A multi-clip spatial flow pipeline system modeling and sensitive clip identification method

Abstract

The present application belongs to the technical field of pipeline dynamics and vibration analysis, and particularly relates to a multi-clip spatial flow pipeline system modeling and sensitive clip identification method. A spatial flow pipeline dynamics equation is established based on a three-dimensional ANCF beam element; a single-clip equivalent stiffness model and a double-clip equivalent stiffness model are established through the virtual work principle; the single-clip support and double-clip constraint action are introduced into the spatial flow pipeline dynamics equation to obtain a multi-clip spatial flow pipeline system dynamics equation; the natural frequency and modal shape of the multi-clip spatial flow pipeline system are obtained by solving the eigenvalue problem corresponding to the multi-clip spatial flow pipeline system dynamics equation; and the sensitive clip is identified based on the clip position sensitivity, and the frequency turning phenomenon caused by the parameter change of the sensitive clip can be analyzed.

Description

Technical Field

[0001] This invention relates to the field of pipeline dynamics and vibration analysis technology, and in particular to a method for modeling and identifying sensitive clamps in a multi-clamp spatial flow pipeline system. Background Technology

[0002] External piping of aircraft engines, pipelines for ship transportation, and transmission pipelines in energy equipment typically exhibit significant three-dimensional spatial bending configurations and are simultaneously subjected to multiple local constraints, including pipe joints, end constraints, single clamp supports, and double clamp connections. Multiple clamp supports can significantly alter the local stiffness distribution and inter-pipe coupling relationships of the piping system, thereby affecting the system's vibration characteristics.

[0003] While existing modeling methods for spatial transmission pipelines can handle some issues related to bends, straight pipes, supports, or local connections, they still have the following shortcomings in complex spatial multi-pipeline assemblies: First, different pipe segments, pipe joints, single clamps, and double clamps are usually modeled separately, making it difficult to achieve constrained assembly within a unified generalized coordinate framework; second, clamps have certain installation widths, directional stiffness, and rotational constraint characteristics, and traditional point support or simplified spring models cannot simultaneously describe the local translational and rotational constraints of clamps; third, double clamps not only provide local support but also coordinate the relative translation and relative rotation angles between adjacent pipes, and existing models do not adequately describe this type of inter-pipe coupling mechanism; fourth, there is a lack of effective sensitive clamp identification methods in multi-clamp spatial transmission pipeline systems.

[0004] Existing pipeline modeling methods mainly include semi-analytical methods, transfer matrix methods, finite element methods, and ANCF modeling methods. Semi-analytical methods offer clear physical meaning and facilitate parameter analysis, typically by establishing the governing equations of the pipeline and solving them using the Galerkin or Rayleigh-Ritz methods. Existing semi-analytical models for multi-clamp spatial pipelines can be used for vibration analysis and clamp layout optimization. The transfer matrix method is suitable for segmented, multi-span systems, has high computational efficiency, and has been used for vibration transmission characteristic analysis and experimental verification of parallel pipelines. The finite element method offers strong flexibility in handling complex boundaries and engineering structures, and can be used for the dynamic analysis of multi-span pipelines and flexible components.

[0005] For pipeline modeling, "Zhang Y, Sun W, Ma H, et al. Semi-analytical modeling and vibration analysis for U-shaped, Z-shaped and regular spatial pipelines supported by multiple clamps. European Journal of Mechanics / A Solids, 2023, 97: 104797" proposed a semi-analytical modeling method for U-shaped, Z-shaped and regular spatial pipelines, and discretized characteristic components such as straight pipes, bends, clamps and connecting springs for vibration analysis and clamp layout optimization; "Guo XM, Ge H, Xiao CL, et al. Vibration transmission characteristics analysis of the parallel fluid-conveying pipes system: Numerical and experimental studies. Mechanical Systems and Signal Processing, 2022, 177: 109180" used the transfer matrix method to establish and experimentally verify the vibration transmission model of liquid-filled parallel pipelines; addressing the problem of identifying the stiffness of flexible components and clamps in pipelines, "Wang ZC, Gao PX, Zhou ZD, et al. A numerically stable flexural dynamics model" The paper "of complex multi-span fluid-conveying pipes with flexible components and its application to clamp stiffness identification. Thin-Walled Structures, 2024, 195: 111488" establishes a numerically stable dynamic model for multi-span fluid-conveying pipes; related research has also been conducted on issues such as clamp position optimization, nonlinear clamps, and clamp parameterization modeling.

[0006] ANCF (Anti-Normal Cross-Sectional Fiber) can handle large displacement and large rotation angle problems, making it well-suited for dynamic analysis of conveying pipelines. The paper "Yuan JR, Ding H. Dynamic model of curved pipe conveying fluid based on the absolute nodal coordinate formulation. International Journal of Mechanical Sciences, 2022, 232: 107625" established a dynamic model of a curved conveying pipe based on ANCF and further applied it to the large-amplitude vibration analysis of conveying pipelines with arbitrary initial spatial configurations and cantilevered conveying pipelines with arbitrary initial configurations. However, existing ANCF research mainly focuses on single-pipe systems with relatively simple boundary conditions. For complex spatial multi-pipe assemblies that simultaneously include multiple clamps, pipe joints, and inter-pipe connections, there is still a lack of unified clamp constraints and directly assembleable equivalent stiffness models.

[0007] The closest existing technologies to this invention are semi-analytical modeling methods for spatial pipelines, vibration suppression methods for spatial pipelines under varying clamp configurations, methods for analyzing the influence of clamp installation positions, nonlinear clamp modeling methods, parametric clamp modeling methods, and three-dimensional ANCF transmission pipeline modeling methods. These methods provide a foundation for pipeline modeling and clamp parameter analysis, but they have not yet formed a modeling method that uniformly incorporates the influence of single clamp support, inter-clamp coupling, pipe joints, and internal fluids into the ANCF generalized coordinate system, nor have they developed an effective method for clamp sensitivity analysis in multi-clamp spatial transmission pipelines.

[0008] The main drawbacks of existing methods for dynamic modeling and clamp parameter analysis of space transport pipelines can be summarized as follows: (1) In complex spatial multi-pipeline systems, pipes, pipe fittings, single clamps and double clamps are usually handled by different modeling strategies, making it difficult to achieve unified assembly under the same coordinate system. Semi-analytical methods are convenient for parameter analysis, but their scalability is insufficient for arbitrary three-dimensional initial configurations, complex pipe fittings and multi-clamp combinations; solid finite element models have high accuracy, but the modeling and calculation costs are high, which is not conducive to the selection and optimization of a large number of clamp parameters.

[0009] (2) Existing clamp models mostly treat clamps as point supports or local springs, making it difficult to simultaneously consider clamp installation width, local directional stiffness, rotational stiffness, and their directional transformations in the spatial coordinate system. For single clamps, the constraint relationship between the foundation support on local translation and rotation has not yet formed a unified expression that is easy to assemble into the ANCF generalized coordinate system; for double clamps, the influence of relative displacement, relative rotation angle between adjacent pipelines, and clamp mass on the coupled vibration of the system still lacks a systematic description.

[0010] (3) Existing studies on the influence of clamp parameters mainly focus on the rise and fall of natural frequency or changes in vibration stress, and pay less attention to the frequency shift phenomenon that occurs in adjacent modes during parameter changes, lacking an explanation of the mechanism of frequency shift.

[0011] (4) Existing models typically only verify a small number of frequencies or a single clamp state in engineering verification. They lack the ability to predict changes in clamp sensitivity after adjustment of sensitive clamp positions and weakening of key stiffness directions, making it difficult to directly guide the optimization of support layout and vibration control of complex spatial pipelines.

[0012] To address the aforementioned issues, this invention proposes a modeling and sensitive clamp identification method for multi-clamp spatial flow transmission pipeline systems. This method equates the local constraints of clamps to ANCF generalized coordinates and further combines position sensitivity analysis, modal correlation analysis, and modal strain energy analysis to achieve rapid modeling, sensitive clamp identification, and frequency shifting mechanism revelation for complex multi-clamp spatial flow transmission pipeline systems. Summary of the Invention

[0013] The technical problem to be solved by this invention is to propose a modeling and sensitive clamp identification method for multi-clamp spatial flow pipeline systems, which integrates spatial pipe segments, pipe joints, single clamps, double clamps, and internal fluid effects into the generalized coordinate framework of Absolute Nodal Coordinate Formulation (ANCF); establishes equivalent translational and rotational stiffness mapping methods for single and double clamps; identifies sensitive clamps; and reveals the clamp-mediated frequency shifting mechanism through modal mode evolution, modal confidence criterion (MAC), and modal strain energy.

[0014] The technical solution of this invention is as follows: A method for modeling and identifying sensitive clamps in a multi-clamp spatial transport pipeline system, comprising the following steps: establishing the dynamic equation of the spatial transport pipeline based on three-dimensional ANCF beam elements; establishing an equivalent stiffness model for a single clamp and an equivalent stiffness model for a double clamp using the principle of virtual work; introducing the support of a single clamp and the constraint of a double clamp into the dynamic equation of the spatial transport pipeline to obtain the dynamic equation of the multi-clamp spatial transport pipeline system; obtaining the natural frequencies and mode shapes of the multi-clamp spatial transport pipeline system by solving the eigenvalue problem corresponding to the dynamic equation of the multi-clamp spatial transport pipeline system; and identifying sensitive clamps based on clamp position sensitivity.

[0015] The process of establishing the dynamic equations of the space transport pipeline is as follows: The three-dimensional ANCF beam element contains two nodes. i and j ,node i coordinate vector r i and nodes j coordinate vector r jEach element contains 7 degrees of freedom; the coordinate vector representation of a 3D ANCF beam element is as follows: (1) in, r i and r j The expression is: (2) in, r i1 , r i2 and r i3 For nodes i The three position coordinates, θ i1 For nodes i The corner , and For nodes i The gradient coordinates of the three positions; r j1 , r j2 and r j3 For nodes j The three position coordinates, θ j1 For nodes j The corner, , and For nodes j The gradient coordinates of the three positions; Position vector of any point on the centerline of any three-dimensional ANCF beam element r m Through the shape function matrix at that position S m With the coordinate vector of this three-dimensional ANCF beam element e Interpolation yields, i.e.: (3) The absolute velocity vector of the fluid element at any point on the centerline of any three-dimensional ANCF beam element. v f for: (4) in, v For fluid velocity, Let be the velocity vector of any point on the centerline of a three-dimensional ANCF beam element. r m0Let be the position vector of any point on the center line of a three-dimensional ANCF beam element under the reference configuration, and the superscript ′ indicates the derivative with respect to the axial coordinate. The kinetic energy and strain energy of the three-dimensional ANCF beam element, as well as the internal fluid kinetic energy, are obtained from the coordinate vector of the three-dimensional ANCF beam element and the absolute velocity vector of the fluid element. Substituting these into the extended Lagrange equation, the dynamic equations of the space transport pipeline are established: (5) In the formula, M For the quality matrix, V The term is the geometrically nonlinear inertia caused by the rotation of the pipe cross-section. G This is the fluid velocity-dependent gyroscope matrix. K The stiffness matrix is ​​related to the internal fluid velocity. N ( q () represents the nonlinear elastic restoring force vector caused by axial tension, bending, and torsion of the pipeline. q , and These are the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the pipeline system, respectively.

[0016] The equivalent stiffness model of the single clamp is established as follows: For a single clamp that fixes the pipeline to the casing, it is equivalent to two sets of spring elements located at the left and right boundaries of the clamping area. Each set of spring elements simultaneously includes local translational stiffness and local rotational stiffness. The generalized coordinate vector of the three-dimensional ANCF beam element is mapped to the local rotational stiffness degree of freedom of the spring element. The displacement increment, torsion angle increment, and slope increment at the position of the single clamp are respectively Δ r c , and Based on the reference configuration, the equivalent rotation increment of a single clamp section is defined as follows: (6) In the formula, t 0 is the unit tangent vector in the reference configuration. J 0 is the tangential modulus of the reference centerline, [ t 0] × for t The antisymmetric matrix corresponding to 0, This is the mapping matrix between the equivalent rotation angle increment of a single clamp section and the generalized coordinate increment; This is the shape function matrix corresponding to the torsion angle at the single clamp position; The mapping matrix between the slope increment and the generalized coordinate increment at the single clamp position; Δ e The generalized coordinate increment vector of the three-dimensional ANCF beam element containing the single clamp; selected with... tNon-parallel reference vectors are used, and a local orthogonal basis is obtained through Gram-Schmidt orthogonalization. An orthogonal transformation matrix from the local coordinate system to the global coordinate system of a single clamp is then constructed. Q c ; The translational stiffness matrix of each spring element in the local coordinate system of a single clamp is: The rotational stiffness matrix is ,pass Q c After transforming to the global coordinate system, the translational stiffness matrix in the global coordinate system is obtained. rotational stiffness matrix in global coordinate system The transformation relationship is as follows: (7) Potential energy of two sets of spring units in a single clamp for: (8) Substituting equations (6) and (7) into equation (8), and based on the second variation of the generalized coordinates using potential energy, we obtain the... a The equivalent stiffness matrix of a single clamp is: (9) In the formula, S r This is the shape function matrix corresponding to the displacement at the single clamp position.

[0017] The equivalent stiffness model for the double clamps is established as follows: for a double clamp connecting two adjacent pipes, it is considered as a pipe coupling group; the generalized coordinate increments of the pipes on both sides of the double clamp are Δ e A and Δ e B The shape function matrices are respectively S A and S B The relative displacement increment on both sides of the double clamps The relative equivalent rotation angle increment on both sides of the double clamp for: (10) Where, Δ e AB =[Δ e A ;Δ e B ]; , is the mapping matrix between the relative displacement increments on both sides of the double clamp and the generalized coordinate increments of the pipelines on both sides of the double clamp; ; and These are the mapping matrices between the relative equivalent rotation angle increments on both sides of the double clamp and the generalized coordinate increments of the pipelines on both sides of the double clamp, respectively. After projecting the relative displacement increments and the relative equivalent rotation increments on both sides of the double clamps onto the local coordinate system, and combining them with the local translational stiffness matrix of the double clamps... and the local rotational stiffness matrix of the double clamp , obtained the l The equivalent stiffness matrix of the double clamps: (11) The first l Double clamp quality m l Mass is applied uniformly to the translational degrees of freedom of the four clamping ends on the left and right boundaries of the pipeline on both sides of the double clamp, with each clamping end receiving a mass distribution. m l / 4, forming the equivalent mass matrix of the double clamps. M d .

[0018] The equivalent stiffness matrix of a single clamp, the equivalent stiffness matrix of a double clamp, and the mass of a double clamp are assembled into the dynamic equations of a space transport pipeline: (12) In the formula, K c The equivalent stiffness matrix after assembling all single clamps. K d The equivalent stiffness matrix after all double clamps are assembled is given; by solving the eigenvalue problem of equation (12), the natural frequency and mode shape of the multi-clamp space transport pipeline system are obtained.

[0019] The method of identifying sensitive clamps based on clamp position sensitivity involves changing the position of a single clamp or a double clamp on the pipeline while keeping other parameters constant, calculating the rate of change of each frequency, and determining the sensitive clamp through the rate of change of the natural frequency.

[0020] The rate of change of frequency: (13) In the formula, For reference, the position of the clamp is below the first n First natural frequency, To only change the first b The first clamp position obtained after the first clamp position n The natural frequency is 1, and the clamp can be any single clamp or double clamp.

[0021] Compared with existing dynamic analysis methods for multi-clamp space transport pipelines, the present invention has the following advantages: (1) Strong uniformity. This invention unifies spatial pipelines, pipe joints, single clamps, double clamps and internal fluid effects into the ANCF generalized coordinate framework, avoiding assembly difficulties caused by different components using different coordinates or different discrete systems.

[0022] (2) The description of clamp constraints is more complete. This invention not only considers the translational constraints of clamps, but also the rotational constraints of clamps and the installation width; it can describe not only the ground support effect of a single clamp, but also the relative translational and relative angular coupling between pipes caused by double clamps.

[0023] (3) High computational efficiency. Compared with the solid finite element model that includes metal cable ties, metal felt, bolts, pipes and supports, the present invention, by using equivalent constraint modeling, can significantly reduce the amount of computation while maintaining the accuracy of low-order modal prediction. Compared with the solid finite element model, the model of the present invention takes about 0.23s from modeling to natural frequency calculation, while the solid finite element model takes about 365s, which improves the computational efficiency by about 1587 times.

[0024] (4) It can reveal the frequency shift mechanism. Existing methods mostly focus on the analysis of frequency change trends. This invention further explains the frequency shift process from the perspectives of modal exchange, reconstruction of dominant vibration regions, and redistribution of modal strain energy, which can provide a clearer theoretical basis for support layout optimization and vibration control. Attached Figure Description

[0025] Figure 1 Schematic diagram of a multi-clamp space conveying pipeline system; Figure 2 Schematic diagrams of the single clamp equivalent model and the double clamp equivalent model; (a) is the single clamp equivalent model, and (b) is the double clamp equivalent model; Figure 3 (a) is a schematic diagram of a three-dimensional ANCF beam element in the generalized coordinate system, and (b) is a schematic diagram of a three-dimensional ANCF beam element in the element coordinate system. Figure 4 The results are as follows: (a) shows a single clamp, and (b) shows a double clamp. Figure 5 The simulation and experimental comparison graphs show the frequency changes before and after the adjustment of the most sensitive clamp. Figure 6 The effect of the position of the sensitive clamp on the natural frequency is shown in (a) and (b) is a magnified view of the 4th and 5th order natural frequencies.

[0026] Figure 7The diagram illustrates the mode switching associated with frequency shifting, where (a) represents M5-1; (b) represents M5-2; (c) represents M5-3; (d) represents M4-1; (e) represents M4-2; and (f) represents M4-3. Figure 8 The changes in the proportion of strain energy in each pipeline before and after the frequency shift are shown in (a) and (b). Detailed Implementation

[0027] This invention provides a method for modeling and identifying sensitive clamps in multi-clamp spatial transmission pipeline systems. It addresses the layout of multi-clamp spatial transmission pipeline systems consisting of multiple spatial pipe segments, pipe fittings, single clamps, and double clamps, such as... Figure 1 As shown; the equivalent models for a single clamp and a double clamp are as follows: Figure 2 As shown. The dynamic equations of a spatial transport pipeline are established based on three-dimensional ANCF beam elements; equivalent stiffness models for a single clamp and a double clamp are established using the principle of virtual work; the support of a single clamp and the constraint of a double clamp are introduced into the dynamic equations of the spatial transport pipeline to obtain the dynamic equations of a multi-clamp spatial transport pipeline system; the natural frequencies and mode shapes of the multi-clamp spatial transport pipeline system are obtained by solving the eigenvalue problem corresponding to the dynamic equations of the multi-clamp spatial transport pipeline system; sensitive clamps are identified based on clamp position sensitivity, and the frequency shifting mechanism is determined. The specific steps are as follows: Step 1: Establish the dynamic equations of the spatial transport pipeline based on the three-dimensional ANCF beam element; the process of establishing the dynamic equations of the spatial transport pipeline is as follows: A schematic diagram of the three-dimensional ANCF beam element is shown below. Figure 3 As shown, the three-dimensional ANCF beam element contains two nodes. i and j Node coordinate vector r i and r j Each element contains 7 degrees of freedom; the coordinate vector representation of a 3D ANCF beam element is as follows: (1) in, r i and r j The expression is: (2) in, r i1 , r i2 and r i3 For nodes i The three position coordinates, θ i1 For nodesi The corner, , and For nodes i The gradient coordinates of the three positions; r j1 , r j2 and r j3 For nodes j The three position coordinates, θ j1 For nodes j The corner, , and For nodes j The gradient coordinates of the three positions.

[0028] Position vector of any point on the centerline of any three-dimensional ANCF beam element r m Through the shape function matrix at that position S m With the coordinate vector of this three-dimensional ANCF beam element e Interpolation yields, i.e.: (3) The absolute velocity vector of the fluid element at any point on the centerline of any three-dimensional ANCF beam element. v f for: (4) in, v For fluid velocity, Let be the velocity vector of any point on the centerline of a three-dimensional ANCF beam element. r m0 Let be the position vector of any point on the center line of a three-dimensional ANCF beam element under the reference configuration, and the superscript ′ indicates the derivative with respect to the axial coordinate. The kinetic energy and strain energy of the three-dimensional ANCF beam element, as well as the internal fluid kinetic energy, are obtained from the coordinate vector of the three-dimensional ANCF beam element and the absolute velocity vector of the fluid element. Substituting these into the extended Lagrange equation, the dynamic equations of the space transport pipeline are established: (5) In the formula, M For the quality matrix, V The term is the geometrically nonlinear inertia caused by the rotation of the pipe cross-section. G This is the fluid velocity-dependent gyroscope matrix. K The stiffness matrix is ​​related to the internal fluid velocity. N ( q() represents the nonlinear elastic restoring force vector caused by axial tension, bending, and torsion of the pipeline. q , and These are the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the pipeline system, respectively.

[0029] For pipe joints, end joints, and intermediate connectors in actual spatial pipelines, volume equivalence and stepped pipe equivalence methods are used to transform them into equivalent structures that can be discretized uniformly with the pipe segments, and their mass and stiffness contributions are assembled into the system matrix. For end pipe joints, fixed boundary constraints are applied according to the actual installation state.

[0030] Step 2: Establish the equivalent stiffness model of a single clamp. For a single clamp connecting the pipeline to the foundation or support fixture, it is equivalent to two sets of discrete spring elements located at the left and right boundaries of the clamping area. Each set of spring elements simultaneously includes local translational stiffness and local rotational stiffness. The equivalent model is shown below. Figure 2 (a) For a single clamp fixing the pipeline to the casing, it is equivalent to two sets of spring elements located at the left and right boundaries of the clamping area. Each set of spring elements simultaneously contains local translational stiffness and local rotational stiffness. Mapping the generalized coordinate vector of the three-dimensional ANCF beam element to the local rotational stiffness degree of freedom of the spring element, the displacement increment, torsion angle increment, and slope increment at the position of the single clamp are respectively Δ r c , and Based on the reference configuration, the equivalent rotation increment of a single clamp section is defined as follows: (6) In the formula, t 0 is the unit tangent vector in the reference configuration. J 0 is the tangential modulus of the reference centerline, [ t 0] × for t The antisymmetric matrix corresponding to 0, This is the mapping matrix between the equivalent rotation angle increment of a single clamp section and the generalized coordinate increment; This is the shape function matrix corresponding to the torsion angle at the single clamp position; The mapping matrix between the slope increment and the generalized coordinate increment at the single clamp position; Δ e The generalized coordinate increment vector of the three-dimensional ANCF beam element containing the single clamp; selected with... t Non-parallel reference vectors are used, and a local orthogonal basis is obtained through Gram-Schmidt orthogonalization. An orthogonal transformation matrix from the local coordinate system to the global coordinate system of a single clamp is then constructed. Q c ; The translational stiffness matrix of each spring element in the local coordinate system of a single clamp is: The rotational stiffness matrix is ,pass Q c After transforming to the global coordinate system, the translational stiffness matrix in the global coordinate system is obtained. rotational stiffness matrix in global coordinate system The transformation relationship is as follows: (7) Potential energy of two sets of spring units in a single clamp for: (8) Substituting equations (6) and (7) into equation (8), and based on the second variation of the generalized coordinates using potential energy, we obtain the... a The equivalent stiffness matrix of a single clamp is: (9) In the formula, S r This is the shape function matrix corresponding to the displacement at the single clamp position.

[0031] Step 3, Equivalent Stiffness Model of Double Clamps. For double clamps connecting two adjacent pipes, they are considered as inter-pipe coupling components. Their equivalent model is shown below. Figure 2 (b). The establishment of the equivalent stiffness model for the double clamp is specifically as follows: for a double clamp connecting two adjacent pipes, it is considered as a pipe coupling group; the generalized coordinate increments of the pipes on both sides of the double clamp are Δ e A and Δ e B The shape function matrices are respectively S A and S B The relative displacement increment on both sides of the double clamps The relative equivalent rotation angle increment on both sides of the double clamp for: (10) Where, Δ e AB =[Δ e A ;Δ e B ]; , is the mapping matrix between the relative displacement increments on both sides of the double clamp and the generalized coordinate increments of the pipelines on both sides of the double clamp; ; and These are the mapping matrices between the relative equivalent rotation angle increments on both sides of the double clamp and the generalized coordinate increments of the pipelines on both sides of the double clamp, respectively. After projecting the relative displacement increments and the relative equivalent rotation increments on both sides of the double clamps onto the local coordinate system, and combining them with the local translational stiffness matrix of the double clamps... and the local rotational stiffness matrix of the double clamp , obtained the l The equivalent stiffness matrix of the double clamps: (11) The first l Double clamp quality m l Mass is applied uniformly to the translational degrees of freedom of the four clamping ends on the left and right boundaries of the pipeline on both sides of the double clamp, with each clamping end receiving a mass distribution. m l / 4, forming the equivalent mass matrix of the double clamps. M d .

[0032] Step 4: Establish the dynamic equations of the multi-clamp space transport pipeline system. Assemble the equivalent stiffness matrix of a single clamp, the equivalent stiffness matrix of two clamps, and the mass of the two clamps into the dynamic equations of the space transport pipeline: (12) In the formula, K c The equivalent stiffness matrix after assembling all single clamps. K d The equivalent stiffness matrix after all double clamps are assembled is given; by solving the eigenvalue problem of equation (12), the natural frequency and mode shape of the multi-clamp space transport pipeline system are obtained.

[0033] Step 5: Conduct clamp position sensitivity analysis. Keeping other parameters constant, change the position of a single clamp or double clamp on the pipeline, calculate the rate of change of each frequency, and determine the sensitive clamps using the natural frequency change rate.

[0034] The rate of change of frequency: (13) In the formula, For reference, the position of the clamp is below the first n First natural frequency, To only change the first b The first clamp position obtained after the first clamp position n The natural frequency is 1, and the clamp can be any single clamp or double clamp.

[0035] Frequency shift determination and mechanism analysis are performed based on the proposed method. When adjacent frequencies become locally close but do not actually cross over due to changes in clamp parameters, the modal shapes before and after the shift are further calculated. If the dominant vibration regions of the modal shapes exchange, frequency shift and modal exchange are determined to exist. The system is further divided according to different pipelines, and the first... n The first mode in the first p The proportion of strain energy in the root canal. When a frequency shift occurs, a significant redistribution of the proportion of strain energy among the critical canals indicates that changes in clamp parameters alter local constraints and inter-pipe coupling relationships, causing reconstruction of the dominant vibration region and modal energy migration.

[0036] The experimental natural frequencies and mode shapes of the space pipeline were obtained based on multi-point hammer impact modal tests. A solid finite element model including metal cable ties, metal felt, bolts, pipelines, and supports was established for comparison. Furthermore, by adjusting the positions of sensitive single clamps and sensitive double clamps, or removing sensitive clamps to simulate local stiffness reduction, the predictive ability of this invention on the frequency influence trend of sensitive clamps was verified.

[0037] The following alternative implementation methods may exist for the above technical solutions, but none of them affect the core idea of ​​the present invention: (1) The spatial tube unit can be the three-dimensional ANCF beam unit, or other higher-order beam units that can express the initial curvature and spatial configuration can be selected according to the pipeline geometry and frequency range; however, as long as the local translation / rotation constraints of the clamp are mapped to a unified generalized coordinate and assembled, they are all equivalent embodiments of the present invention.

[0038] (2) Pipe joints can be represented by volume equivalent stepped pipes, or by lumped mass-moment of inertia equivalence, local short beam equivalence, or finite element methods. The left and right boundaries of a single clamp can be described by two sets of discrete springs, or further discretized into multiple sets of springs according to the clamp width, or by using continuously distributed springs for integral equivalence. The mass of a double clamp can be uniformly distributed to the four clamping ends, or a non-uniform distribution method can be adopted according to the actual structural mass center, clamping contact area, or experimental identification results.

[0039] (3) In addition to MAC and modal strain energy, frequency steering identification can also be combined with modal curvature, participation factor, modal kinetic energy ratio or local vibration energy density as auxiliary criteria. Sensitive clamp verification can be achieved by position movement, stiffness reduction, clamp removal, replacement of soft and hard shims or adjustment of preload.

[0040] This invention has been verified through numerical simulation, solid finite element comparison, and modal experiments. The verification object is a complex multi-clamp spatial flow transmission pipeline system containing eight spatial pipes, multiple pipe joints, twelve single clamps, and three double clamps. Its system layout and discrete model are as follows: Figure 1As shown, the eight spatial pipes are designated as spatial pipe P1, spatial pipe P2, spatial pipe P3, spatial pipe P4, spatial pipe P5, spatial pipe P6, spatial pipe P7, and spatial pipe P8. In the model, the pipe segments are discretized using three-dimensional ANCF beam elements, and the pipe joints are treated as volume-equivalent stepped pipes. Single and double clamps are assembled according to the equivalent stiffness and mass methods of this invention, respectively.

[0041] In the experimental phase, modal testing of the multi-clamp spatial piping system was conducted using the hammer impact method. A total of 144 impact points were set up during the test, and accelerometers were placed in different areas. To fully excite the structural modes, each point was impacted along... X Xianghe Y The experiment yielded the first five natural frequencies, which were compared with the model of this invention and the solid finite element model. The three models were generally consistent in terms of dominant mode shape and frequency values.

[0042] For finite element verification, a solid finite element model was established, including metal cable ties, metal felt, bolts, pipes, and supports. This solid finite element model contains 409,840 elements and 487,983 nodes. Comparative results show that the maximum relative difference between the predicted first five natural frequencies of the model of this invention and the results of the solid finite element model is 6.27%, and the maximum relative difference between the model and the experimental results is 7.81%. Furthermore, the computation time of the model of this invention is approximately 0.23 seconds, while the computation time of the solid finite element model is approximately 365 seconds, representing an improvement in computational efficiency of approximately 1587 times.

[0043] Regarding clamp sensitivity verification, position sensitivity calculations were performed on all single and double clamps, with typical results as follows: Figure 4 As shown in the figure. The results show that the maximum sensitivity to changes in the position of a single clamp can reach 40.21%, while the maximum sensitivity to changes in the position of a double clamp is approximately 22.56%. Based on the sensitivity screening results, position-sensitive single clamps and critical double clamps were selected for further analysis and experimental verification. The simulation and experimental comparison of frequency changes before and after clamp adjustment are shown below. Figure 5 As shown, this further illustrates that the present invention has a good predictive ability for the changing trend of clamp parameters.

[0044] In terms of sensitivity and frequency shift analysis, we take a single clamp that is sensitive to clamp position as an example for analysis. Figure 6 To understand the effect of the position of a sensitive single clamp on the natural frequency, from Figure 6 As shown in (a), changes in the position of the sensitive single clamp can cause significant frequency shifts between modes, and multiple frequency shift regions exist, such as VR1, VR2, VR3, and VR4. A detailed analysis is conducted using frequency shift region VR2. Figure 6 As shown in (b). Figure 7M5-1, M5-2, and M5-3 are the fifth mode shapes before, during, and after the frequency shift, respectively, while M4-1, M4-2, and M4-3 are the fourth mode shapes before, during, and after the frequency shift, respectively. Figure 8 The change in the proportion of strain energy in each pipeline before and after the turn is shown. Figure 8 (a) The distribution of strain energy proportions of the 4th and 5th modes in each pipeline before and after the frequency shift is given, where M4-1, M4-3, M5-1 and M5-3 represent the 4th and 5th modes before and after the shift, respectively. Figure 8 (b) The changes in the proportion of strain energy in the dominant vibrational pipe during the normalized clamp position change are presented. M4-P2 and M4-P3 represent the proportion of strain energy of the 4th mode in the second spatial pipe P2 and the third spatial pipe P3, respectively. M5-P2 and M5-P3 represent the proportion of strain energy of the 5th mode in the second spatial pipe P2 and the third spatial pipe P3, respectively. The results show that during the frequency shift, the dominant vibrational pipes of the 4th and 5th modes shift between the second spatial pipe P2 and the third spatial pipe P3, indicating that the mechanism of the frequency shift phenomenon is the redistribution of modal energy between different pipes.

Claims

1. A method for modeling and identifying sensitive clamps in a multi-clamp spatial flow transmission pipeline system, characterized in that, The process includes the following steps: establishing the dynamic equations of the spatial transport pipeline based on a three-dimensional ANCF beam element; establishing equivalent stiffness models for a single clamp and a double clamp using the principle of virtual work; introducing the support of a single clamp and the constraint of a double clamp into the dynamic equations of the spatial transport pipeline to obtain the dynamic equations of the multi-clamp spatial transport pipeline system; obtaining the natural frequencies and mode shapes of the multi-clamp spatial transport pipeline system by solving the eigenvalue problem corresponding to the dynamic equations of the multi-clamp spatial transport pipeline system; identifying sensitive clamps based on clamp position sensitivity; the process of establishing the dynamic equations of the spatial transport pipeline is as follows: the three-dimensional ANCF beam element contains two nodes. i and j ,node i coordinate vector r i and nodes j coordinate vector r j Each element contains 7 degrees of freedom; the coordinate vector representation of a 3D ANCF beam element is as follows: (1) in, r i and r j The expression is: (2) in, r i1 , r i2 and r i3 For nodes i The three position coordinates, θ i1 For nodes i The corner, , and For nodes i The gradient coordinates of the three positions; r j1 , r j2 and r j3 For nodes j The three position coordinates, θ j1 For nodes j The corner , and For nodes j The gradient coordinates of the three positions; Position vector of any point on the centerline of any three-dimensional ANCF beam element r m Through the shape function matrix at that position S m With the coordinate vector of this three-dimensional ANCF beam element e Interpolation yields, i.e.: (3) The absolute velocity vector of the fluid element at any point on the centerline of any three-dimensional ANCF beam element. v f for: (4) in, v For fluid velocity, Let be the velocity vector of any point on the centerline of a three-dimensional ANCF beam element. r m0 Let be the position vector of any point on the center line of a three-dimensional ANCF beam element under the reference configuration, and the superscript ′ indicates the derivative with respect to the axial coordinate. The kinetic energy and strain energy of the three-dimensional ANCF beam element, as well as the internal fluid kinetic energy, are obtained from the coordinate vector of the three-dimensional ANCF beam element and the absolute velocity vector of the fluid element. Substituting these into the extended Lagrange equation, the dynamic equations of the space transport pipeline are established: (5) In the formula, M For the quality matrix, V The term is the geometrically nonlinear inertia caused by the rotation of the pipe cross-section. G This is the fluid velocity-dependent gyroscope matrix. K The stiffness matrix is ​​related to the internal fluid velocity. N ( q () represents the nonlinear elastic restoring force vector caused by axial tension, bending, and torsion of the pipeline. q , and These are the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the pipeline system, respectively.

2. The method for modeling and identifying sensitive clamps in a multi-clamp spatial transmission pipeline system according to claim 1, characterized in that, The equivalent stiffness model of the single clamp is established as follows: For a single clamp that fixes the pipeline to the casing, it is equivalent to two sets of spring elements located at the left and right boundaries of the clamping area. Each set of spring elements simultaneously includes local translational stiffness and local rotational stiffness. The generalized coordinate vector of the three-dimensional ANCF beam element is mapped to the local rotational stiffness degree of freedom of the spring element. The displacement increment, torsion angle increment, and slope increment at the position of the single clamp are respectively Δ r c , and Based on the reference configuration, the equivalent rotation increment of a single clamp section is defined as follows: (6) In the formula, t 0 is the unit tangent vector in the reference configuration. J 0 is the tangential modulus of the reference centerline, [ t 0] × for t The antisymmetric matrix corresponding to 0, This is the mapping matrix between the equivalent rotation angle increment of a single clamp section and the generalized coordinate increment; This is the shape function matrix corresponding to the torsion angle at the single clamp position; The mapping matrix between the slope increment and the generalized coordinate increment at the single clamp position; Δ e The generalized coordinate increment vector of the three-dimensional ANCF beam element containing the single clamp; selected with... t Non-parallel reference vectors are used, and a local orthogonal basis is obtained through Gram-Schmidt orthogonalization. An orthogonal transformation matrix from the local coordinate system to the global coordinate system of a single clamp is then constructed. Q c ; The translational stiffness matrix of each spring element in the local coordinate system of a single clamp is: The rotational stiffness matrix is ,pass Q c After transforming to the global coordinate system, the translational stiffness matrix in the global coordinate system is obtained. rotational stiffness matrix in global coordinate system The transformation relationship is as follows: (7) Potential energy of two sets of spring units in a single clamp for: (8) Substituting equations (6) and (7) into equation (8), and based on the second variation of the generalized coordinates using potential energy, we obtain the... a The equivalent stiffness matrix of a single clamp is: (9) In the formula, S r This is the shape function matrix corresponding to the displacement at the single clamp position.

3. The method for modeling and identifying sensitive clamps in a multi-clamp spatial transmission pipeline system according to claim 1, characterized in that, The equivalent stiffness model for the double clamps is established as follows: for a double clamp connecting two adjacent pipes, it is considered as a pipe coupling group; the generalized coordinate increments of the pipes on both sides of the double clamp are Δ e A and Δ e B The shape function matrices are respectively S A and S B The relative displacement increment on both sides of the double clamps The relative equivalent rotation angle increment on both sides of the double clamp for: (10) Where, Δ e AB =[Δ e A ;Δ e B ]; , is the mapping matrix between the relative displacement increments on both sides of the double clamp and the generalized coordinate increments of the pipelines on both sides of the double clamp; ; and These are the mapping matrices between the relative equivalent rotation angle increments on both sides of the double clamp and the generalized coordinate increments of the pipelines on both sides of the double clamp, respectively. After projecting the relative displacement increments and the relative equivalent rotation increments on both sides of the double clamps onto the local coordinate system, and combining them with the local translational stiffness matrix of the double clamps... and the local rotational stiffness matrix of the double clamp , obtained the l The equivalent stiffness matrix of the double clamps: (11) The first l Double clamp quality m l Mass is applied uniformly to the translational degrees of freedom of the four clamping ends on the left and right boundaries of the pipeline on both sides of the double clamp, with each clamping end receiving a mass distribution. m l / 4, forming the equivalent mass matrix of the double clamps. M d .

4. The method for modeling and identifying sensitive clamps in a multi-clamp spatial transmission pipeline system according to claim 3, characterized in that, The equivalent stiffness matrix of a single clamp, the equivalent stiffness matrix of a double clamp, and the mass of a double clamp are assembled into the dynamic equations of a space transport pipeline: (12) In the formula, K c The equivalent stiffness matrix after assembling all single clamps. K d The equivalent stiffness matrix after all double clamps are assembled is given; by solving the eigenvalue problem of equation (12), the natural frequency and mode shape of the multi-clamp space transport pipeline system are obtained.

5. The method for modeling and identifying sensitive clamps in a multi-clamp spatial transmission pipeline system according to claim 1, characterized in that, The method of identifying sensitive clamps based on clamp position sensitivity involves changing the position of a single clamp or a double clamp on the pipeline while keeping other parameters constant, calculating the rate of change of each frequency, and determining the sensitive clamp through the rate of change of the natural frequency.

6. The method for modeling and identifying sensitive clamps in a multi-clamp spatial transmission pipeline system according to claim 5, characterized in that, The rate of change of frequency: (13) In the formula, For reference, the position of the clamp is below the first n First natural frequency, To only change the first b The first clamp position obtained after the first clamp position n The natural frequency is 1, and the clamp can be any single clamp or double clamp.

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