A calculation method, device and equipment for fluid-structure interaction vibration of a fluid transmission pipeline

Abstract

A calculation method, device and equipment for fluid-structure interaction vibration of a fluid-conveying pipeline, which relates to the technical field of fluid-structure interaction dynamics characteristics of a fluid-conveying pipeline, and solves the technical problem of "how to provide a method for solving fluid-structure interaction vibration of a fluid-conveying pipeline that is widely applicable". The method includes: obtaining the parameters of the fluid-conveying pipeline, fluid parameters and load parameters; establishing the motion equation of the pipeline micro-element and its boundary conditions based on the parameters of the fluid-conveying pipeline, fluid parameters and load parameters; calculating the modal function of the fluid-conveying pipeline by using the differential transformation method based on the motion equation of the pipeline micro-element and its boundary conditions; performing regularization processing on the modal function of the fluid-conveying pipeline; calculating the natural frequency and steady-state displacement response of the fluid-conveying pipeline by using the Galerkin method based on the regularized modal function of the fluid-conveying pipeline and the motion equation of the pipeline micro-element. This method organically combines the differential transformation method and the Galerkin method, has a wider application range, and can be applied to the analysis of fluid-structure interaction dynamics characteristics of fluid-conveying pipelines.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid-structure interaction dynamics characteristics of fluid-conveying pipelines. Background Art

[0002] Fluid-conveying pipelines are commonly found in the transportation of petroleum and natural gas, the propulsion systems of rocket liquid fuels, the water supply, gas supply, and hydraulic systems inside combat vehicles, and the transportation of liquid raw materials in the chemical industry. They are often an important part of the entire working system. During use, affected by the use environment (loads, temperature, humidity, etc.), various pipelines will have different failure phenomena, such as leakage, plastic deformation, or even fracture. The fluid-structure interaction vibration of fluid-conveying pipelines is one of the main reasons for the above failure modes. Therefore, the problem of fluid-structure interaction vibration of fluid-conveying pipelines has received extensive attention in the past century.

[0003] Calculating and obtaining the dynamic characteristics of fluid-conveying pipelines can help designers find appropriate methods to avoid or weaken the generation of resonance, thereby increasing their service life and improving the reliability of the system. However, the fluid-structure interaction motion of fluid-conveying pipelines is very complex. Usually, the finite element method is used to solve it according to the steps of establishing a model, dividing the grid, setting boundary conditions and initial conditions, solving, and generating results. However, once a parameter in the pipeline system, such as the pipeline size, load form, parameters of the fluid, etc., changes, it is necessary to repeat all or part of the above steps. The solution process is time-consuming, has a high calculation cost, and is not conducive to forming regular conclusions. By establishing and solving the motion equation, the above deficiencies can be made up for. All variables in the system can be regarded as forces and are functions of time or space. In this way, only the variable to be examined needs to be transformed into a mathematical expression and introduced into the motion equation, and the equation can be simplified and deduced by certain mathematical methods to obtain the influence of the variable on the natural frequency and steady-state displacement response of the pipeline.

[0004] In recent years, many methods for solving the fluid-structure interaction vibration problem of fluid-conveying pipelines have emerged. Typical methods mainly include: differential transformation method, differential quadrature method, Galerkin method, transfer matrix method, Green's function method, etc. However, each of the above methods is limited by the principle of the formation method, resulting in a narrow scope of application and only being able to show advantages in a certain type of problem. For example, in solving high-order differential equations, the differential transformation method is characterized by high accuracy and short time consumption, but it is only applicable to solving homogeneous motion equations; while the Galerkin method is based on the superposition principle, so its scope of application is wide, but it is necessary to first know the shape function before solving homogeneous and non-homogeneous motion equations. Existing solutions all have limitations, and there is a lack of a method with a wider scope of application that can calculate the vibration characteristics of pipelines with various shapes and various support forms.

[0005] Therefore, how to provide a widely applicable method for solving the fluid-structure interaction vibration problem of fluid conveying pipelines has become an urgent technical problem in this field. Summary of the Invention

[0006] In order to solve the technical problem of the narrow application range of the vibration calculation method for fluid conveying pipelines in the prior art, the present invention provides a method, device and equipment for calculating the fluid-structure interaction vibration of fluid conveying pipelines. This method organically combines the differential transformation method and the Galerkin method, making full use of their advantages and having a wider application range.

[0007] Based on the same inventive concept, the present invention has four independent technical solutions:

[0008] 1. A method for calculating the fluid-structure interaction vibration of a fluid conveying pipeline, used to calculate the natural frequency and steady-state displacement response of the fluid conveying pipeline. The method includes the following steps:

[0009] S1. Obtain the pipeline parameters, fluid parameters and load parameters of the fluid conveying pipeline;

[0010] S2. Based on the pipeline parameters, fluid parameters and load parameters of the fluid conveying pipeline, establish the pipeline micro-element motion equation and its boundary conditions;

[0011] S3. Based on the pipeline micro-element motion equation and its boundary conditions, use the differential transformation method to calculate the modal function of the fluid conveying pipeline;

[0012] S4. Regularize the modal function of the fluid conveying pipeline;

[0013] S5. Based on the regularized modal function of the fluid conveying pipeline and the pipeline micro-element motion equation, use the Galerkin method to calculate the natural frequency and steady-state displacement response of the fluid conveying pipeline.

[0014] Further, the pipeline micro-element motion equation is established based on the Euler-Bernoulli beam model.

[0015] Further, after step S2, it also includes: non-dimensionalizing the pipeline micro-element motion equation and its boundary conditions.

[0016] Further, step S3 includes:

[0017] S31. Remove the fluid quantity and external load quantity in the pipeline micro-element motion equation to obtain the pipeline free vibration differential equation;

[0018] S32. Separate the time quantity and space quantity in the pipeline free vibration differential equation;

[0019] S33. Perform differential transformation on the space quantity to obtain the characteristic solution of the pipeline free vibration differential equation, and then obtain the modal function of the fluid conveying pipeline.

[0020] Furthermore, the modal function of the fluid delivery pipeline is regularized and expressed by the following formula:

[0021]

[0022] Among them, y n (ξ) is the nth order mode function of the fluid delivery pipeline, represents the nth-order mode function of the flow pipeline after regularization.

[0023] Further, step S5 includes:

[0024] S51, removing the external load in the pipeline microelement motion equation to obtain the fluid induced motion equation;

[0025] S52, separating and simplifying the fluid-induced motion equation to obtain a stiffness matrix, a mass matrix and a damping matrix, and then calculating the natural frequency of the fluid delivery pipeline;

[0026] S53, retaining the external load in the pipeline microelement motion equation, and performing variable separation and simplification to obtain a stiffness matrix, a mass matrix, a damping matrix and an external load matrix, and then calculating the steady-state displacement response of the fluid delivery pipeline;

[0027] Furthermore, the fluid delivery pipeline is a straight fluid delivery pipe, and the elements of the stiffness matrix, damping matrix, mass matrix and external load matrix of the straight fluid delivery pipe are respectively expressed as:

[0028]

[0029] Among them, K mn , G mn 、M mn 、f mn They represent the elements of the mth row and nth column of the stiffness matrix, damping matrix, mass matrix and external load matrix of the straight pipe, respectively. ξ, β, u, τ, and f(ξ,τ) are all dimensionless quantities introduced in the dimensionless treatment. represents the n-th type function, represents the mth shape function, which is the modal function of the flow pipeline after regularization.

[0030] 2. A fluid-solid coupling vibration calculation device for a fluid transmission pipeline, comprising:

[0031] A parameter acquisition module is used to obtain the flow pipeline parameters and fluid parameters;

[0032] A model building module, used to establish pipeline microelement motion equations and boundary conditions based on the fluid delivery pipeline parameters and fluid parameters;

[0033] A modal function calculation module, configured to calculate the modal function of the fluid conveying pipeline by using the differential transformation method based on the micro-element motion equation of the pipeline and its boundary conditions;

[0034] A regularization processing module, configured to perform regularization processing on the modal function of the fluid conveying pipeline;

[0035] A vibration calculation module, configured to calculate the natural frequency and steady-state displacement response of the fluid conveying pipeline by using the Galerkin method based on the regularized modal function of the fluid conveying pipeline and the micro-element motion equation of the pipeline.

[0036] 3. An electronic device, including a processor and a storage device, wherein the storage device stores multiple instructions, and the processor is configured to read the multiple instructions in the storage device and execute the above method.

[0037] 4. A computer-readable storage medium, storing a computer program, wherein the computer program, when executed by a processor, implements the above method.

[0038] The fluid-structure interaction vibration calculation method, device and equipment provided by the present invention have at least the following beneficial effects:

[0039] (1) When calculating the fluid-structure interaction vibration of the fluid conveying pipeline, this method organically combines the differential transformation method and the Galerkin method, makes full use of their advantages, can be applied to multiple scenarios and does not necessarily require a known type function. By performing regularization processing on the modal function obtained by the differential transformation method, a type function that can be used as the input of the Galerkin method is obtained, and then the Galerkin method is used to superimpose a finite number of modal functions to solve the fluid-induced and forced vibration problems. This calculation method is applicable not only to straight pipes but also to similar problems of bent pipes, and is also applicable to various support forms, with a wide range of applications.

[0040] (2) This method uses the Euler-Bernoulli beam equation to establish a calculation model, and all application scenarios that can conform to the Euler-Bernoulli beam model are applicable to this method to calculate vibration characteristics, with a wider range of applications, and it has a reference effect on the research of fluid-structure interaction problems in other fields.

[0041] (3) This method has a small algorithm scale, simple operation, is easy to transplant and modify, and is easy to implement in engineering. Description of the Drawings

[0042] Figure 1 It is a flowchart of an embodiment of the fluid-structure interaction vibration calculation method provided by the present invention;

[0043] Figure 2Schematic diagram of a structural embodiment of a pipeline micro-element model in the fluid-structure interaction vibration calculation method for the fluid delivery pipeline provided by the present invention;

[0044] Figure 3 Schematic diagram of the result comparison of calculating the natural frequency of a straight fluid delivery pipe by using the fluid-structure interaction vibration calculation method provided by the present invention and the single differential transformation method;

[0045] Figure 4 Schematic diagram of the result comparison of calculating the steady-state displacement response of a straight fluid delivery pipe by using the fluid-structure interaction vibration calculation method provided by the present invention and the Green's function method. Detailed implementation manners

[0046] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings of the specification and specific implementation manners.

[0047] In the following description, specific details such as specific system structures and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present application. However, those skilled in the art should clearly understand that the present application can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present application.

[0048] It should be understood that when used in this specification and the appended claims, the term "including" indicates the presence of the described features, wholes, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or their combinations.

[0049] It should also be understood that the terms used in the specification of the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the specification of the present application and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an", and "the" are intended to include the plural forms.

[0050] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0051] In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application may also be implemented in other ways different from those described herein. Those skilled in the art may make similar extensions without departing from the connotation of the present application. Therefore, the present application is not limited by the specific embodiments disclosed below.

[0052] Embodiment 1:

[0053] A calculation method for fluid-structure interaction vibration of a straight pipe conveying fluid

[0054] Refer to Figure 1 , this method is used to calculate the natural frequency and steady-state displacement response of a fluid-conveying pipeline, and specifically includes the following steps:

[0055] S1. Obtain the parameters of the fluid-conveying pipeline, fluid parameters, and load parameters;

[0056] S2. Based on the parameters of the fluid-conveying pipeline, fluid parameters, and load parameters, establish the motion equation of the pipeline micro-element and its boundary conditions;

[0057] S3. Based on the motion equation of the pipeline micro-element and its boundary conditions, use the differential transformation method to calculate the modal function of the fluid-conveying pipeline;

[0058] S4. Regularize the modal function of the fluid-conveying pipeline;

[0059] S5. Based on the regularized modal function of the fluid-conveying pipeline and the motion equation of the pipeline micro-element, use the Galerkin method to calculate the natural frequency and steady-state displacement response of the fluid-conveying pipeline.

[0060] In this embodiment, a straight pipe conveying fluid is taken as an example to calculate its fluid-structure interaction vibration.

[0061] It should be noted that there are various different support forms for a straight pipe conveying fluid, including but not limited to: cantilever type, fixed-fixed type, fixed-simply supported type, and simply supported-simply supported type. In this embodiment, the above four typical support forms are taken as examples to introduce the calculation method for fluid-structure interaction vibration of a straight pipe conveying fluid.

[0062] Specifically, in step S1, the obtained parameters of the straight pipe conveying fluid include the length of the straight pipe conveying fluid, the shear force and bending moment in the cross-section, the inertial force per unit length of the straight pipe, the mass per unit length of the straight pipe, the elastic modulus of the pipe material, and the moment of inertia of the cross-section. The obtained fluid parameters include the force exerted by the fluid on the straight pipe per unit length, the mass of the fluid per unit length, and the average fluid velocity. The obtained load parameter is the external load distribution.

[0063] In step S2, the motion equation of the straight pipe microelement is established based on the Euler-Bernoulli beam model. The motion of the slender straight pipe conveying fluid is regarded as the Euler-Bernoulli beam model, and the flow of the internal fluid is regarded as a plug flow with a constant flow velocity and density. According to the dynamic-static method, the motion equation of the straight pipe microelement is established, and the force of the fluid microelement on the straight pipe microelement, the load on the straight pipe microelement other than the fluid force, and the inertial forces of both are considered. Refer to Figure 2 , if the straight pipe conveying fluid with a circular cross-section bears a distributed load, its length is L, w and x represent the lateral displacement and the coordinate in the axial direction respectively. Now, a microelement with a length of dx is taken, and its mechanical model is as Figure 2 shown. Among them, Q and M represent the shear force and the bending moment in the cross-section respectively, f I is the inertial force of the straight pipe per unit length, f f represents the force exerted by the fluid on the straight pipe per unit length, and p represents the distributed load.

[0064] The motion equation of the straight pipe microelement is expressed by the following formula:

[0065]

[0066] In the formula, E and I are the elastic modulus and the moment of inertia of the cross-section of the pipe material respectively, U represents the average flow velocity in the cross-section, t is the time, m f and m p are the masses of the straight pipe per unit length and the fluid respectively, w and x represent the lateral displacement and the coordinate in the axial direction respectively, and p represents the distributed load.

[0067] The boundary conditions of four typical support forms can be expressed as follows:

[0068] Cantilever type: w(0, t) = w′(0, t) = w″(L, t) = w″′(L, t) = 0; (2)

[0069] Fixed-fixed type: w(0, t) = w′(0, t) = w(L, t) = w′(L, t) = 0; (3)

[0070] Fixed-simply supported type: w(0, t) = w′(0, t) = w(L, t) = w″(L, t) = 0; (4)

[0071] Simply supported-simply supported type: w(0, t) = w″(0, t) = w(L, t) = w″(L, t) = 0; (5)

[0072] In the formula, L represents the length of the straight pipe conveying fluid.

[0073] As a preferred embodiment, after step S2, it further includes: performing non-dimensionalization on the motion equation of the straight pipe micro-element and its boundary conditions. Non-dimensionalizing the motion equation of the straight pipe micro-element and the boundary condition equations of four typical support forms is for facilitating the derivation and calculation in subsequent steps. In subsequent steps, the non-dimensionalized equations are used for subsequent operations.

[0074] Specifically, the following variables are introduced:

[0075]

[0076] Using equation (6) to non-dimensionalize each physical quantity in equations (1)-(5), the motion equation of the straight pipe micro-element and the boundary conditions under four support forms can be obtained respectively:

[0077] Motion equation of the straight pipe micro-element:

[0078] Cantilever type: η(0,τ) = η′(0,τ) = η″(1,τ) = η″′(1,τ) = 0; (8)

[0079] Fixed-fixed type: η(0,τ) = η′(0,τ) = η(1,τ) = η′(1,τ) = 0; (9)

[0080] Fixed-simply supported type: η(0,τ) = η′(0,τ) = η(1,τ) = η″(1,τ) = 0; (10)

[0081] Simply supported-simply supported type: η(0,τ) = η″(0,τ) = η(1,τ) = η″(1,τ) = 0; (11)

[0082] Preferably, step S3 includes:

[0083] S31. Removing the fluid quantity and external load quantity in the motion equation of the straight pipe micro-element to obtain the free vibration differential equation of the straight pipe;

[0084] S32. Separating the time quantity and space quantity in the free vibration differential equation of the straight pipe;

[0085] S33. Performing differential transformation on the space quantity to obtain the characteristic solution of the free vibration differential equation of the straight pipe, and further obtaining the mode function of the fluid-conveying straight pipe.

[0086] Specifically, in step S31, after removing the fluid quantity and external load quantity, the free vibration differential equation of the Euler-Bernoulli beam corresponding to equation (7) is:

[0087]

[0088] In step S32, the solution of formula (12) can be expressed as:

[0089] η(ξ,τ)=y(ξ)exp(iωτ) (13)

[0090] In the formula, represents the dimensionless characteristic solution, and m b represents the mass of a unit length beam made of the same material and with the same outer diameter as the straight pipe.

[0091] Among them, y(ξ) is the spatial quantity, and exp(iωτ) is the time quantity, separating the time quantity and the spatial quantity for the free vibration differential equation of the straight pipe.

[0092] In step S33, based on the principle of the differential transformation method, ω n (representing the nth natural frequency) under different support forms can be derived, and at the same time, the corresponding modal functions can be obtained as follows:

[0093] Cantilever type:

[0094] Fixed-fixed type:

[0095] Fixed-simply supported type:

[0096] Simply supported-simply supported type:

[0097] In the formula, N0 represents the number of iterations in the differential transformation method.

[0098] In step S4, the modal function is not directly substituted into the Galerkin method. It needs to be regularized by the following formula before use, that is:

[0099]

[0100] Among them, y n (ξ) is the nth order modal function of the fluid conveying pipeline, represents the nth order modal function of the fluid conveying pipeline after regularization processing.

[0101] In the Galerkin method, it is necessary to solve the differential equation by superimposing several regularized shape functions. Therefore, the modal function of the fluid conveying straight pipe obtained in step S3 needs to be regularized, and the result is regarded as the shape function in the Galerkin method for subsequent analysis and solution.

[0102] Preferably, step S5 includes:

[0103] S51. Remove the external load quantity in the motion equation of the straight pipe microelement to obtain the fluid-induced motion equation;

[0104] S52. Perform variable separation and simplification on the fluid-induced motion equation to obtain the stiffness matrix, mass matrix, and damping matrix, and then calculate the natural frequency of the straight pipe conveying fluid;

[0105] S53. Retain the external load quantity in the motion equation of the straight pipe microelement, perform variable separation and simplification to obtain the stiffness matrix, mass matrix, damping matrix, and external load matrix, and then calculate the steady-state displacement response of the straight pipe conveying fluid.

[0106] Based on the principle of the Galerkin method, the solution of Equation (7) can be expressed as follows:

[0107]

[0108] where N represents the number of shape functions, represents the nth shape function, that is, the modal function in the regular form mentioned in Equation (18), and q n (τ) is the time-dependent term.

[0109] Through simplification, finally, we can obtain:

[0110]

[0111] where K, G, and M are the stiffness matrix, damping matrix, and mass matrix respectively, and f is the external load matrix.

[0112] The elements of the stiffness matrix, damping matrix, mass matrix, and external load matrix of the straight pipe conveying fluid are respectively expressed as:

[0113]

[0114] where K mn , G mn , M mn , f mn respectively represent the elements of the mth row and nth column of the stiffness matrix, damping matrix, mass matrix, and external load matrix of the straight pipe conveying fluid. ξ, β, u, τ, and f(ξ,τ) are all dimensionless quantities introduced in the dimensionless treatment, represents the nth shape function, represents the mth shape function, and the shape function is the modal function of the regularized straight pipe conveying fluid.

[0115] Let f N×1 = 0 to obtain the fluid-induced motion equation in step S51, and the fluid-induced motion equation is expressed as follows:

[0116]

[0117] The solution of Equation (22) can be assumed to be:

[0118] q = q0exp(iωτ) (23)

[0119] In the formula, represents the dimensionless characteristic solution of the straight pipe.

[0120] Substitute the formula into the formula, and noting that q0 is not zero, the characteristic equation is obtained as:

[0121] |K + iωG - ω 2 M| = 0 (24)

[0122] By numerically solving Equation (24), the characteristic solutions ω i (i = 1, 2, 3, …, N) can be obtained. The real part of the characteristic solutions is the dimensionless natural frequency of the straight pipe.

[0123] In the above steps, when ignoring the external load, the straight pipe conveying fluid is only affected by the force of the internal fluid, and the motion equation of the infinitesimal element of the straight pipe is homogeneous. Using the Galerkin method, first, the modal function after regularization in step S4 is used to separate variables for this homogeneous differential equation, and then through simplification, the stiffness matrix, mass matrix, and damping matrix of the system can be constructed, and further the characteristic equation of the system and the expression for solving the characteristic solutions can be derived. The characteristic solutions obtained here are complex numbers, and the real part represents the natural frequency during the vibration of the straight pipe.

[0124] Correspondingly, in step S53, the external load quantity in the motion equation of the infinitesimal element of the straight pipe is retained to obtain the forced vibration equation. When considering the external load quantity, the straight pipe conveying fluid is affected by both the internal fluid and the external load, and the forced vibration equation at this time is non - homogeneous. Using the Galerkin method, first, the modal function after regularization in step S4 is used to separate variables for this equation, and then through simplification, the stiffness matrix, mass matrix, damping matrix, and external load matrix of the system can be constructed, and further the displacement response of the system during steady - state vibration can be derived. The displacement response obtained here is still a complex number, and through the real - part extraction step, the steady - state displacement response of the straight pipe conveying fluid in the time domain can be obtained.

[0125] Example Two:

[0126] A calculation method for fluid - structure interaction vibration of a pipe conveying fluid with a bend

[0127] In this example, a pipe conveying fluid with a bend is taken as an example to calculate its fluid - structure interaction vibration. The pipeline is a pipe conveying fluid with a bend.

[0128] It should be noted that there are various different support forms for the fluid-conveying elbow. Different from the fluid-conveying straight pipe, the support forms include but are not limited to: fixed-fixed, fixed-simply supported, and simply supported-simply supported. In this embodiment, taking the above three typical support forms as examples, the calculation method for the fluid-structure interaction vibration of the fluid-conveying elbow is introduced. For the parts that are the same as those in the method steps of Embodiment 1, they will not be elaborated in Embodiment 2.

[0129] In step S2, the motion equation and its boundary conditions of the elbow micro-element after non-dimensionalization can be expressed as follows.

[0130] The non-dimensional motion equation of the elbow is:

[0131]

[0132] Wherein,

[0133]

[0134] In the formula, E and I are respectively the elastic modulus and the cross-sectional moment of inertia of the pipe material, w represents the tangential displacement, R is the radius of the axis of the elbow, U represents the average flow velocity in the cross-section, Θ and t are respectively the angular coordinate and time, m f and m p are respectively the mass per unit length of the pipeline and the fluid, θ c represents the included angle of the elbow, and γ represents the included angle between the external load and the tangential direction of the center line of the elbow.

[0135] The boundary conditions of the typical support forms can be respectively expressed as:

[0136] Fixed-fixed:

[0137] Fixed-simply supported:

[0138] Simply supported-simply supported:

[0139] Preferably, step S3 includes:

[0140] S31. Remove the fluid quantity and the external load quantity in the motion equation of the elbow micro-element to obtain the differential equation of the free vibration of the elbow;

[0141] S32. Separate the time quantity and the space quantity in the differential equation of the free vibration of the elbow;

[0142] S33. Perform differential transformation on the space quantity to obtain the characteristic solution of the differential equation of the free vibration of the elbow, and then obtain the modal function of the fluid-conveying elbow.

[0143] In step S31, by removing the fluid quantity and the external load quantity, the differential equation of free vibration of the Euler - Bernoulli beam corresponding to Equation (25) is obtained as follows:

[0144]

[0145] In step S32, the solution of Equation (29) can be expressed as:

[0146] ξ(θ,τ) = y(θ)exp(iωτ); (30)

[0147] In the formula, represents the dimensionless characteristic solution, and m b represents the mass of a unit - length beam with the same material and outer diameter as the pipeline.

[0148] In step S33, based on the principle of the differential transform method, ω n (representing the n - th natural frequency) under different support forms can be derived, and at the same time, the expression of the corresponding mode function y n (θ) can be obtained.

[0149] Preferably, step S5 includes:

[0150] S51. Remove the external load quantity in the motion equation of the elbow micro - element to obtain the fluid - induced motion equation;

[0151] S52. Perform variable separation and simplification on the fluid - induced motion equation to obtain the elbow stiffness matrix, elbow mass matrix, and elbow damping matrix, and then calculate the natural frequency of the fluid - conveying elbow;

[0152] S53. Retain the external load quantity in the motion equation of the elbow micro - element, and perform variable separation and simplification to obtain the elbow stiffness matrix, elbow mass matrix, elbow damping matrix, and elbow external load matrix, and then calculate the steady - state displacement response of the fluid - conveying elbow.

[0153] Among them, the elbow stiffness matrix, elbow damping matrix, elbow mass matrix, and elbow external load matrix of the fluid - conveying elbow are respectively expressed as:

[0154]

[0155] It can be seen from Example 1 and Example 2 that the fluid - structure interaction vibration calculation method for the fluid - conveying pipeline provided in this example can be used for straight - pipe calculation and also for elbow calculation, with a wide range of applications.

[0156] Example 3:

[0157] A device for calculating fluid - structure interaction vibration of a fluid - conveying pipeline

[0158] This device includes the following modules:

[0159] A parameter acquisition module, configured to acquire the parameters of the fluid delivery pipeline and the parameters of the fluid;

[0160] A model establishment module, configured to establish a pipeline element motion equation and its boundary conditions based on the parameters of the fluid delivery pipeline and the parameters of the fluid;

[0161] A modal function calculation module, configured to calculate the modal function of the fluid delivery pipeline by using the differential transformation method based on the pipeline element motion equation and its boundary conditions;

[0162] A regularization processing module, configured to perform regularization processing on the modal function of the fluid delivery pipeline;

[0163] A vibration calculation module, configured to calculate the natural frequency and steady-state displacement response of the fluid delivery pipeline by using the Galerkin method based on the regularized modal function of the fluid delivery pipeline and the pipeline element motion equation.

[0164] Embodiment 4:

[0165] An electronic device

[0166] The electronic device includes a processor and a storage device. A plurality of instructions are stored in the storage device, and the processor is configured to read the plurality of instructions in the storage device and execute the above method.

[0167] Embodiment 5:

[0168] A computer-readable storage medium

[0169] The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the above method is implemented.

[0170] The beneficial effects of the present invention will be further described below through a comparative test experiment.

[0171] A section of real water supply straight pipe is taken as the research object, and its data is shown in Table 1.

[0172] Table 1 Physical parameters of a section of water supply pipeline

[0173]

[0174] The parameters of the external load are: f0 = 0.686, a = 0.5, u = 1.868.

[0175] At the same time, the method provided by the present invention and the single differential transformation method are used to calculate the relationship between the natural frequencies of the straight pipes conveying fluid with four typical support forms under the above working conditions and the fluid flow velocity. During the process, the number of shape functions N = 6 is taken; at the same time, the method of the present invention and the Green's function method are used to calculate the relationship between the steady-state displacement responses of the straight pipes conveying fluid with four typical support forms under the above working conditions and the coordinates. During the process, the number of shape functions N = 6 is still taken.

[0176] Analysis of evaluation results:

[0177] The relationship between the natural frequencies and the fluid flow velocity is as Figure 3 shown. The results of the smooth curves in the figure come from the differential transformation method, and the results of the marked points come from the method of the present invention. It can be seen that the calculation results of the two methods are in good agreement. The relationship between the steady-state displacement responses and the coordinates is as Figure 4 shown. The results of the smooth curves in the figure come from the method of the present invention, and the results of the marked points come from the Green's function method. It can be seen that the calculation results of the two methods are still in very good agreement.

[0178] It can be seen from this that the embodiments of the present invention provide a new vibration calculation method for fluid-conveying pipelines. Its technical effect can basically reach the level of the existing technology, and the algorithm has a small scale, simple operation, is easy to transplant and modify, and is easy to implement in engineering.

[0179] Moreover, in the prior art, there are only methods for calculating the fluid-structure interaction vibration characteristics of fluid-conveying pipelines by using a single differential transformation method, Green's function method or Galerkin method, and there is no method that combines the differential transformation method and the Galerkin method. Since the application of the Galerkin method requires known shape functions, and the differential transformation method can only calculate homogeneous equations, the requirements for the known conditions are relatively harsh when applying the Galerkin method or the single differential transformation method in the prior art, and the application scenarios are greatly limited. The method provided in this embodiment uses the modal functions obtained by regularizing the differential transformation method, and can handle the vibration calculation of fluid-conveying pipelines in application scenarios with various known conditions, and has a wider application range. Further, this method uses the Euler-Bernoulli beam equation to establish a calculation model, and all application scenarios that can conform to the Euler-Bernoulli beam model are applicable to this method to calculate the vibration characteristics, with a wider application range, and it has a reference effect on the research of fluid-structure interaction problems in other fields.

[0180] It should be understood that in the embodiments of this application, the so-called processor may be a central processing unit (CPU), and this processor may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or this processor may also be any conventional processor, etc.

[0181] The memory may include a read-only memory, a flash memory, and a random access memory, and provide instructions and data to the processor. A part or all of the memory may also include a non-volatile random access memory.

[0182] It should be understood that if the above integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it may be stored in a computer-readable storage medium. Based on such an understanding, to implement all or part of the processes in the above method embodiments of this application, it may also be completed by instructing relevant hardware through a computer program. The above computer program may be stored in a computer-readable storage medium. When the computer program is executed by the processor, the steps of the above method embodiments may be implemented. Among them, the above computer program includes computer program code, and the above computer program code may be in the form of source code, object code, executable file, or some intermediate form, etc. The above computer-readable medium may include: any entity or device capable of carrying the above computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disc, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content included in the above computer-readable storage medium may be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction.

[0183] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made to these embodiments by those skilled in the art once they learn of the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art can make various changes and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these modifications and variations.

Claims

1. A fluid-solid coupling vibration calculation method for a fluid delivery pipeline, used to calculate the natural frequency and steady-state displacement response of the fluid delivery pipeline, characterized in that: The method includes the following steps: S1. Obtain the parameters of the fluid delivery pipeline, fluid parameters, and load parameters; S2. Based on the parameters of the fluid delivery pipeline, fluid parameters, and load parameters, establish the micro-element motion equation of the pipeline and its boundary conditions; S3. Based on the micro-element motion equation of the pipeline and its boundary conditions, use the differential transformation method to calculate the modal function of the fluid delivery pipeline; S4. Perform regularization processing on the modal function of the fluid delivery pipeline; S5. Based on the regularized modal function of the fluid delivery pipeline and the micro-element motion equation of the pipeline, use the Galerkin method to calculate the natural frequency and steady-state displacement response of the fluid delivery pipeline; Step S5 includes: S51. Remove the external load quantity from the micro-element motion equation of the pipeline to obtain the fluid-induced motion equation; S52. Perform variable separation and simplification on the fluid-induced motion equation to obtain the stiffness matrix, mass matrix, and damping matrix, and then calculate the natural frequency of the fluid delivery pipeline; S53. Retain the external load quantity in the micro-element motion equation of the pipeline, and perform variable separation and simplification to obtain the stiffness matrix, mass matrix, damping matrix, and external load matrix, and then calculate the steady-state displacement response of the fluid delivery pipeline; The fluid delivery pipeline is a straight fluid delivery pipeline, and the elements of the stiffness matrix, damping matrix, mass matrix, and external load matrix of the straight fluid delivery pipeline are respectively expressed as: Among them, respectively represent the elements of the stiffness matrix, damping matrix, mass matrix of the straight pipe for fluid transportation, and the m row and n column of the external load matrix. They are all non-dimensional quantities introduced in the non-dimensionalization process. represents the n th shape function. represents the m th shape function, and the shape function is the modal function of the fluid-transporting pipeline after regularization. The regularization processing of the modal function of the fluid delivery pipeline is represented by the following formula: Among them, is the n order modal function of the fluid conveying pipeline, represents the n order modal function of the fluid conveying pipeline after regularization processing.

2. The method according to claim 1, wherein Based on the Euler-Bernoulli beam model, establish the micro-element motion equation of the pipeline.

3. The method according to claim 1, characterized in that, After step S2, it further includes: performing non-dimensionalization processing on the micro-element motion equation of the pipeline and its boundary conditions.

4. The method according to claim 1, characterized in that Step S3 includes: S31. Remove the fluid quantity and external load quantity from the micro-element motion equation of the pipeline to obtain the differential equation of free vibration of the pipeline; S32. Separate the time quantity and space quantity of the differential equation of free vibration of the pipeline; S33. Perform differential transformation on the space quantity to obtain the characteristic solution of the differential equation of free vibration of the pipeline, and then obtain the modal function of the fluid delivery pipeline.

5. An electronic device, comprising a processor and a storage device, characterized in that, The storage device stores multiple instructions, and the processor is configured to read the multiple instructions in the storage device and execute the method according to any one of claims 1-4.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method according to any one of claims 1-4.

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