A method, program, apparatus, and storage medium for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube.

Abstract

This invention belongs to the field of vibration and sound propagation technology for liquid-filled pipelines, specifically relating to a method, program, device, and storage medium for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube. Based on three-dimensional linear elasticity theory and wave equations, this invention obtains the governing equations and boundary conditions for the propagation modes of an infinitely long, uniform, isotropic liquid-filled elastic tube. Differential matrices are constructed and solved to obtain the dispersion curves, displacement distributions, and stress distributions of the modes. The power flow of the modes in the fluid and the tube wall is then calculated, ultimately yielding the energy distribution of the modes. This invention only requires the inner diameter, wall thickness, density of the tube wall material, Young's modulus, Poisson's ratio, and density of the liquid inside the elastic tube to obtain the dispersion curves and modal energy distributions of an infinitely long liquid-filled elastic tube. It can accurately, conveniently, and quickly obtain the vibration and sound propagation characteristics of a liquid-filled elastic tube, providing guidance for selecting a suitable pipeline system.

Description

Technical Field

[0001] This invention belongs to the field of vibration and sound propagation technology of liquid-filled pipelines, specifically relating to a method, program, device, and storage medium for calculating the modal dispersion characteristics and energy distribution of liquid-filled elastic pipes. Background Technology

[0002] Piping systems are widely used in engineering practice. Components such as pumps and valves generate vibrations during operation, and this vibration energy propagates as waves through the liquid and pipe walls, adversely affecting system performance and the surrounding environment. Water-filled pipes of the same size but with different wall materials exhibit different vibration and sound propagation characteristics. This manifests as different dispersion characteristics of the axially propagating modes with varying frequencies, and different energy distributions of these modes within the liquid and pipe walls. To achieve better vibration reduction and noise reduction in the frequency range where liquid-filled pipes vibrate within the piping system, it is necessary to analyze the dispersion characteristics and energy distribution of propagating modes in water-filled elastic pipes made of different materials.

[0003] The common procedure for calculating the dispersion characteristics of axially propagating modes in a liquid-filled elastic tube is as follows: (1) Select a suitable physical theory to establish the dispersion relationship expressed by the characteristic equation; (2) Use a numerical algorithm to find the roots of the characteristic equation and obtain the dispersion curve; (3) Substitute these roots into the governing equation to calculate the displacement and stress distribution of the modes. This calculation process is called the root-finding method. 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 propagating modes in a liquid-filled elastic tube. Currently, 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 this invention is to provide a method, program, apparatus, and storage medium for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube. 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 inside the elastic tube, the dispersion curve and modal energy distribution of the infinitely long liquid-filled elastic tube can be obtained.

[0005] A method for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube includes 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 inside 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 face 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; construct the governing equations for the propagation of fluid and waves in the tube wall of an infinitely long, uniform, and isotropic liquid-filled elastic tube.

[0008]

[0009] Wherein, 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; by taking discrete points, the differential matrices of the first and second derivatives of each potential function to be solved are constructed respectively, and then the matrix L in the governing equations is obtained.

[0010] Step 3: Add boundary conditions to matrix L to form a matrix Introducing matrix Q, we solve the generalized eigenvalue problem: By changing the value of frequency ω, different values ​​of (ω, k) can be obtained. z According to (ω,k) z Plot the modal dispersion curves (f, c) based on the relationship. p ), f=ω / (2π), c p =ω / k z Meanwhile, based on the obtained potential function φ fl ,φ, h3 obtains the displacement and stress distribution in the radial direction of the axially propagating mode inside the liquid-filled elastic tube at a frequency of ω;

[0011] Step 4: Calculate the power flow of the mode in the liquid inside 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, step 2 specifically includes:

[0013] Step 2.1: Displacement field function The scalar potential function Φ and the 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 r2. Based on the inner diameter r1 of the elastic tube obtained in Step 1, take N1 discrete points in the interval (0, r1) and N2 discrete points in the interval (r1, r2); for the unknown potential function φ of the liquid in the elastic tube... flThe vectors corresponding to the N1 discrete points are Constructing the differential matrix and satisfy The superscripts (1) and (2) represent the first-order differential and the second-order differential, respectively;

[0017] For an unknown potential function φ of a wave in the pipe wall, the vector corresponding to N2 discrete points is: Constructing the differential matrix and satisfy Similarly, for h3, construct the differential matrix respectively and

[0018] Step 2.3: Construct the differential matrix L f L1, L2, L3, L4, and thus obtain matrix L;

[0019]

[0020] Among them, c fl denoted as , where is the velocity of sound in the liquid inside the elastic tube; c1 and c2 are the longitudinal and shear wave velocities of the tube wall material, respectively; I1 is the N1×N1 identity matrix; and I2 is the N2×N2 identity matrix.

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

[0022]

[0023] in,

[0024] Furthermore, in step 3, based on the obtained potential function φ fl ,φ, The displacement and stress distribution in the radial direction of the axially propagating mode inside the fluid-filled elastic tube at a frequency of ω, obtained by h3, are as follows:

[0025] The differential matrix of the displacement vector components of the wall of the elastic tube:

[0026]

[0027] in,

[0028] The differential matrix of the stress tensor components of the elastic tube wall:

[0029]

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

[0031] Differential matrix of displacement vector components of fluid inside elastic tube:

[0032]

[0033] in, ufd3=-L f ;

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

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

[0036]

[0037] in, r iα ρ is the distance from the αth discrete point taken in the interval (0, r1) in step 2 to the axis of the elastic tube; fl This is the density of the liquid inside the elastic tube.

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

[0039] If n is 0, i.e., axisymmetric mode, then P shell =P flexure +P extension ;

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

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

[0042]

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

[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 as follows:

[0045]

[0046] A computer device / equipment / system includes 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 described above for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube.

[0047] A computer-readable storage medium having a computer program / instructions stored thereon, 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 / instructions that, when executed by a processor, implement the steps of the method described above for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube.

[0049] The beneficial effects of this invention are as follows:

[0050] This invention addresses the vibration and noise reduction problem in water-filled pipelines by proposing a numerical algorithm for calculating the dispersion characteristics and energy distribution of propagation modes in a liquid-filled elastic tube. Based on three-dimensional linear elasticity theory and wave equations, the governing equations and boundary conditions for the propagation modes of an infinitely long, uniform, and isotropic liquid-filled elastic tube are obtained. Differential matrices are constructed and solved to obtain the dispersion curves, displacement distributions, and stress distributions of the modes. The power flow of each mode in the fluid and the tube wall is then calculated, ultimately yielding the energy distribution of the modes. This invention can accurately, conveniently, and quickly obtain the vibration and sound propagation characteristics of a liquid-filled elastic tube, providing guidance for selecting a suitable pipeline system. Attached Figure Description

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

[0052] Figure 2This is a matrix and boundary condition distribution diagram for a single-layer liquid-filled elastic tube.

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

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

[0055] Figure 5 The modal energy distribution curve for the propagation mode n=0 in a water-filled PE pipe.

[0056] Figure 6 The modal energy distribution curves for the propagation mode n=1 of a water-filled PE pipe are shown. Detailed Implementation

[0057] The present invention will now be further described with reference to the accompanying drawings.

[0058] The shortcomings 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 with the number of model layers, making the solution of the characteristic equation extremely slow.

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

[0062] This invention addresses the shortcomings of existing technologies by providing a numerical calculation method for the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube. It only requires providing the inner diameter r1 (m), wall thickness h (m), and density ρ (kg / m³) of the tube wall material. 3 Young's modulus E (Pa), Poisson's ratio υ, and the density ρ of the liquid inside the elastic tube. fl This allows us to obtain the dispersion curve and modal energy distribution of an infinitely long liquid-filled elastic tube. The algorithm is simple to calculate, fast, and accurate, making it suitable for rapid analysis and comparison of the vibration and sound propagation characteristics of pipelines.

[0063] Establish a zr-θ cylindrical coordinate system with the center of the front end face 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 point in the cylindrical coordinate system and the origin and the r-axis.

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

[0065]

[0066] Where λ and μ are Lamé constants, Represents the Laplace operator. Represents the differential operator; The displacement field function 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] Where c1 and c2 are the longitudinal wave velocity and shear wave velocity of the pipe wall material, respectively.

[0071] Vector potential function In cylindrical coordinates, the form is:

[0072]

[0073] The potential function solution satisfying equation (3) has the following form:

[0074]

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

[0076]

[0077] After a series of mathematical transformations, the governing equations for wave propagation in an infinitely long, uniform, and isotropic liquid-filled elastic tube wall can be obtained as follows:

[0078]

[0079] In equation (7), φ, h1, h2, and h3 are potential functions that depend only on r.

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

[0081]

[0082] The subscript fl indicates fluid, c fl The velocity of sound of the fluid inside the pipe.

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

[0084]

[0085] In the formula φ fl It is a potential function that depends only on r.

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

[0087]

[0088] Choose appropriate boundary conditions: If the elastic tube wall is composed of multiple layers of materials, 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 Surface stress component τ rr τ rθ τ rz All are equal to the corresponding components in solid 2, as shown in equation (11), where the subscripts s1 and s2 represent solid 1 and solid 2 respectively, and r = r i This refers to the interface.

[0089]

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

[0091]

[0092] If the viscosity of the fluid is negligible, then the interface exhibits perfect slip boundary conditions, meaning the radial components of the displacements of the solid and fluid are equal, while the circumferential and axial components are discontinuous. The surface stress components remain equal, and the shear stress of the inviscid fluid is zero, i.e., τ rθf =τ rzf =0, as shown in equation (13):

[0093]

[0094] The outer pipe wall satisfies the stress-free boundary condition, as shown in Equation (14), where the subscript s represents the solid pipe wall and r = r2 represents the outer pipe wall boundary.

[0095]

[0096] In addition, for infinitely long pipes, the following conditions must be met on the outer and inner walls of the pipe:

[0097]

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

[0099]

[0100] Substitute equation (5) into the equation and express it using h1, h2, h3. available:

[0101]

[0102]

[0103] in:

[0104]

[0105] The stress tensor components in an elastic tube wall can be obtained by the following formula:

[0106]

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

[0108]

[0109] In addition, in cylindrical coordinates:

[0110]

[0111] use h3 indicates have to:

[0112]

[0113] The expression for the displacement components of an inviscid fluid is:

[0114]

[0115] The stress tensor components of the nonviscous fluid are as follows:

[0116]

[0117] Take N1 discrete points in the interval (0, r1) and N2 discrete points in the interval (r1, r2);

[0118] For an unknown potential function φ of a liquid inside an elastic tube fl The vectors corresponding to the N1 discrete points are Constructing the differential matrix and satisfy The superscripts (1) and (2) represent the first-order differential and the second-order differential, respectively;

[0119] For an unknown potential function φ of a wave in the pipe wall, the vector corresponding to N2 discrete points is: Constructing the differential matrix and satisfy Similarly, for h3, construct the differential matrix respectively and

[0120] The governing equations in an elastic tube wall are expressed using a differential matrix as follows:

[0121]

[0122] Where L is a 4N²×4N² differential matrix, and we have:

[0123]

[0124]

[0125] Where diag represents a diagonal matrix, I1 is an N1×N1 identity matrix, and I2 is an N2×N2 identity matrix.

[0126] The governing equations in fluid dynamics are expressed using differential matrices as follows:

[0127]

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

[0129]

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

[0131]

[0132] in,

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

[0134] in,

[0135] The differential matrix expression of equation (15) is:

[0136]

[0137] Where gs1=0·I2,

[0138] The differential matrix expression for the displacement vector components of the fluid is:

[0139]

[0140] in, ufd3=-L f ;

[0141] Stress tensor component τ in fluid rrf The expression for the differential matrix is:

[0142] τ rrf =(rs1)φ fl (47)

[0143] in,

[0144] In the matrix Add boundary conditions to form a matrix ~L, for example, as shown below. Figure 2 As shown; introduce matrix Q to solve the generalized eigenvalue problem:

[0145]

[0146] in, The generalized eigenvalue problem can be solved using MATLAB functions. Please provide a solution.

[0147]

[0148] By changing the value of frequency ω, different values ​​of (ω, k) can be obtained using equation (48). z According to (ω,k) z Plot the modal dispersion curves (f, c) based on the relationship. p ), f=ω / (2π), c p =ω / k z Meanwhile, based on the obtained potential function φ fl ,φ, h3, by substituting the displacement vector component (43), 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, the displacement and stress distribution of the axially propagating mode in the filling pipe at frequency ω can be obtained.

[0149] The axial acoustic intensity I in the fluid is:

[0150]

[0151] The power flow of the axially propagating modes in the fluid is then:

[0152]

[0153] In the formula, n represents the circumferential order of the mode, and n = 0 represents the axisymmetric mode.

[0154] Based on the obtained φ fl (r i The integral in equation (52) is written as:

[0155]

[0156] In the above formula, N is the number of discrete points of the fluid layer in the spectral method algorithm, and r iα Let α be the distance from the axis of the elastic tube to the αth discrete point taken in the interval (0, r1); therefore, the power flow P of the mode in the liquid inside the elastic tube is finally calculated. fluid The formula is:

[0157]

[0158] The power flow propagating along the axial direction in the pipe wall can be categorized into the following three types:

[0159]

[0160] Among them, P flexure P represents the power of the radial bending wave of the pipe wall. extension P represents the power of the longitudinal tensile wave in the pipe wall. torsion This represents the power of the circumferential torsional wave of the pipe wall. In the formula, 'a' represents the distance between the center plane of the pipe wall and the axis, and M... z Q represents the bending torque in the z-direction. z Represents radial shear force, N z Represents axial force, N zθ This represents the circumferential shear force. Its expressions for the axial, tangential, and radial components u, v, w based on modal displacement are as follows:

[0161]

[0162]

[0163] D represents tensile stiffness, and K represents bending stiffness.

[0164]

[0165] Where E is the Young's modulus of the pipe wall material, υ is the Poisson's ratio, and h is the pipe wall thickness.

[0166] Based on the assumption (5) regarding the form of the potential function, the axial displacement component u, the circumferential displacement component v, and the radial displacement component w of the mode in the elastic tube wall have the following forms:

[0167]

[0168] 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. Finally, the expressions for the power flow of the three types of waves propagating axially in the pipe wall are as follows:

[0169]

[0170]

[0171] For the axisymmetric mode, since the torsional wave is completely decoupled from the motion in other directions, the total power flow inside the tube wall is:

[0172] P shell =P flexure +P extension (70)

[0173] For the non-axisymmetric mode, the total power flow inside the tube wall is:

[0174] P shell =P flexure +P extension +P torsion (71)

[0175] Based on the axial wavenumber k of the obtained mode (n,m) nm and the amplitude U of the displacement component at the center plane of the pipe wall nm V nm W nm Substituting into equations (67) and (69), we obtain P. flexure P extension and P torsion This allows us to calculate the total power flow in the pipe wall for both axisymmetric and non-axisymmetric modes.

[0176] Calculate the energy distribution E of the mode in the liquid-filled elastic tube. ratio :

[0177]

[0178] This invention addresses the vibration and noise reduction problem in water-filled pipelines by proposing a numerical algorithm for calculating the dispersion characteristics and energy distribution of propagation modes in a liquid-filled elastic tube. Based on three-dimensional linear elasticity theory and wave equations, the governing equations and boundary conditions for the propagation modes of an infinitely long, uniform, and isotropic liquid-filled elastic tube are obtained. Differential matrices are constructed and solved to obtain the dispersion curves, displacement distributions, and stress distributions of the modes. The power flow of each mode in the fluid and the tube wall is then calculated, ultimately yielding the energy distribution of the modes. The results show that the numerical algorithm of this invention can accurately, conveniently, and quickly obtain the vibration and sound propagation characteristics of a liquid-filled elastic tube, providing guidance for selecting a suitable pipeline system.

[0179] Example 1:

[0180] Step 1: Set the parameters of the liquid-filled elastic tube. For an infinitely long liquid-filled PE tube model, establish the following... Figure 1 The cylindrical coordinate system shown assumes an inner radius r1 = 101.5 mm, a wall thickness h = 8 mm, and a PE density ρ = 960 kg / m³. 3 Young's modulus E = 2.7 GPa, Poisson's ratio ν = 0.399, and the density of water is 1000 kg / m³. 3 .

[0181] Step 2: Write the governing equations and boundary conditions for both the elastic pipe wall and the water in the form of differential matrices, and...

[0182] according to Figure 2 The construction shown Matrix. The differential matrix can be generated by the MATLAB program CHEBDIF.

[0183] Step 3: Establish the equation and use MATLAB functions to change the value of the frequency ω. Solving equation (48) yields different (ω,k) results. z According to (ω,k) z The relationship can be used to plot the modal dispersion curves, such as... Figure 3 , Figure 4 The figures show the dispersion curves of the propagation modes of the water-filled PE pipe with n=0 and n=1 in the range of 0-30kHz.

[0184] Step 4: Substitute the obtained potential function into the displacement vector component equation (43) and stress tensor component equation (44) of the mode in the pipe wall, and the displacement vector component equation (46) and stress tensor component equation (47) of the mode in the fluid, to obtain the displacement and stress distribution of the axially propagating mode in the filling pipe at frequency ω in the radial direction.

[0185] Step 5: Substitute the potential function obtained in Step 3 into Equation (55) to obtain the power flow of the mode 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 power flow of the mode in the pipe wall. Then, obtain the energy distribution of the mode in the water-filled PE pipe from Equation (72). Figure 4 , Figure 5 The figures show the energy distribution of the propagation modes of the water-filled PE pipe with n=0 and n=1 in the range of 0-30kHz.

[0186] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube, characterized in that, Includes the following steps: Step 1: Obtain the inner diameter, wall thickness, density of the wall material, Young's modulus, Poisson's ratio, and density of the liquid inside 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 face 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; construct the governing equations for the propagation of fluid and waves in the tube wall of an infinitely long, uniform, and isotropic liquid-filled elastic tube. Wherein, 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; by taking discrete points, the differential matrices of the first and second derivatives of each potential function to be solved are constructed respectively, and then the matrix L in the governing equations is obtained. Step 3: Add boundary conditions to matrix L to form a matrix Introducing matrix Q, we solve the generalized eigenvalue problem: By changing the value of frequency ω, different values ​​of (ω, k) can be obtained. z According to (ω,k) z Plot the modal dispersion curves (f, c) based on the relationship. p ), f=ω / (2π), c p =ω / k z Meanwhile, based on the obtained potential function φ fl ,φ, h3 obtains the displacement and stress distribution in the radial direction of the axially propagating mode inside the liquid-filled elastic tube at a frequency of ω; Step 4: Calculate the power flow of the mode in the liquid inside the elastic tube and the power flow of the mode in the tube wall to obtain the energy distribution of the mode in the liquid-filled elastic tube.

2. The method for calculating the modal dispersion characteristics and energy distribution of a liquid-filled elastic tube according to claim 1, characterized in that: Step 2 specifically involves: Step 2.1: Displacement field function The scalar potential function Φ and the 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: Let the outer diameter of the elastic tube be r2. Based on the inner diameter r1 obtained in Step 1, take N1 discrete points in the interval (0, r1) and N2 discrete points in the interval (r1, r2). For the unknown potential function φfl of the liquid in the elastic tube, the vector corresponding to the N1 discrete points is... Constructing the differential matrix and satisfy The superscripts (1) and (2) represent the first-order differential and the second-order differential, respectively; For an unknown potential function φ of a wave in the pipe wall, the vector corresponding to N2 discrete points is: Constructing the differential matrix and satisfy Similarly, for h3, construct the differential matrix respectively and Step 2.3: Construct the differential matrix L f L1, L2, L3, L4, and thus obtain matrix L; Among them, c fl Let be the sound velocity of the liquid inside the elastic tube; c1 and c2 are the longitudinal wave velocity and shear wave velocity of the tube wall material, respectively; I1 is the N1×N1 identity matrix; I2 is the N2×N2 identity matrix.

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

6. The method for calculating the 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 mode in the wall of the elastic tube is calculated. shell The specific method is as follows: If n is 0, i.e., axisymmetric mode, then P shell =P flexure +P extension ; If n is not equal to 0, i.e., it is a non-axisymmetric mode, then P shell =P flexure +P extension +P torsion ; Among them, P flexure P is the power of the radial bending wave of the elastic tube wall. extension P is the power of the longitudinal tensile wave in the wall of the elastic tube. torsion The power of the circumferential torsional wave of the elastic tube wall is given by the axial wave number k of mode (n,m). nm and the amplitude U of its displacement component at the center plane of the elastic tube wall. nm V nm W nm calculate: Where K is the bending stiffness. h represents the wall thickness of the elastic tube; E and ν represent the Young's modulus and Poisson's ratio of the tube wall material, respectively; D represents the tensile stiffness. 'a' represents the distance between the center plane of the tube wall and the axis of the elastic tube.

7. The method for calculating the 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 as follows:

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 / instructions stored thereon, characterized in that: When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 7.

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

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