A method for analyzing the vibration transmission characteristics of a parallel liquid-filled pipeline system

Abstract

The present invention relates to a method for analyzing the vibration transfer characteristics of a parallel liquid-filled pipeline system, and for the first time establishes a vibration transfer model of a parallel liquid-filled pipeline system. It can provide an efficient dynamic model for the vibration transfer analysis and identification of the main transfer path of the parallel liquid-filled pipeline system. Since the power flow signal containing velocity and force information matches the state vector in the model of the present invention well, the model of the present invention has the natural advantages of simple operation and high computational efficiency when evaluating the vibration transfer characteristics of parallel liquid-filled pipelines. Based on the proposed model, numerical and experimental methods were used to study the vibration transfer characteristics of the pipeline system from four different positions to the target position, and the main transmission path of the vibration was identified by collecting the power flow signal during the vibration transfer process. The present invention can provide a prerequisite for the vibration reduction design of fluid conveying pipelines in subsequent projects.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical dynamics, and in particular to a method for analyzing vibration transfer characteristics of a parallel liquid-filled pipeline system. Background Art

[0002] Parallel fluid-filled piping systems, consisting of multiple pipes, are widely used for fluid transportation in aerospace, marine, nuclear energy, and chemical industries. Excessive vibrations at critical locations in these systems can lead to fluid leakage and even damage the piping structure. In practical applications, parallel fluid-filled piping systems may be subject to external excitation at various local locations, but the vibration state at target (critical) locations on the structure is of general concern, as this affects vibration transmission.

[0003] Vibration transfer characteristic analysis is an essential component of complex mechanical system dynamics research. Transfer path analysis and its derivatives are experimentally based methods used to evaluate and control the transfer paths of vibration energy. Using velocity or force as the research variable and combining it with the corresponding transfer function, the contribution of each path is determined. This method is widely used in fields such as automobiles and agricultural machinery. Vibration is transmitted within a system as a combination of force and motion. The newly developed power flow analysis integrates force and velocity information into a single indicator, directly reflecting the nature of vibration transmission and possessing promising application prospects. In general, power flow analysis can characterize the transmission patterns of vibration within a structure, facilitate the identification of primary transfer paths, and provide support for subsequent vibration reduction design.

[0004] Over the past few decades, significant progress has been made in the dynamic analysis of single fluid-filled pipelines. To better understand the impact of fluid-structure interaction (FSI) on the vibration behavior of fluid-filled pipelines, researchers have established several mathematical models using methods such as semi-analytical methods, finite element methods, and transfer matrix methods. Semi-analytical methods can address the nonlinear vibration of fluid-filled pipelines, but their demanding modal shape functions make them difficult to apply to complex pipeline systems. Finite element methods can effectively handle the structural vibration of pipelines, but their handling of fluids is weaker. The transfer matrix method is suitable for chained pipeline structures. Compared with the finite element method, the transfer matrix method significantly reduces the matrix dimension and offers greater applicability than the semi-analytical method. However, the traditional transfer matrix method can only be applied to single fluid-filled pipelines. Existing research has emphasized the impact of fluid-structure interaction on the vibration characteristics of single fluid-filled pipelines, providing valuable insights into the vibration mechanisms of fluid-filled pipelines. However, research on the dynamic behavior of parallel fluid-filled pipelines is limited.

[0005] In recent years, some literature has studied the heat transfer characteristics of parallel liquid-filled pipes, and vibration transmission is also an important part of the transmission characteristics analysis of parallel liquid-filled pipes. Although some scholars have studied the vibration and transmission characteristics of a single liquid-filled pipe, most of the research focuses on a single liquid-filled pipe, and the dynamic analysis of the parallel liquid-filled pipe system is not sufficient. Summary of the Invention

[0006] In response to the above problems, the purpose of the present invention is to provide a method for analyzing the vibration transfer characteristics of a parallel liquid-filled pipeline system. The method has high solution efficiency and can simultaneously consider fluid-solid coupling and structural coupling, filling the gap in the research on vibration transfer of parallel infusion pipelines and providing useful support for subsequent infusion pipeline vibration control.

[0007] The technical solution adopted in the present invention is as follows:

[0008] A method for analyzing the vibration transfer characteristics of a parallel liquid-filled pipeline system proposed in the present invention includes the following steps:

[0009] S1. Based on the power flow method and the improved transfer matrix method, a dynamic model of the parallel liquid-filled pipeline system is established;

[0010] S2. Verify the parallel liquid-filled pipeline model established in S1;

[0011] S3. Use the verified model in S2 to draw the power flow curve and transfer path contribution chromatogram of each transfer path to identify the main transfer path.

[0012] Furthermore, the step S1 specifically includes:

[0013] (1.1) Establish the differential equation of motion of the liquid-filled tube

[0014]

[0015] Assuming that the state vector of the pipeline at the initial time (t = 0) is η(z, 0) = 0, the above equation can be converted into a frequency domain equation through Laplace transform:

[0016]

[0017] Among them, the state vector Φ(z,s)=L[η(z,t)], R s (z,s)=L[r s (z,t)]; the subscript 's' indicates a straight pipe, s is the Laplace variable s = (2πi)f; the symbol unit of f is Hz, i indicates an imaginary number; A s , B s and C s Represents the constant coefficient matrix of the liquid-filled pipe, where the coefficient matrix A sis the unit matrix (14×14); D s is a vector related to gravity; R s is a vector consisting of environmental stimuli;

[0018] (1.2) Derivation of the field transfer matrix of a single liquid-filled tube

[0019] The relationship between the state vectors of the starting point and the end point of the tube can be expressed as:

[0020] Φ(0,s)=UΦ(L i ,s)+Q

[0021] Where U is the field transfer matrix, Q represents the state vector consisting of external excitation, gravity and field transfer matrix;

[0022]

[0023] Where V s yes The eigenvector of

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] in yes The characteristic value of

[0030] (1.3) Derive the coupling equation between the two pipes

[0031] Due to the presence of the double clamp, the vibrations of the two pipes conveying fluids will affect each other, thus forming structural coupling. Based on the deformation coordination conditions of the two pipes, the coordination equation of pipe I in the coupling region is derived:

[0032]

[0033]

[0034] At the same time, the deformation coordination equation of tube II is obtained as follows:

[0035]

[0036]

[0037] The subscripts 'R' and 'L' represent the left and right ends of the coupling region, respectively. Combining the above formula, we can get the coupling matrix of the two liquid-filled pipes. The subscripts I and II represent pipe I and pipe II. V is the flow rate and P is the pressure. is the speed of the tube in three directions, is the angular velocity of the tube in three directions, f x ,f y ,f z is the force in three directions of the tube, m x ,m y ,m z is the moment in the three directions of the tube; k x 、k y 、k z 、k θx 、k θy 、k θz are the translational stiffness and torsional stiffness of the double clamp in three directions, ξ x ,ξ y ,ξ z , γ θx , γ θy , γ θz Respectively represent the translational damping and torsional damping of the double clamp in three directions;

[0038]

[0039]

[0040]

[0041]

[0042] Where T couple is the coupling matrix.

[0043] (1.4) Based on the principle of logical structure alignment, the parallel liquid-filled pipeline system is divided into various areas, and a transfer relationship is established for each area;

[0044] (1.5) Connecting the various regions to form the entire field transfer matrix of the parallel liquid-filled pipe system;

[0045]

[0046]

[0047]

[0048] In the following table, 'start' and 'end' represent the start and end of the entire pipeline system, respectively, and I is the unit matrix; the meanings of other symbols are the same as in step (1.2);

[0049] (1.6) Combine the overall transfer matrix in step (1.5) with the boundary conditions to form the final field transfer relationship;

[0050] D tot Φ tot =F tot

[0051] in D tot and F tot are the overall boundary condition matrix and the overall force vector respectively;

[0052] (1.7) gives the expression of power flow P and makes it dimensionless

[0053] The power flow in the y direction of the pipeline is:

[0054]

[0055] For the convenience of calculation, W0 is defined as the reference power flow; the power flow is dimensionless as follows:

[0056]

[0057] Furthermore, the step S2 specifically includes modal verification based on hammering experiments and response verification based on power flow.

[0058] Furthermore, the test instruments required for the modal verification include a three-axis accelerometer, a force hammer, and a 12-channel LMS system. To ensure the accuracy of the test results, the natural frequency of the infusion pipeline system was obtained through multiple hammer tests. The transfer matrix method was used to identify the natural frequency of the liquid-filled pipeline through the frequency corresponding to the resonance peak in the frequency response under external excitation. The model was verified by comparing the frequency results of the two.

[0059] Furthermore, the response verification specifically includes: using a flexible rod exciter to excite the parallel infusion pipeline, applying a 10N simple harmonic excitation along the y-direction to the excitation point, and setting the analysis frequency band to 80-340Hz; a signal generator generates a constant control voltage in the 80-340Hz frequency band, and drives the flexible rod exciter to excite the liquid-filled pipeline through the excitation force control module; the force and acceleration signals at the target position are processed by the LMS SCADAS mobile front end and transmitted to the LMS mobile workstation; and multiple fixed-frequency excitations are used to achieve the same effect as swept frequency.

[0060] Furthermore, the specific process of the multiple fixed-frequency excitations is as follows: three fixed-frequency excitations are performed every 1 Hz, and the acceleration signal and force signal are collected respectively by an acceleration sensor and a force sensor, and then the three results of each frequency are averaged; the collected acceleration signal is divided by the corresponding frequency to obtain the velocity signal, and then the steady-state amplitude is obtained through Fourier transform; similarly, the steady-state amplitude of the force signal is obtained; the velocity signal and the force signal are multiplied to obtain the tested power flow; the power flow at the target position is extracted using the same harmonic excitation as the experiment; and the model is further verified by comparing the power flow signals obtained by simulation and experiment.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] This model offers high solution efficiency and simultaneously accounts for both fluid-structure and structural coupling. First, based on deformation coordination conditions and matrix dimensionality expansion, a dynamic model of a parallel fluid-filled pipeline system was derived, and its accuracy was verified through impact tests. Numerical and experimental analysis of power flow along different transmission paths was then performed, identifying the primary transmission path during vibration transmission. This approach fills a gap in the research on vibration transmission in parallel fluid delivery pipelines and provides valuable support for subsequent pipeline vibration control. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Flowchart of the vibration transfer characteristics analysis method of the parallel liquid-filled pipeline system of the present invention;

[0064] Figure 2 This is a schematic diagram of the parallel liquid-filled pipeline model of the present invention;

[0065] Figure 3 Schematic diagram of modal test results of the parallel liquid-filled pipe system of the present invention;

[0066] Figure 4 Schematic diagram of the vibration velocity response of the parallel liquid delivery pipeline system of the present invention in the x-direction and the y-direction;

[0067] Figure 5 This is a schematic diagram of the vibration transmission test process of the present invention;

[0068] Figure 6 Schematic diagram of comparison between the numerical and experimental results of the transmission paths S1, S2, S3 and S4 of the present invention;

[0069] Figure 7 Schematic diagram of power flow experimental results and simulation results of each transmission path of the present invention;

[0070] Figure 8 Schematic diagram of the chromatogram experimental results and simulation results contributing to the four transfer paths of the present invention. DETAILED DESCRIPTION

[0071] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0072] The present invention proposes a method for analyzing the vibration transfer characteristics of a parallel liquid-filled pipeline system, taking three parallel liquid-filled pipes as an example. Figure 1 and 2 As shown, the specific steps include:

[0073] S1. Based on the power flow method and the improved transfer matrix method, a dynamic model of the parallel liquid-filled pipe system is established. The specific process is as follows:

[0074] The differential equation of motion of the liquid-filled tube III is described by fourteen equations:

[0075]

[0076] Assuming that the state vector of the pipeline at the initial time (t = 0) is η(z, 0) = 0, then formula (1) can be transformed into the frequency domain equation through Laplace transform

[0077]

[0078] Where Φ(z,s)=L[η(z,t)], R s (z,s)=L[r s (z,t)]. The subscript 's' indicates a straight pipe, s is the Laplace variable s = (2πi)f. The symbol unit of f is Hz, and i indicates an imaginary number. A s , B s , and C s Represents the constant coefficient matrix of the liquid-filled pipe, where the coefficient matrix A s is the unit matrix (14×14). s is a vector related to gravity. R s is a vector consisting of environmental stimuli.

[0079] The vector Φ(z,s) contains 14 independent variables, including flow rate and pressure (V III , P III ),speed Angular velocity Force (f xIII , f yIII , f zIII ), torque (m xIII , m yIII , m zIII) in three directions of tube III

[0080]

[0081] The relationship between the state vectors of the start and end points of tube III can be expressed as:

[0082] Φ(0,s)=UΦ(L i ,s)+Q (4)

[0083] where U is the field transfer matrix and Q represents the state vector consisting of the external excitation, gravity, and the field transfer matrix.

[0084]

[0085] Where V s yes The eigenvector of

[0086]

[0087]

[0088]

[0089]

[0090] in yes The eigenvalue of .

[0091] Take the coupling area between pipelines I and II as an example (see Figure 1 ), due to the presence of the double clamp, the vibrations of pipes I and II conveying fluids will affect each other, thus forming structural coupling. Based on the deformation coordination conditions of the two pipes, the coordination equation of pipe I in the coupling region is derived:

[0092]

[0093]

[0094] At the same time, the compatibility equation of tube II is obtained as follows:

[0095]

[0096]

[0097] The subscripts 'R' and 'L' denote the left and right ends of the coupling region, respectively. Combining equations (10) and (11), the coupling matrix of the two liquid-filled pipes can be obtained. V is the flow rate and P is the pressure, is the speed of the tube in three directions, is the angular velocity of the tube in three directions, f x ,f y ,f z is the force in three directions of the tube, m x ,m y ,m z is the moment in the three directions of the tube; k x 、k y 、k z 、k θx 、k θy 、k θz are the translational stiffness and torsional stiffness of the double clamp in three directions, ξ x ,ξ y ,ξ z , γ θx , γ θy , γ θz Respectively represent the translational damping and torsional damping of the double clamp in three directions.

[0098]

[0099]

[0100]

[0101]

[0102] The derivation of the coupling equations between pipelines II and III is similar and will not be described here. Each pipeline has 14 variables, for a total of 28 variables in Equation (12). The subscripts I and II denote pipelines I and II.

[0103] According to the principle of logical structure alignment, the parallel liquid-filled pipeline system is divided into 23 areas (such as Figure 2 However, some areas have only one pipeline, some areas have two pipelines, and some areas have three pipelines. How to unify these different types of areas is a problem that the improved transfer matrix model proposed in this invention needs to solve.

[0104] Taking several typical areas as examples, we will explain how the improved transfer matrix model handles different areas. First, we take the L1 area with only one pipe as an example. Pipe II has elastic support and satisfies:

[0105]

[0106] in represents the state vector of tube II on the left side of region L1, represents the state vector of tube II on the right side of region L1. is the field transfer matrix of pipeline II in the region. represents the point transfer matrix corresponding to the elastic support of pipe II. represents the state vector consisting of the external excitation, gravity, and field transfer matrix of the L1 region II tube.

[0107] Since the three parallel pipelines are integrated together, when forming the matrix form, it is necessary to expand the matrix dimension to achieve logical alignment. The overall matrix form can be expressed as:

[0108]

[0109] The matrix dimensions are 54×54, where the identity matrix and Used to replace virtual pipes I and III in the L1 area; and is used to represent the external excitation vectors of the two tubes in this region.

[0110] According to this principle, there are pipelines I and II in the L4 region, and their transfer relationship can be expressed as

[0111]

[0112] In the L5 region containing three pipe segments, the following equations are satisfied

[0113]

[0114] Its matrix form can be expressed as

[0115]

[0116] The above three typical areas are all non-coupling areas. 10 When the coupling region (see Figure 2 ), the state vectors on the left and right sides of the cross section of the coupling spring-damper connection are no longer consistent, and the transfer relationship is:

[0117]

[0118] In L 10 Region, the transitive relationship should be expressed as:

[0119]

[0120] Among them P1 Ι and P1 II is the point transfer matrix of the concentrated mass points attached to pipes I and II, which can be found in the Appendix; in L 12 District and L 13 The structural coupling of tube II and tube III is formed between the zones, and the coupling relationship can be expressed as:

[0121]

[0122] According to the above processing principles for each typical area, the field transfer matrix of other areas is similar. Finally, the entire field transfer matrix of the parallel liquid-filled pipe system is expressed as:

[0123]

[0124]

[0125] Combine Equation (22) with the boundary conditions to solve the state vector of the parallel liquid-filled pipe system. There are six boundary equations at both ends of the three parallel pipes.

[0126]

[0127] in and are the starting state vectors of the three tubes respectively; are the state vectors at the ends of the three tubes respectively; and are the excitation vectors at both ends of the three parallel pipes; at both ends of the three parallel pipes, and are the boundary matrices respectively; combining formulas (22) and (23), the entire transfer matrix can be obtained.

[0128]

[0129] Formula (24) can be written as a more general expression:

[0130] D tot Φ tot =F tot (25)

[0131] in D tot and F tot It is consistent with formula (23).

[0132] At this point, it is easy to get the state vector of the parallel liquid-filled pipe system:

[0133]

[0134] Φ tot Contains the state vector of the starting end of pipe I After solving formula (26), it is easy to obtain Φ tot Then, using the transfer relationships between the pipes, the frequency responses at other locations can be calculated.

[0135] In general, force and velocity can be expressed in complex excitation form as:

[0136] F(t)=Re(Fe jωt ) (27a)

[0137] V(t)=Re(Ve jωt ) (27b)

[0138] where ω is the circular frequency,

[0139] The average power flow in the steady state during one excitation cycle is:

[0140]

[0141] The superscript '*' indicates a complex conjugate operation, and T indicates the time of one excitation cycle.

[0142] After performing a Laplace transform on the fluid-structure coupling equation for a liquid-filled pipe, the resulting model does not contain time-domain information, but rather the amplitude of the state vector at each frequency. The present invention focuses on the power flow in the y direction delivered to the starting end of the II tube. Based on the definition of power flow, it can be written as:

[0143]

[0144] For the convenience of calculation, W0 is defined as the reference power flow. The power flow is dimensionless as:

[0145]

[0146] During the vibration process, the power flow signal contains information about speed and force, and the model established by the present invention also contains speed and force, and the two have a high degree of matching. Therefore, the model established by the present invention has a natural advantage in studying the vibration transfer characteristics of parallel liquid-filled pipes. Combined with the improved transfer moment model and power flow analysis, the model operation steps proposed by the present invention are simple and clear, and are particularly suitable for engineering applications of vibration transfer analysis of liquid-filled pipes. Except for the inverse operation of formula (26), the matrix multiplication and division operations are always controlled within the dimension of 42×42, which is relatively small in dimension. Therefore, the model established by the present invention has the advantage of high computational efficiency and is very suitable for computer programming.

[0147] S2. Perform model verification on the parallel liquid-filled pipeline model established in S1, including modal verification based on hammer experiments and response verification based on power flow.

[0148] For the model established by the present invention, modal verification is first performed. The parameters of the parallel pipeline system are shown in Table 1. The length of each pipe section (see Figure 2) See Table 2. The test instruments required for the modal experiment include a three-axis accelerometer (PCB 356A01), a force hammer (PCB 086C01) and a 12-channel LMS system (SC-XS12-A). The single clamps are taken from the same batch, so it is assumed that the six single clamps have the same stiffness. The stiffness of the two double clamps is also assumed to be the same. The clamp consists of two straps and metal rubber, and the clamp damping is usually not easy to obtain. For ease of analysis, it is assumed that the clamp damping in the three directions is the same, as shown in Table 1. Using a self-designed fixture, the stiffness of the clamp can be obtained through multiple measurements. In order to ensure the accuracy of the test results, the natural frequency of the infusion pipeline system was obtained through multiple hammer tests. There are 6 natural frequencies from 0 to 350 Hz, such as Figure 3 As shown. Using the transfer matrix method, it is necessary to identify the natural frequency of the liquid-filled pipe by the frequency corresponding to the resonance peak in the frequency response under external excitation. At the starting end of pipe II, impact excitation along the x and y directions is applied respectively, and the velocity at the starting end of pipe I is extracted. The amplitude-frequency response of the system is obtained as follows Figure 4 shown.

[0149] Table 1 Parameters of the parallel liquid-filled pipeline system.

[0150]

[0151] Table 2 Lengths of various pipe sections in parallel liquid-filled pipelines.

[0152]

[0153] The frequency results obtained from simulation and experiment are shown in Table 3. Compared with the experimental results, the maximum error of the model proposed in this invention is 3.83%. The frequency calculation results of the two methods are in good agreement, verifying the correctness of the constructed model.

[0154] Table 3 Comparison of simulation and experimental frequencies of parallel liquid-filled pipe system

[0155]

[0156] Based on the above dynamic model, the power flow analysis method is used to study the vibration transmission characteristics of the parallel liquid-filled pipe system. The schematic diagram of the vibration transmission test process is shown in the figure. Figure 5 As shown. In the present invention, the starting point of pipeline II is the target position (pickup point). First, four transfer paths are defined respectively. S1 is the transfer path of pipeline III from the starting point (rightmost) to the target position; S2 is the transfer path from the end of pipeline III (leftmost) to the target position; S3 is the transfer path from pipeline I to the target position; S4 is the transfer path from the end of pipeline I to the target position. Keeping the output parameters of the exciter unchanged, the same harmonic excitation is applied to the four positions respectively, and the transfer characteristics of these vibration signals along S1, S2, S3, and S4 to the target position are analyzed.

[0157] A flexible rod vibrator was used to excite the parallel fluid delivery pipeline. Due to experimental conditions (flexible rod vibrator lifting and lowering), the present invention only conducted excitation experiments in the y-direction; the experiments in other directions were similar. A 10N simple harmonic excitation was applied to the excitation point along the y-direction, and the analysis frequency band was set to 80-340 Hz. A signal generator generated a constant control voltage in the 80-340 Hz frequency band. The excitation force control module (SINOCERA-YE2706A) drove the flexible rod vibrator to excite the fluid-filled pipeline. The force and acceleration signals at the target position were processed by the LMS SCADAS mobile front end and transmitted to the LMS mobile workstation. It is worth noting that due to limited experimental equipment, direct scanning performance was poor. Therefore, the present invention employed multiple fixed-frequency excitations to achieve the same effect as frequency sweeping. The specific operation was as follows: three fixed-frequency excitations were performed every 1 Hz. The acceleration and force signals were collected by the acceleration sensor (PCB 356A01) and the force sensor (PCB 208C04), respectively. The three results for each frequency were then averaged. The collected acceleration signal is divided by the corresponding frequency to obtain the velocity signal, and then the steady-state amplitude is obtained by Fourier transform. Similarly, the steady-state amplitude of the force signal is obtained. The velocity signal and the force signal are multiplied to obtain the power flow of the test. The simulation can directly obtain the power flow at the target position by sweeping the frequency from 80 to 340 Hz. The power flow at the target position is extracted using the same harmonic excitation as the experiment. The power flow comparison results of the four transfer paths are shown in Figure 2. Figure 6 shown.

[0158] like Figure 6 As shown in Figure 2, both numerical and experimental results show that when the external excitation frequency is close to the natural frequency of the parallel liquid-filled pipe system, the amplitude amplification phenomenon occurs and the power flow increases significantly. The second, fourth and sixth order natural frequencies (f n2 , f n4 , and f n6 ) is excited by simple harmonic excitation in the y direction. In general, the numerical results of the four transfer paths are consistent with the experimental results in terms of trend, but there are certain fluctuations in the experimental results, and there are certain differences in amplitude from the numerical results. The possible reason is that the output power of the exciter is unstable. Although the flexible rod exciter is set within a constant excitation range, its output excitation varies with the change of frequency, which is caused by the non-rigid structure of the flexible rod exciter itself. Another reason is that the assumed clamp damping adopted by the present invention has a certain deviation from the actual damping, which will also cause the deviation between the simulation and the experiment.

[0159] S3. Use the verified model in S2 to draw the power flow curve and transfer path contribution chromatogram of each transfer path to identify the main transfer path.

[0160] In order to facilitate the determination of the main transfer path, the power flow results of the four paths are plotted together, as shown in Figure 7 The chromatograms contributed by the four pathways are shown in Figure 8 As shown. In general, in the range of 80-340hz, the power flow increases with the increase of the excitation frequency. Compared with the other three paths, the total power flow of S3 is larger. This shows that when the external excitation acts on the starting point of pipeline I, the vibration loss is small, and more vibration energy is transferred to the target position (the starting point of pipeline II), that is, the vibration transfer path of S3 is the main transfer path. In the vibration reduction design, the main transfer path should be structurally modified. After removing the fluctuation of the experimental results, the distribution trend of the numerical spectrum is basically consistent with that of the experimental spectrum (see Figure 8 ). The effectiveness of the proposed model is further verified by comparing the experimental and numerical power flow responses.

[0161] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A method for analyzing the vibration transfer characteristics of a parallel liquid-filled piping system, characterized by: The method comprises the following steps: S1. Based on the power flow method and the improved transfer matrix method, a dynamic model of the parallel liquid-filled pipeline system is established; S2. Verify the parallel liquid-filled pipeline model established in S1; S3. Use the verified model in S2 to draw the power flow curve and transfer path contribution chromatogram of each transfer path to identify the main transfer path; Said step S2 specifically includes modal verification based on hammer test and response verification based on power flow; The test instruments required for modal verification include a three-axis accelerometer, a force hammer, and a 12-channel LMS system. To ensure the accuracy of the test results, the natural frequency of the infusion pipeline system was obtained through multiple hammer tests. The transfer matrix method was used to identify the natural frequency of the liquid-filled pipeline through the frequency corresponding to the resonance peak in the frequency response under external excitation. The model was verified by comparing the two frequency results.

2. The method for analyzing the vibration transfer characteristics of a parallel liquid-filled pipeline system according to claim 1, characterized in that: The response verification specifically includes: using a flexible rod vibrator to excite the parallel fluid delivery pipeline, applying a 10N simple harmonic excitation along the y-direction to the excitation point, and setting the analysis frequency band to 80-340 Hz; a signal generator generates a constant control voltage in the 80-340 Hz frequency band, and the excitation force control module drives the flexible rod vibrator to excite the fluid-filled pipeline; the force and acceleration signals at the target position are processed by the LMS SCADAS mobile front end and transmitted to the LMS mobile workstation; and multiple fixed-frequency excitations are used to achieve the same effect as swept-frequency excitation.

3. The method for analyzing the vibration transfer characteristics of a parallel liquid-filled pipeline system according to claim 2, characterized in that: The specific process of the multiple fixed-frequency excitation is as follows: three fixed-frequency excitations are performed every 1 Hz, and an acceleration sensor and a force sensor are used to collect acceleration signals and force signals respectively, and then the three results for each frequency are averaged; the collected acceleration signal is divided by the corresponding frequency to obtain a velocity signal, and then a steady-state amplitude is obtained through Fourier transform; Similarly, the steady-state amplitude of the force signal is obtained; the speed signal and the force signal are multiplied to obtain the tested power flow; the power flow at the target position is extracted using the same harmonic excitation as the experiment; and the model is further verified by comparing the power flow signals obtained by simulation and experiment.

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