A parallel pipeline modeling method based on semi-analytical method considering clamp soft nonlinearity

Abstract

The application provides a parallel pipeline modeling method based on a semi-analytical method and considering the soft nonlinearities of a clamp. The method comprises the following steps: based on the semi-analytical method, a dynamic model of a parallel flow pipeline system considering the soft nonlinearities of single and double clamps is established; the established dynamic model of the parallel flow pipeline system is verified; the soft nonlinear parameters of the single and double clamps are identified, and then the parameters of the single clamp are substituted into a control equation of the parallel pipeline to identify the nonlinear parameters of the parallel pipeline; the position of the double clamp is changed, and the identified nonlinear parameters of the parallel pipeline are substituted into the dynamic model of the parallel flow pipeline system to prove the universality of the identified parameters. The soft nonlinear parameters of the clamp are identified for the first time, which provides support for subsequent vibration analysis of the parallel flow pipeline. The method considers the nonlinear effect of the clamp, and improves the prediction accuracy of the vibration response.

Description

Technical Field

[0001] This invention relates to the field of mechanical dynamics technology, and more particularly to a method for modeling parallel pipelines based on a semi-analytical approach that considers the soft nonlinearity of clamps. Background Technology

[0002] Aero-engine piping systems play a crucial role in modern aircraft, exhibiting complex and varied structures, primarily employing a parallel configuration. Clamps are vital support and connecting components of the piping system, featuring a segmented structure where metal-rubber gaskets are welded to the clamps and then secured with bolts. When subjected to external excitation, friction between the metal wires within the rubber generates nonlinear forces. Therefore, treating the clamps as linear models can negatively impact the accurate prediction of piping vibration response. Establishing a nonlinear model for the clamps is of significant importance for the dynamic analysis of the piping system. Performing dynamic analysis on these complex structures is essential for ensuring the safe operation of aero-engine piping.

[0003] Some researchers have studied the nonlinearity of single-joint clamps, but no research on the nonlinearity of parallel clamps has been published. Current research on the dynamics of parallel pipelines focuses on the overall modeling of the parallel pipeline and the linear stiffness of double clamps. However, these studies do not consider the soft nonlinear support of the clamps in parallel pipelines. The equivalent linearization method cannot describe the energy dissipation mechanism at the interface, nor can it explain the complex nonlinear response phenomena observed in experiments. Furthermore, it is usually only applicable to specific experimental conditions and cannot meet the requirements of dynamic prediction in design-oriented scenarios. In practical engineering applications, the soft nonlinear characteristics of the clamps have a significant impact on the resonance peak shift of the pipeline. Therefore, studying the dynamic characteristics of aero-engine parallel pipeline systems that consider the soft nonlinear behavior of clamps has important theoretical and engineering significance. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a semi-analytical method for modeling parallel pipelines that considers the soft nonlinearity of clamps. This invention is the first to identify the soft nonlinear parameters of clamps, providing support for subsequent vibration analysis of parallel flow pipelines.

[0005] The technical means employed in this invention are as follows:

[0006] A semi-analytical method for modeling parallel pipelines considering the nonlinearity of clamp-type flexible pipes includes:

[0007] S1. Based on the semi-analytical method, a dynamic model of the parallel flow transmission pipeline system considering the nonlinearity of single and double clamps is established.

[0008] S2. Verify the established dynamic model of the parallel transmission pipeline system;

[0009] S3. Identify the nonlinear parameters of single and double clamps, and then substitute the single clamp parameters into the parallel pipeline control equation to identify the nonlinear parameters of the parallel pipeline.

[0010] S4. Change the position of the double clamps and substitute the identified nonlinear parameters of the parallel pipeline into the dynamic model of the parallel flow pipeline system to prove the universality of the identified parameters.

[0011] Further, step S1 includes:

[0012] S11. Establish a parallel flow transmission pipeline model;

[0013] S12. Derive the modal vibration function of each pipeline based on the boundary conditions;

[0014] S13. Solve for the assumed coefficients based on the continuity and deformation compatibility conditions of the pipeline.

[0015] Further, step S11 specifically includes:

[0016] S111, the kinetic energy T of the parallel transmission pipeline. i and potential energy V i Represented as:

[0017]

[0018]

[0019] In the formula, the elastic modulus is E, the subscript i represents the nth pipe, and l i v represents the length of the two pipes. i (x,t) and w i (x,t) represents the translational displacements of pipes 1 and 2 along the y-axis and z-axis, respectively, φ i (x,t) and A represents the torsional displacement of pipes 1 and 2 about the y and z axes, respectively. p A represents the cross-sectional area of ​​the pipe. f Let κ represent the fluid surface area, κ represent the shear correction factor, G represent the shear modulus, and ρ represent the fluid surface area. p ρ represents the density of the pipeline. f Let p represent fluid density, μ represent fluid pressure, I represent Poisson's ratio, and Г represent the moment of inertia about the y-axis and z-axis.

[0020] S112. The potential energy generated by single and double clamps can be expressed as:

[0021]

[0022]

[0023] In the formula, and These represent the positions of the springs in the single-joint clamps on pipes 1 and 2, respectively. and The positions of the springs in the double clamps on pipes 1 and 2;

[0024] S113. Calculate the nonlinear restoring force of the clamp. The calculation formula is as follows:

[0025]

[0026] In the formula, r is the weighting coefficient, and k c and k e These represent the nonlinear stiffness coefficient and the linear stiffness coefficient, respectively; z j (t)(j=1,2) represents the hysteretic damping force of the single and double clamps, calculated using the improved Bouc-Wen model:

[0027]

[0028] S114. Due to the nonlinear restoring force of the clamp. It is expressed in the form of differential equations. To simplify the model, the restoring force functions of each spring in the single-link and double-link clamps are expressed as follows:

[0029]

[0030] In the formula and Let k be the restoring force of each spring in the single-joint and double-joint clamps in the w direction. sw k swn c sw and c swn The linear and nonlinear stiffness, linear damping and nonlinear damping of a single clamp are respectively given by k. dw k dwn c dw and c dwn These are the linear stiffness, nonlinear stiffness, linear damping, and nonlinear damping of the double clamp;

[0031] S115. Regarding clamp damping, an equivalent viscous damping coefficient is introduced to replace the complex damping mechanism. This coefficient represents the single and double clamps in multiple directions, and the specific formula is as follows:

[0032]

[0033] In the formula, λ = 0.2 is the damping loss factor, ω represents the excitation frequency; the stiffness and damping of the single-link clamp are expressed by k. sj and csj It means (j = v, The stiffness and damping of the double clamp are expressed in k. dj and c sj express;

[0034] S116. Applying Hamilton's principle, the governing equations for parallel pipelines considering the nonlinearity of clamp-type flexible pipes are obtained, as follows:

[0035]

[0036] In the formula, T = T1 + T2, V = V1 + V2 + U s +U d δW includes the virtual work of lateral restoring force and damping force, specifically expressed as:

[0037]

[0038] In the formula, f(t) is the external excitation, and δ is the variational symbol. Represents the Dirac function;

[0039] S117. The elastic potential energy generated by single and double clamps is expressed by the following formula:

[0040]

[0041] The dynamic equations for pipe 1 and pipe 2 are then obtained as follows:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049] Further, step S12 specifically includes:

[0050] S121. Segment at each spring support and make modal assumptions for each segment; each pipe has k spring supports, thus forming (k+1) segments. The transverse displacement mode shape functions along the z-axis for each segment of pipe 1 and pipe 2 are assumed as follows:

[0051]

[0052] In the formula, and The translational displacement mode functions of pipes 1 and 2 along the z-axis are represented. and These are the characteristic values ​​of each section of pipe 1 and pipe 2, respectively, where:

[0053]

[0054]

[0055] S122. Set the following coordination conditions at each elastic support:

[0056]

[0057]

[0058]

[0059]

[0060] S123. Calculate the assumed modal vibration function of pipe 2, and write the compatibility conditions of the elastic support points as the following matrix relationship:

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Furthermore, step S13 specifically includes:

[0073] S131. Since the boundary conditions at both ends of the pipeline are free, the following characteristic equation is derived:

[0074]

[0075]

[0076] S132. The characteristic equation is expressed as:

[0077]

[0078]

[0079]

[0080] S133. Calculate the coefficients of the first and last paragraphs using the following formula:

[0081]

[0082]

[0083] S134. Since the only condition for a non-zero solution is that the determinant of its coefficients is zero, we solve for the eigenvalues ​​and calculate the modal coefficients:

[0084]

[0085] S135. An approximate solution is obtained using the Galerkin method, introducing the canonical coordinates of pipe 1. and the regular coordinates of pipe 2 and For pipe 2, calculate the displacement of the pipe in different directions as follows:

[0086]

[0087]

[0088]

[0089]

[0090] S136. The dynamic equation of the system is expressed as:

[0091]

[0092] Further, in step S2, the established dynamic model of the parallel pipeline system is validated based on the parallel pipeline impact test, wherein: the testing instruments required for the parallel pipeline impact test include a triaxial accelerometer, a force hammer, and a 12-channel LMS system; the validation process includes:

[0093] S21. To ensure the accuracy of the experimental results, the natural frequency of the parallel pipeline system was obtained through multiple hammer impact experiments.

[0094] S22. The natural frequency of the transmission pipeline is obtained using a semi-analytical method.

[0095] S23. The correctness of the model is verified by comparing the natural frequency of the parallel pipeline system obtained in step S21 with the natural frequency of the transmission pipeline obtained in step S22.

[0096] Furthermore, step S3 specifically includes:

[0097] S31. Conduct a frequency sweep experiment on the single clamp-mass block system to identify the nonlinear parameters. Then, substitute the single clamp parameters into the parallel pipeline control equation to identify the nonlinear parameters of the parallel pipeline.

[0098] S32. The Bouc-Wen model is used to describe the hysteresis force of the clamp. The experimental error and simulation error are used as objective functions, and the particle swarm optimization (PSO) algorithm is used to identify the hysteresis parameters of the single clamp.

[0099] S33. Then, based on the experiment, the nonlinear parameters of the double clamp are back-derived and identified.

[0100] Compared with the prior art, the present invention has the following advantages:

[0101] 1. The parallel pipeline modeling method based on the semi-analytical method considering the soft nonlinearity of clamps provided by this invention is the first to consider the influence of the soft nonlinearity of clamps on parallel pipelines; using Hamilton's principle, the multi-degree-of-freedom partial differential equations of motion of parallel pipelines are derived; the model is verified through modal and response experiments; the numerical calculation results are in good agreement with the experimental results, proving the accuracy of the semi-analytical modeling method.

[0102] 2. The parallel pipeline modeling method based on semi-analytical method considering the nonlinearity of clamps provided by this invention uses the Bouc-Wen model to describe the hysteresis force of the clamps. First, using experimental error and simulation error as objective functions, the particle swarm optimization (PSO) algorithm is used to identify the hysteresis parameters of single clamps. Then, the nonlinear parameters of double clamps are back-inferred and identified based on experiments. By changing the position of the double clamps and substituting the identified single and double clamp parameters into the proposed model, the universality of the identified parameters is proved.

[0103] 3. The parallel pipeline modeling method based on the semi-analytical method considering the nonlinearity of clamps provided by this invention takes into account the nonlinear effect of clamps and improves the accuracy of vibration response prediction.

[0104] Based on the above reasons, this invention can be widely applied in fields such as mechanical dynamics. Attached Figure Description

[0105] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0106] Figure 1 This is a flowchart of the method of the present invention.

[0107] Figure 2 This is a schematic diagram of a parallel flow transmission pipeline provided in an embodiment of the present invention.

[0108] Figure 3 This is a schematic diagram showing the comparison between numerical and experimental results of a parallel flow transmission pipeline provided in an embodiment of the present invention.

[0109] Figure 4 A schematic diagram of the testing instruments required for the parallel pipeline hammering experiment provided in an embodiment of the present invention.

[0110] Figure 5 A flowchart for identifying nonlinear parameters of a single-link clamp provided in this embodiment of the invention.

[0111] Figure 6 A schematic diagram of the parallel clamp nonlinear parameter test provided in this embodiment of the invention.

[0112] Figure 7 The present invention provides experimental schematic diagrams of the nonlinear parameters of single and double clamps under different double clamp positions.

[0113] Figure 8 The simulation comparison diagram of the nonlinear parameters of single and double clamps under different double clamp positions provided in the embodiments of the invention. Detailed Implementation

[0114] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0115] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0116] like Figure 1 , 2 As shown, this invention provides a semi-analytical method for modeling parallel pipelines considering the nonlinearity of clamps, comprising:

[0117] S1. Based on the semi-analytical method, a dynamic model of the parallel flow transmission pipeline system considering the nonlinearity of single and double clamps is established.

[0118] S2. Verify the established dynamic model of the parallel transmission pipeline system;

[0119] S3. Identify the nonlinear parameters of single and double clamps, and then substitute the single clamp parameters into the parallel pipeline control equation to identify the nonlinear parameters of the parallel pipeline.

[0120] S4. Change the position of the double clamps and substitute the identified nonlinear parameters of the parallel pipeline into the dynamic model of the parallel flow pipeline system to prove the universality of the identified parameters.

[0121] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes:

[0122] S11. Establish a parallel flow transmission pipeline model;

[0123] S12. Derive the modal vibration function of each pipeline based on the boundary conditions;

[0124] S13. Solve for the assumed coefficients based on the continuity and deformation compatibility conditions of the pipeline.

[0125] In a specific implementation, as a preferred embodiment of the present invention, step S11 specifically includes:

[0126] S111, the kinetic energy T of the parallel transmission pipeline. i and potential energy V i Represented as:

[0127]

[0128]

[0129] In the formula, the elastic modulus is E, the subscript i represents the nth pipe, and l i v represents the length of the two pipes. i (x,t) and w i (x,t) represents the translational displacements of pipes 1 and 2 along the y-axis and z-axis, respectively, φ i (x,t) and A represents the torsional displacement of pipes 1 and 2 about the y and z axes, respectively. p A represents the cross-sectional area of ​​the pipe. f Let κ represent the fluid surface area, κ represent the shear correction factor, G represent the shear modulus, and ρ represent the fluid surface area. p ρ represents the density of the pipeline. f Let p represent fluid density, μ represent fluid pressure, I represent Poisson's ratio, and Г represent the moment of inertia about the y-axis and z-axis.

[0130] S112. The potential energy generated by single and double clamps can be expressed as:

[0131]

[0132]

[0133] In the formula, and These represent the positions of the springs in the single-joint clamps on pipes 1 and 2, respectively. and The positions of the springs in the double clamps on pipes 1 and 2;

[0134] S113. Calculate the nonlinear restoring force of the clamp. The calculation formula is as follows:

[0135]

[0136] In the formula, r is the weighting coefficient, and k c and k eThese represent the nonlinear stiffness coefficient and the linear stiffness coefficient, respectively; z j (t)(j=1,2) represents the hysteretic damping force of the single and double clamps, calculated using the improved Bouc-Wen model:

[0137]

[0138]

[0139] The parameters of the single clamp were determined based on the frequency sweep test of the mass block-single clamp system.

[0140] S114. Due to the nonlinear restoring force of the clamp. It is expressed in the form of differential equations. To simplify the model, the restoring force functions of each spring in the single-link and double-link clamps are expressed as follows:

[0141]

[0142] In the formula and Let k be the restoring force of each spring in the single-joint and double-joint clamps in the w direction. sw k swn c sw and c swn These represent the linear and nonlinear stiffness, linear damping, and nonlinear damping of a single clamp, respectively. The hysteresis form of a double clamp is similar to that of a single clamp; simply replace it with the corresponding parameters of a double clamp. dw k dwn c dw and c dwn These are the linear stiffness, nonlinear stiffness, linear damping, and nonlinear damping of the double clamp;

[0143] S115. Regarding clamp damping, an equivalent viscous damping coefficient is introduced to replace the complex damping mechanism. This coefficient represents the single and double clamps in multiple directions, and the specific formula is as follows:

[0144]

[0145] In the formula, λ = 0.2 is the damping loss factor, ω represents the excitation frequency; the stiffness and damping of the single-link clamp are expressed by k. sj and c sj It means (j = v, The stiffness and damping of the double clamp are expressed in k. dj and c sj express;

[0146] S116. Applying Hamilton's principle, the governing equations for parallel pipelines considering the nonlinearity of clamp-type flexible pipes are obtained, as follows:

[0147]

[0148] In the formula, T = T1 + T2, V = V1 + V2 + U s +U d δW includes the virtual work of lateral restoring force and damping force, specifically expressed as:

[0149]

[0150] In the formula, f(t) is the external excitation, and δ is the variational symbol. Represents the Dirac function;

[0151] S117. The elastic potential energy generated by single and double clamps is expressed by the following formula:

[0152]

[0153]

[0154] The dynamic equations for pipe 1 and pipe 2 are then obtained as follows:

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] In a specific implementation, as a preferred embodiment of the present invention, step S12 specifically includes:

[0164] S121. Segment at each spring support and make modal assumptions for each segment; each pipe has k spring supports, thus forming (k+1) segments. The transverse displacement mode shape functions along the z-axis for each segment of pipe 1 and pipe 2 are assumed as follows:

[0165]

[0166] In the formula, and The translational displacement mode functions of pipes 1 and 2 along the z-axis are represented. and These are the characteristic values ​​of each section of pipe 1 and pipe 2, respectively, where:

[0167]

[0168] S122. Set the following coordination conditions at each elastic support:

[0169]

[0170]

[0171]

[0172]

[0173] S123. Calculate the assumed modal vibration function of pipe 2, and write the compatibility conditions of the elastic support points as the following matrix relationship:

[0174]

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185] In a specific implementation, as a preferred embodiment of the present invention, step S13 specifically includes:

[0186] S131. Since the boundary conditions at both ends of the pipeline are free, the following characteristic equation is derived:

[0187]

[0188]

[0189] S132. The characteristic equation is expressed as:

[0190]

[0191]

[0192]

[0193] S133. Calculate the coefficients of the first and last paragraphs using the following formula:

[0194]

[0195] S134. Since the only condition for a non-zero solution is that the determinant of its coefficients is zero, we solve for the eigenvalues ​​and calculate the modal coefficients:

[0196]

[0197] S135. An approximate solution is obtained using the Galerkin method, introducing the canonical coordinates of pipe 1. and the regular coordinates of pipe 2 and For pipe 2, calculate the displacement of the pipe in different directions as follows:

[0198]

[0199]

[0200]

[0201]

[0202] S136. The dynamic equation of the system is expressed as:

[0203]

[0204] In a specific implementation, as a preferred embodiment of the present invention, in step S2, the established dynamic model of the parallel flow pipeline system is verified based on the parallel pipeline impact test, wherein: the testing instruments required for the parallel pipeline impact test include a triaxial accelerometer, a force hammer, and a 12-channel LMS system; the verification process includes:

[0205] S21. To ensure the accuracy of the experimental results, the natural frequency of the parallel pipeline system was obtained through multiple hammer impact experiments.

[0206] S22. The natural frequency of the transmission pipeline is obtained using a semi-analytical method.

[0207] S23. The correctness of the model is verified by comparing the natural frequency of the parallel pipeline system obtained in step S21 with the natural frequency of the transmission pipeline obtained in step S22.

[0208] In this embodiment, the parameters of the connecting pipeline system are shown in Table 1. The test instruments required for the modal experiment include a triaxial accelerometer, a force hammer, and a 12-channel LMS system. The force hammer range is set to 0-1.786N, and the accelerometer range is set to 0-347m / s². 2 A correspondence was established between each channel and the experimental measurement points, with the hammer signal used as the trigger signal. The trigger level was set to 5% of the maximum value. The sampling frequency was set to 20kHz, with 32768 analysis points and 1024 sampling points. The negative delay point was set to 100 points. Pipeline 1 was divided into 9 measurement points along the axial direction, and pipeline 2 was divided into 11 measurement points along the axial direction. Two excitation methods were used in the experiment: single-point excitation and multi-point excitation. The generation mode shape of nodes located inside and outside the xoy plane was distinguished. Each group was averaged twice to reduce the influence of noise, improve the signal-to-noise ratio, ensure good coherence between each two hammer blows, and select a set of experimental data with good coherence for analysis. To ensure the accuracy of the experimental results, the frequency response function of the parallel pipeline system was obtained through multiple hammer blow experiments, such as... Figure 3 As shown, there are three natural frequencies in and out of the 0-1000Hz plane. The natural frequencies of the pipeline are identified by the peak values ​​of the frequency response function. The frequency response function diagrams obtained from experiments and simulations show good agreement, proving the feasibility of the semi-analytical modal method.

[0209] Table 1 Parallel Piping Parameters

[0210]

[0211] In a specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0212] S31. Conduct a frequency sweep experiment on the single clamp-mass block system to identify the nonlinear parameters. Then, substitute the single clamp parameters into the parallel pipeline control equation to identify the nonlinear parameters of the parallel pipeline.

[0213] S32. The Bouc-Wen model is used to describe the hysteresis force of the clamp. The experimental error and simulation error are used as objective functions, and the particle swarm optimization (PSO) algorithm is used to identify the hysteresis parameters of the single clamp.

[0214] S33. Then, based on the experiment, the nonlinear parameters of the double clamp are back-derived and identified.

[0215] In this embodiment, the nonlinear parameters of the single-link clamp in the dynamic model proposed in step S1 are identified. Before conducting the frequency scanning experiment, a feedback sensor is placed on the upper surface of the fixture. An accelerometer is positioned on the additional mass to capture the output signal of the test system. Excitation and response signals are continuously recorded and stored in real time on a laptop workstation, generating the corresponding frequency response plot. The scanning frequency bandwidth includes a range of 40 Hz, and each test lasts for 2.5 minutes. A three-dimensional waterfall plot can be used to obtain the corresponding frequency response curve. The shift of the resonant peak can be clearly observed, such as... Figure 4 To determine the unknown coefficients of the clamp, it was established as a single-degree-of-freedom system. The input (excitation) and output (response) parameters were derived from experimental results. Frequency and response amplitude errors were used as optimization targets for both experimental and simulation errors. The single-clamp parameters were calculated using particle swarm optimization at different amplitudes; the specific hysteresis parameters of the single-clamp are shown in Table 2.

[0216] Table 2 Hysteresis Parameters of Single-Link Clamp

[0217]

[0218] The nonlinear parameters of the double clamps were identified. Frequency sweep tests were conducted on the parallel pipeline under different excitation amplitudes. The identified nonlinear parameters of the single clamp were substituted into the parallel pipeline dynamic equation in S1, and then the nonlinear parameters of the double clamps were inversely identified based on the experimental results. By changing the position of the double clamps and substituting the identified clamp parameters into the proposed model, the universality of the identified parameters was demonstrated. Specific experimental and simulation results are compared as follows: Figure 6 The nonlinear parameters of single and double clamps are listed in Table 3.

[0219] Table 3 Nonlinear parameters of single and double clamps

[0220]

[0221] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A modeling method for parallel pipelines based on a semi-analytical approach, considering the nonlinearity of clamp-type flexible pipes, characterized in that, include: S1. Based on the semi-analytical method, a dynamic model of the parallel flow transmission pipeline system considering the nonlinearity of single and double clamps is established, including: S11. Establish a parallel flow transmission pipeline model, specifically including: S111, the kinetic energy of the parallel transmission pipeline. and potential energy Represented as: In the formula, the elastic modulus is subscript This represents which pipe number. Represents the lengths of the two pipes. and Representing pipes 1 and 2 along y shaft and z Translational displacement of the axis. and Representing pipes 1 and 2 regarding y Torsional displacements of the z-axis and z-axis, Indicates the cross-sectional area of ​​the pipe. Indicates the fluid surface area. This represents the shear correction factor. Indicates shear modulus, Indicates pipeline density. Indicates fluid density, Indicates fluid pressure. Represents Poisson's ratio, regarding y shaft and z The moment of inertia of the axis is used express, Indicates flow rate; S112. Calculate the nonlinear restoring force of the clamp. The calculation formula is as follows: In the formula, These are the weighting coefficients. and These represent the nonlinear stiffness coefficient and the linear stiffness coefficient, respectively. This represents the hysteresis damping force of single-joint and double-joint clamps, where, The results were obtained through calculations using the improved Bouc-Wen model: S113, due to the nonlinear restoring force of the clamp. It is expressed in the form of differential equations. To simplify the model, the restoring force functions of each spring in the single-link and double-link clamps are expressed as follows: In the formula, and The springs in the single-joint clamp and the double-joint clamp are respectively Restoring force in the direction, , , and These represent the linear and nonlinear stiffness, linear damping, and nonlinear damping of a single-link clamp, respectively. , , and These are the linear stiffness, nonlinear stiffness, linear damping, and nonlinear damping of the double clamp; S114. Regarding clamp damping, an equivalent viscous damping coefficient is introduced to replace the complex damping mechanism. This coefficient represents the single and double clamps in multiple directions, and the specific formula is as follows: , In the formula, The damping loss factor, Indicates the excitation frequency; the stiffness and damping of a single clamp are expressed in terms of... and express, The stiffness and damping of the double clamp are used and express, ; S115. Applying Hamilton's principle, the governing equations for parallel pipelines considering the nonlinearity of clamp-type flexible pipes are obtained, as follows: In the formula, , , The virtual work, including lateral restoring force and damping force, is specifically expressed as: In the formula, It is an external incentive. It is a variational symbol. Represents the Dirac function; S116. The elastic potential energy generated by single and double clamps is expressed by the following formula: The dynamic equations for pipe 1 and pipe 2 are then obtained as follows: In the formula, and These represent the positions of the springs in the single-joint clamps on pipes 1 and 2, respectively. and The positions of the springs in the double clamps on pipes 1 and 2; S12. Derive the modal vibration function of each pipeline based on the boundary conditions; S13. Solve for the assumed coefficients based on the continuity and deformation compatibility conditions of the pipeline; S2. Verify the established dynamic model of the parallel transmission pipeline system; S3. Identify the nonlinear parameters of single and double clamps, and then substitute the single clamp parameters into the parallel pipeline control equation to identify the nonlinear parameters of the parallel pipeline. S4. Change the position of the double clamps and substitute the identified nonlinear parameters of the parallel pipeline into the dynamic model of the parallel flow pipeline system to prove the universality of the identified parameters.

2. The parallel pipeline modeling method based on semi-analytical method considering the nonlinearity of clamps as described in claim 1, characterized in that, Step S12 specifically includes: S121. Segment at each spring support and make modal assumptions for each segment; each pipe route k A spring support, thus forming ( k +1) segments, each segment of pipe 1 and pipe 2 along z The transverse displacement mode shape function of the shaft is assumed to be as follows: In the formula, and Indicates that pipes 1 and 2 are along z Translational displacement mode functions of the axis, and These are the characteristic values ​​of each section of pipe 1 and pipe 2, respectively, where: , , ; S122. Set the following coordination conditions at each elastic support: S123. Calculate the assumed modal vibration function of pipe 2, and write the compatibility conditions of the elastic support points as the following matrix relationship: 。 3. The parallel pipeline modeling method based on semi-analytical method considering the nonlinearity of clamps as described in claim 1, characterized in that, Step S13 specifically includes: S131. Since the boundary conditions at both ends of the pipeline are free, the following characteristic equation is derived: S132. The characteristic equation is expressed as: S133. Calculate the coefficients of the first and last paragraphs using the following formula: S134. Since the only condition for a non-zero solution is that the determinant of its coefficients is zero, we solve for the eigenvalues ​​and calculate the modal coefficients: S135. An approximate solution is obtained using the Galerkin method, introducing the canonical coordinates of pipe 1. , , , and the regular coordinates of pipe 2 , , , The displacement of the pipeline in different directions is calculated as follows: S136. The dynamic equation of the system is expressed as: 。 4. The parallel pipeline modeling method based on semi-analytical method considering the nonlinearity of clamps as described in claim 1, characterized in that, In step S2, the established dynamic model of the parallel pipeline system is validated based on the parallel pipeline impact test. The testing instruments required for the parallel pipeline impact test include a triaxial accelerometer, a force hammer, and a 12-channel LMS system. The validation process includes: S21. To ensure the accuracy of the experimental results, the natural frequency of the parallel pipeline system was obtained through multiple hammer impact experiments. S22. The natural frequency of the transmission pipeline is obtained using a semi-analytical method. S23. The correctness of the model is verified by comparing the natural frequency of the parallel pipeline system obtained in step S21 with the natural frequency of the transmission pipeline obtained in step S22.

5. The parallel pipeline modeling method based on semi-analytical method considering the nonlinearity of clamps as described in claim 1, characterized in that, Step S3 specifically includes: S31. Conduct a frequency sweep experiment on the single clamp-mass block system to identify the nonlinear parameters. Then, substitute the single clamp parameters into the parallel pipeline control equation to identify the nonlinear parameters of the parallel pipeline. S32. The Bouc-Wen model is used to describe the hysteresis force of the clamp. The experimental error and simulation error are used as objective functions, and the particle swarm optimization (PSO) algorithm is used to identify the hysteresis parameters of the single clamp. S33. Then, based on the experiment, the nonlinear parameters of the double clamp are back-derived and identified.

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