plane of the elastic tube wall nm 、V nm , W nm calculate:

[0042]

[0043] Where K is the bending stiffness, h is the wall thickness of the elastic tube, E and ν are the Young's modulus and Poisson's ratio of the wall material of the elastic tube respectively; D is the tensile stiffness, a is the distance between the center plane of the elastic tube wall and the axis.

[0044] Furthermore, in step 4, the energy distribution E of the mode in the liquid-filled elastic tube is obtained. ratio The specific method is:

[0045]

[0046] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube.

[0047] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the method for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube.

[0048] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the method for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube.

[0049] The beneficial effects of the present invention are:

[0050] Aiming at the vibration reduction and noise reduction problem of water-filled pipelines, the present invention proposes a numerical algorithm for calculating the dispersion characteristics and energy distribution of propagation modes in liquid-filled elastic tubes. Based on the three-dimensional linear elastic theory and the wave equation, the control equations and boundary conditions of the propagation modes of infinitely long, uniform, and isotropic liquid-filled elastic tubes are obtained. Differential matrices are constructed and solved respectively. After obtaining the dispersion curve, displacement distribution, and stress distribution of the mode, the power flow of the mode in the fluid and the pipe wall is calculated respectively, and finally the energy distribution of the mode is obtained. The present invention can accurately, conveniently, and quickly obtain the vibration and sound propagation characteristics of liquid-filled elastic tubes, and provide guidance for selecting a suitable pipeline system. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A cylindrical coordinate system diagram for an infinitely long, uniform, isotropic fluid-filled elastic tube model with the axial direction as the z-axis.

[0052] Figure 2 Matrix and boundary condition distribution diagram of a single-layer liquid-filled elastic tube.

[0053] Figure 3 It is the dispersion curve of the propagation mode of water-filled PE pipe n=0.

[0054] Figure 4 It is the dispersion curve of the propagation mode of water-filled PE pipe n=1.

[0055] Figure 5 It is the modal energy distribution curve of the propagation mode of water-filled PE pipe n=0.

[0056] Figure 6 It is the modal energy distribution curve of the propagation mode of water-filled PE pipe n=1. DETAILED DESCRIPTION

[0057] The present invention is further described below in conjunction with the accompanying drawings.

[0058] Deficiencies of existing technology:

[0059] 1. When the thickness of the multi-layer model is large or the solution frequency is high, the transfer matrix method is prone to numerical instability.

[0060] 2. For the global matrix method, the matrix size increases as the number of model layers increases, and the solution to the characteristic equation becomes extremely slow.

[0061] 3. Commercial finite element software has copyright restrictions, and when using it to calculate high-frequency modes, it has high requirements on computer performance and consumes a lot of computing resources.

[0062] In view of the shortcomings of the prior art, the present invention provides a numerical calculation method for modal dispersion characteristics and energy distribution of a liquid-filled elastic tube.1 (m), wall thickness h(m), density of pipe wall material ρ(kg / m 3 ), Young's modulus E(Pa), Poisson's ratio υ, and the density ρ of the liquid in the elastic tube fl , the dispersion curve and modal energy distribution of the infinite length of the liquid-filled elastic tube can be obtained. The algorithm is simple to calculate, fast, and accurate, and is suitable for rapid analysis and comparison of the vibration and sound propagation characteristics of pipelines.

[0063] A zr-θ cylindrical coordinate system is established with the center of the front end surface of the elastic tube as the origin, the radius direction of the elastic tube as the r axis, and the length direction of the elastic tube as the z axis; θ is the angle between the line connecting a certain point in the cylindrical coordinate system and the origin and the r axis.

[0064] For an infinitely long, uniform, isotropic, fluid-filled elastic tube model, in a cylindrical coordinate system with the z-axis as the axial direction, the motion equation satisfied by the wave in the tube wall is:

[0065]

[0066] Where λ and μ are the Lamé constants, represents the Laplace operator, represents a differential operator; Represents the displacement field function, which can be represented by the scalar potential function Φ and the vector potential function describe:

[0067]

[0068] Substituting (2) into (1), we have:

[0069]

[0070] Among them, c 1 、c 2 are the bulk longitudinal wave velocity and bulk shear wave velocity of the pipe wall material, respectively.

[0071] Vector potential function The form in the cylindrical coordinate system is:

[0072]

[0073] The potential function solution that satisfies equation (3) is:

[0074]

[0075] Substitute (5) into (2) and omit And order:

[0076]

[0077] After a series of mathematical transformations, the governing equation for wave propagation in an infinitely long, uniform, isotropic fluid-filled elastic tube wall is obtained as follows:

[0078]

[0079] In formula (7), φ, h 1 ,h 2 ,h 3 They are all potential functions that are only related to r.

[0080] The wave equation satisfied by the wave propagating axially in the fluid is:

[0081]

[0082] The subscript fl indicates fluid, c fl is the speed of sound of the fluid in the tube.

[0083] The displacement potential function Φ that satisfies (8) fl The expression is:

[0084]

[0085] Where φ fl is the potential function that is only related to r.

[0086] Substituting equation (9) into (8) we can obtain the governing equation for the propagation of sound waves in the fluid:

[0087]

[0088] Choose appropriate boundary conditions: If the elastic tube wall is composed of multiple layers of material, the continuity condition that needs to be satisfied at the interface between solid 1 and solid 2 is the displacement component u in solid 1. r 、u θ 、u z and surface stress component τ rr , τ rθ , τ rz are equal to the corresponding components in solid 2, as shown in formula (11), where subscripts s1 and s2 represent solid 1 and solid 2, respectively, and r = r i Represents this interface.

[0089]

[0090] For the solid-fluid interface, if the viscosity of the fluid cannot be ignored, the continuity condition on the interface is that the displacement component and the surface stress component in the solid are equal to the corresponding components in the viscous fluid, as shown in formula (12), where the subscripts s and f represent the solid and the viscous fluid, respectively.

[0091]

[0092] If the viscosity of the fluid can be ignored, the interface is a perfect slip boundary condition, that is, the radial components of the displacement of the solid and the fluid are equal, the circumferential and axial components of the displacement are discontinuous, the surface stress components are still equal, and the shear stress of the inviscid fluid is 0, that is, τ rθf =τ rzf =0, as shown in formula (13):

[0093]

[0094] The outer tube wall satisfies the stress-free boundary condition, as shown in equation (14), where the subscript s represents the solid of the tube wall, and r = r 2 Represents the outer pipe wall boundary.

[0095]

[0096] In addition, for infinite length tubes, the outer and inner tube walls must also meet the following conditions:

[0097]

[0098] In an elastic tube wall, the displacement vector have:

[0099]

[0100] Substitute equation (5) into h 1 ,h 2 ,h 3 express available:

[0101]

[0102]

[0103] in:

[0104]

[0105] The stress tensor components in the elastic tube wall can be obtained from the following formulas:

[0106]

[0107] Substitute equations (19), (20) and (21) into τ rr , τ rθ and τ rz In the expression of , we get:

[0108]

[0109] In addition, in the cylindrical coordinate system:

[0110]

[0111] use h 3 express have to:

[0112]

[0113] The displacement component expression of the inviscid fluid is:

[0114]

[0115] The components of the stress tensor for an inviscid fluid are:

[0116]

[0117] In (0,r 1 ) Take N in the interval 1 discrete points, in (r 1 ,r 2 ) Take N in the interval 2 discrete points;

[0118] For the unknown potential function φ of the liquid in the elastic tube fl , N 1 The vector corresponding to the discrete point is Constructing the differentiation matrix and satisfy The superscripts (1) and (2) represent the first-order differential and the second-order differential, respectively;

[0119] For the unknown potential function φ of the wave in the tube wall, N 2 The vector corresponding to the discrete point is Constructing the differentiation matrix and satisfy Similarly, for h 3 , respectively construct the differential matrix and

[0120] The governing equations in the elastic tube wall are expressed by differential matrices as follows:

[0121]

[0122] Where L is 4N 2 ×4N 2 The differential matrix of , and:

[0123]

[0124]

[0125] Where diag represents a diagonal matrix, I 1 N 1 ×N 1 The identity matrix of 2 N 2 ×N 2 The identity matrix of .

[0126] The governing equations in the fluid are expressed in terms of differential matrices:

[0127]

[0128] Then the differential matrix expression of the control equations for wave propagation in a liquid-filled elastic tube is as follows:

[0129]

[0130] Similarly, the differential matrix expression of the displacement vector components in the elastic tube wall is:

[0131]

[0132] in,

[0133] The differential matrix expression of the stress tensor components in the elastic tube wall is:

[0134] in,

[0135]

[0136] The differential matrix expression of formula (15) is:

[0137]

[0138] Where gs1 = 0·I 2 ,

[0139] The differential matrix expression of the displacement vector components of the fluid is:

[0140]

[0141] in, ufd3=-L f ;

[0142] The component τ of the stress tensor in the fluid rrf The differential matrix expression of is:

[0143] τ rrf =(rs1)φ fl (47)

[0144] in,

[0145] In the matrix Add boundary conditions to form a matrix ~L. For example, Figure 2 As shown; introduce the matrix Q to solve the generalized eigenvalue problem:

[0146]

[0147] in, For generalized eigenvalue problems, you can use the MATLAB function Please solve.

[0148]

[0149] By changing the value of frequency ω, different (ω, k z ), according to (ω,k z ) relationship to draw the mode dispersion curve (f,c p ), f = ω / (2π), c p =ω / k z , and according to the obtained potential function φ fl 、φ、 h 3 , by substituting the displacement vector component (43) and stress tensor component (44) of the mode in the pipe wall and the displacement vector component (46) and stress tensor component (47) of the mode in the fluid, we can obtain the displacement and stress distribution in the radial direction of the axially propagating mode in the liquid-filled pipe when the frequency is ω.

[0150] The sound intensity I along the axial direction in the fluid is:

[0151]

[0152] Then the power flow of the mode propagating along the axial direction in the fluid is:

[0153]

[0154] In the formula, n represents the circumferential order of the mode, and n=0 represents an axisymmetric mode.

[0155] According to the obtained φ fl (r i), the integral in formula (52) is written as:

[0156]

[0157] In the above formula, N is the number of discrete points in the fluid layer in the spectral method algorithm, r iα For (0,r 1 ) is the distance from the axis of the elastic tube to the αth discrete point in the interval; therefore, the final calculated modal power flow P in the liquid in the elastic tube fluid The formula is:

[0158]

[0159] There are three types of power flow in the axial propagation mode in the pipe wall:

[0160]

[0161] Among them, P flexure It represents the power of radial bending wave of pipe wall, P extension Represents the power of the longitudinal tensile wave of the pipe wall, P torsion Indicates the power of the circumferential torsional wave of the tube wall. Where a represents the distance between the center plane of the tube wall and the axis, M z represents the bending moment in the z direction, Q z Indicates radial shear force, N z Indicates axial force, N zθ Represents the circumferential shear force. Its expressions based on the axial component, tangential component, and radial component u, v, and w of the modal displacement are:

[0162]

[0163]

[0164] D represents tensile stiffness and K represents bending stiffness:

[0165]

[0166] Where E is the Young's modulus of the tube wall material, υ is the Poisson's ratio, and h is the tube wall thickness.

[0167] According to the assumption (5) about the potential function form, the axial displacement component u, circumferential displacement component v and radial displacement component w of the modal in the elastic tube wall have the following forms:

[0168]

[0169] Since the vibration amplitude may be complex, the net power flow is obtained by calculating the real part of the time average of each term in the formula. The final power flow expressions for the three types of waves propagating axially in the pipe wall are

[0170]

[0171]

[0172] For the axisymmetric mode, since the torsional wave is completely decoupled from the motion in other directions, the total power flow in the tube wall is:

[0173] P shell =P flexure +P extension (70)

[0174] For the non-axisymmetric mode, the total power flow in the pipe wall is:

[0175] P shell =P flexure +P extension +P torsion (71)

[0176] According to the obtained mode (n, m) axial wave number k nm and its displacement component amplitude U at the center plane of the tube wall nm 、V nm , W nm , Substitute into equation (67)-(69), and we get P flexure , P extension and P torsion , and then the total power flow in the pipe wall of the axisymmetric mode and the non-axisymmetric mode can be calculated respectively.

[0177] Calculate the energy distribution E of the mode in the fluid-filled elastic tube ratio :

[0178]

[0179] Aiming at the vibration reduction and noise reduction problem of water-filled pipelines, the present invention proposes a numerical algorithm for calculating the dispersion characteristics and energy distribution of propagation modes in liquid-filled elastic tubes. Based on the three-dimensional linear elastic theory and the wave equation, the control equations and boundary conditions of the propagation modes of infinitely long, uniform, and isotropic liquid-filled elastic tubes are obtained. Differential matrices are constructed and solved respectively. After obtaining the dispersion curve, displacement distribution, and stress distribution of the mode, the power flow of the mode in the fluid and the pipe wall is calculated respectively, and finally the energy distribution of the mode is obtained. The results show that the vibration and sound propagation characteristics of the liquid-filled elastic tube can be accurately, conveniently, and quickly obtained by using the numerical algorithm of the present invention, providing guidance for selecting a suitable pipeline system.

[0180] Embodiment 1:

[0181] Step 1: Set the parameters of the liquid-filled elastic tube. For an infinitely long liquid-filled PE tube model, establish Figure 1 The cylindrical coordinate system shown, assuming that its inner radius r 1 =101.5mm, wall thickness h=8mm, PE density ρ=960kg / m 3 , Young's modulus E = 2.7 GPa, Poisson's ratio ν = 0.399, the density of water is 1000 kg / m 3 .

[0182] Step 2: Write the control equations of the elastic pipe wall and water and the boundary conditions in the form of differential matrices, and

[0183] according to Figure 2 Shown build Matrix. The differential matrix can be generated by the MATLAB program CHEBDIF.

[0184] Step 3: Establish the equation and use the MATLAB function by changing the value of frequency ω Solving equation (48) yields different (ω,k z ), according to (ω,k z ) relationship can be used to draw the mode dispersion curve, such as Figure 3 , Figure 4 As shown, they are the dispersion curves of the propagation modes of n=0 and n=1 of the water-filled PE pipe at 0-30kHz.

[0185] Step 4: Substitute the obtained potential function into the displacement vector component formula (43) and stress tensor component formula (44) of the mode in the pipe wall and the displacement vector component formula (46) and stress tensor component formula (47) of the mode in the fluid, and the displacement and stress distribution in the radial direction of the axially propagating mode in the liquid-filled pipe at a frequency of ω can be obtained.

[0186] Step 5: Substitute the potential function obtained in step 3 into equation (55) to obtain the modal power flow in the fluid, substitute the displacement at the center plane of the pipe wall obtained in step 4 into equations (70) and (71) to obtain the modal power flow in the pipe wall, and then obtain the modal energy distribution in the water-filled PE pipe from equation (72). Figure 4 , Figure 5 As shown, they are the energy distribution of the propagation modes of n=0 and n=1 of the water-filled PE pipe at 0-30kHz.

[0187] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube, characterized in that: The following steps are involved: Step 1: Obtain the inner diameter, wall thickness, density of the wall material, Young's modulus, Poisson's ratio and density of the liquid in the elastic tube, and set boundary conditions according to the calculation conditions; Step 2: Establish a cylindrical coordinate system with the center of the front end of the elastic tube as the origin, the radius of the elastic tube as the r axis, and the length of the elastic tube as the z axis; construct a set of governing equations for wave propagation in the fluid and tube wall of an infinitely long, uniform, isotropic liquid-filled elastic tube; Among them, Θ is the potential function vector to be solved, including the potential function of liquid propagation in the elastic tube and the potential function of wave propagation in the tube wall of the elastic tube; the differential matrices of the first-order differential and the second-order differential of each potential function to be solved are constructed in the form of discrete points, and then the matrix L in the control equation group is obtained; Step 3: Add boundary conditions to matrix L to form matrix Introduce the matrix Q to solve the generalized eigenvalue problem: By changing the value of frequency ω, different (ω, k z ), according to (ω,k z ) relationship to draw the mode dispersion curve (f,c p ), f = ω / (2π), c p =ω / k z , and according to the obtained potential function φ fl 、φ、 h3 obtains the displacement and stress distribution in the radial direction of the axial propagation mode in the liquid-filled elastic tube when the frequency is ω; Step 4: Calculate the power flow of the mode in the liquid in the elastic tube and the power flow of the mode in the tube wall of the elastic tube respectively to obtain the energy distribution of the mode in the liquid-filled elastic tube.

2. A method for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1: Displacement Field Function By scalar potential function Φ and vector potential function describe, set up Where n represents the circumferential order of the mode, which is a natural number. When n is 0, it represents an axisymmetric mode, and when n is not equal to 0, it represents a non-axisymmetric mode. Step 2.2: Assume that the outer diameter of the elastic tube is r2. According to the inner diameter r1 of the elastic tube obtained in step 1, select N1 discrete points in the interval (0, r1) and N2 discrete points in the interval (r1, r2). For the potential function φfl of the unknown liquid in the elastic tube, the vector corresponding to the N1 discrete points is Constructing the differentiation matrix and satisfy The superscripts (1) and (2) represent the first-order differential and the second-order differential, respectively; For the unknown potential function φ of the wave in the tube wall, the vectors corresponding to the N2 discrete points are Constructing the differentiation matrix and satisfy Similarly, for h3, respectively construct differential matrices and Step 2.3: Construct the differential matrix L f , L1, L2, L3, L4, and then get the matrix L; Among them, c fl is the sound velocity of the liquid in the elastic tube; c1 and c2 are the body longitudinal wave velocity and body shear wave velocity of the tube wall material respectively; I1 is the unit matrix of N1×N1; I2 is the unit matrix of N2×N2.

3. The method for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube according to claim 2, characterized in that: The matrix Q in step 3 is: in, 4. The method for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube according to claim 3, characterized in that: In step 3, the potential function φ is obtained fl 、φ、 The displacement and stress distribution in the radial direction of the axial propagation mode in the liquid-filled elastic tube when the h3 acquisition frequency is ω are as follows: Differentiation matrix of the displacement vector components of the wall of an elastic tube: in, uzs4=0·I2; Differentiation matrix of the stress tensor components of the wall of an elastic tube: in, λ and μ are Lamé constants, Differentiation matrix of the displacement vector components of a liquid in an elastic tube: in, ufd3=-L f ; The component τ of the stress tensor of the liquid in the elastic tube rrf The differential matrix of: τ rrf =(rs1)φ fl , 5. The method for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube according to claim 4, characterized in that: The power flow P of the modal in the liquid in the elastic tube is calculated in step 4. fluid The specific method is: in, r iα is the distance from the αth discrete point in the interval (0, r1) taken in step 2 to the axis of the elastic tube; ρ fl is the density of the liquid in the elastic tube.

6. The method for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube according to claim 5, characterized in that: In step 4, the power flow P of the modal in the wall of the elastic tube is calculated. shell The specific method is: If n is 0, that is, axisymmetric mode, then P shell =P flexure +P extension ; If n is not equal to 0, that is, non-axisymmetric mode, then P shell =P flexure +P extension +P torsion ; Among them, P flexure is the power of the radial bending wave of the elastic tube wall, P extension is the power of the longitudinal tensile wave of the elastic tube wall, P torsion is the power of the circumferential torsional wave of the elastic tube wall, according to the axial wave number k of the mode (n, m) nm and its displacement component amplitude U at the center plane of the elastic tube wall nm 、V nm , W nm calculate: Where K is the bending stiffness, h is the wall thickness of the elastic tube, E and ν are the Young's modulus and Poisson's ratio of the wall material of the elastic tube respectively; D is the tensile stiffness, a is the distance between the center plane of the elastic tube wall and the axis.

7. The method for calculating modal dispersion characteristics and energy distribution of a liquid-filled elastic tube according to claim 6, characterized in that: In step 4, the energy distribution E of the mode in the liquid-filled elastic tube is obtained. ratio The specific method is:

8. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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