A structural vibration displacement prediction method based on tube bundle segmented power spectrum conversion

Abstract

The application provides a structural vibration displacement prediction method based on tube bundle segmented power spectrum conversion and relates to the field of structural dynamic response prediction.The method comprises the following steps: step S1, obtaining a dimensionless power spectrum density; step S2, dividing the tube bundle length at equal intervals, and calculating the autospectrum density of each tube bundle through the dimensionless power spectrum density; step S3, performing inverse Fourier transform on the autospectrum density of each tube bundle to generate a time-domain force; and step S4, using a matlab program and adopting a transient integral method to generate the displacement response of the tube bundle.The application solves the key problem that the measurement accuracy and engineering applicability are difficult to unify in the prior art, realizes accurate calculation of the tube bundle vibration displacement, significantly improves the accuracy and calculation stability of the structural vibration displacement prediction, and provides a reliable technical means for flow-induced vibration analysis of the tube bundle in a complex industrial scene.

Description

Technical Field

[0001] This invention relates to the field of structural dynamic response prediction, and in particular to a method for predicting structural vibration displacement based on segmented power spectrum conversion of tube bundles. Background Technology

[0002] Currently, fluid-induced tube bundle vibration is becoming increasingly prominent in industrial equipment such as heat exchangers. In particular, fatigue damage caused by fluid disturbance has become a key factor affecting the safety and reliability of equipment.

[0003] Existing technologies mainly analyze tube bundle vibration by modeling the applied force through the overall power spectrum. However, this method ignores the lack of correlation between the force timing of different segments, which may lead to an underestimation of the actual response.

[0004] In the measurement of tube bundle vibration displacement, the mainstream method is based on the theory of random vibration. The core of this theory is the root-mean-square equation for tube bundle deflection, which is derived from the equation of motion of forced beam vibration, and Pettigrew and Gorman proposed a final applicable form for cross-flow conditions. However, this method has significant limitations: on the one hand, it cannot provide displacement time-series diagrams or maximum displacement values, limiting further analysis and evaluation; on the other hand, the calculation relies on numerous assumptions and simplifications, leading to errors in the root-mean-square calculation results, and the calculation method is singular and lacks flexibility.

[0005] Therefore, there is an urgent need to develop a new method that can both improve calculation accuracy and meet the actual needs of engineering in order to overcome the shortcomings of existing technologies. Summary of the Invention

[0006] The purpose of this invention is to provide a structural vibration displacement prediction method based on tube bundle segmented power spectrum conversion, which solves the problem that existing vibration calculation methods are difficult to effectively unify between measurement accuracy and engineering applicability.

[0007] To achieve the above objectives, this invention provides a structural vibration displacement prediction method based on tube bundle segmented power spectrum conversion, comprising the following steps:

[0008] Step S1: Obtain the dimensionless power spectral density;

[0009] Step S2: Divide the tube bundle length into equal intervals and calculate the autospectral density of each tube bundle segment using dimensionless power spectral density;

[0010] Step S3: Perform an inverse Fourier transform on the autospectral density of each tube segment to generate time-domain forces;

[0011] Step S4: Use the MATLAB program and the transient integration method to generate the displacement response of the tube bundle.

[0012] Preferably, the specific content of step S2 is as follows:

[0013] Step S201: Divide the tube bundle length into several segments at equal intervals. Assuming each segment is a rigid segment, the specific expression is as follows:

[0014]

[0015] Where Δx represents the integration length; L represents the tube bundle length; and N represents the number of tube bundle segments.

[0016] Step S202: Calculate the autospectral density Φ of each tube segment. F (f), the specific expression is:

[0017]

[0018] Where a represents the modal correlation coefficient; L0 represents the tube bundle reference length; D represents the tube bundle diameter; D0 represents the reference diameter; p0 and f0 represent the two-phase flow normalization factors; and f represents the frequency. This represents the dimensionless power spectral density.

[0019] Preferably, the specific content of step S3 is as follows:

[0020] Step S301: Calculate the autospectral density Φ of each tube segment. F (f) Perform an inverse Fourier transform to generate several segments of uncorrelated time-domain forces F. i (t), the specific expression is:

[0021]

[0022] Among them, f k Φ represents the k-th frequency; F (f k ) represents frequency f k The autospectral density at a given location; Δf represents the frequency interval, Δf = f k+1 -f k t represents time; θ ik This indicates that the i-th segment of the tube bundle is at frequency f k Random phase at the location;

[0023] Step S302: Calculate the correlation coefficient C between the temporal forces of each tube segment. ij To verify whether there is a correlation between the time-domain forces of different tube segments, the specific expression is as follows:

[0024]

[0025] Among them, F i (t) represents the temporal force of the i-th segment of the bundle; F j (t) represents the temporal force of the j-th segment of the control; E <Fi (t)F j (t)> represents the covariance between the temporal force of the i-th segment and the temporal force of the j-th segment of the bundle; E <F i (t)F i (t)> represents the value of the autocorrelation function of the time-domain force of the i-th segment of the bundle at zero time delay, i.e., the mean square value of the time-domain force of the i-th segment of the bundle; E <F j (t)F j (t)> represents the value of the autocorrelation function of the time-domain force of the j-th segment of the bundle at zero time delay, that is, the mean square value of the time-domain force of the j-th segment of the bundle.

[0026] Preferably, in step S4, the displacement response of the tube bundle includes the displacement response curve and the root mean square displacement of the tube bundle.

[0027] Preferably, in step S4, the specific expression for the root mean square of the displacement is:

[0028]

[0029] Among them, X RMS Represents the root mean square of the displacement; X(t) represents the displacement response at time t; N t This represents the total number of time steps.

[0030] Therefore, the present invention employs the above-mentioned structural vibration displacement prediction method based on segmented power spectrum conversion of tube bundles, and the beneficial technical effects are as follows:

[0031] (1) This invention innovatively divides the overall structural tube bundle into multiple independent calculation segments, calculates the autospectral density for each segment independently, generates time-domain forces, and obtains the displacement response of each segment, which can more accurately reflect the local dynamic characteristics of different structural locations. Compared with traditional random vibration theory calculation methods, the method of this invention significantly improves the accuracy of overall displacement prediction.

[0032] (2) The method of the present invention provides a more accurate prediction of the flow-induced vibration response of elastic tube bundles compared with experimental results. Comparative experimental results show that the error between the root mean square displacement of the tube bundle calculated by the method of the present invention and the measured value is controlled within 23%, which greatly improves the reliability and accuracy of the simulation calculation.

[0033] (3) This invention is not only applicable to excitation response analysis of multimodal and complex structures, but can also be extended to multimodal superposition analysis. It also performs well in complex structures with multiple segments such as nuclear power plants and aerospace heat exchangers, and has good adaptability. It can be combined with various dynamic methods such as transient integration and modal superposition, showing high computational flexibility.

[0034] (4) This invention has broad engineering application prospects and can be widely used in fields such as heat exchanger tube bundle life assessment, flow-induced vibration safety margin analysis, and pipe member fatigue simulation. It is particularly suitable for systems with strong local turbulence disturbances, large structural spans, and localized concentrated vibration responses, which can improve design reliability and reduce the costs caused by overly conservative designs. Attached Figure Description

[0035] Figure 1 This is a flowchart of the measurement method according to an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram of the elastic tube structure according to an embodiment of the present invention;

[0037] Figure 3 This is a schematic diagram of a tube bundle divided into multiple segments according to an embodiment of the present invention;

[0038] Figure 4 This is one of the time-domain force time history diagrams of a tube bundle divided into 15 segments according to an embodiment of the present invention;

[0039] Figure 5 For this embodiment of the invention, the temporal force correlation calculation is performed by dividing the tube bundle into 15 segments to verify the correlation of the generated temporal force.

[0040] Figure 6 This is a flow-induced vibration displacement time sequence diagram calculated by dividing the tube bundle into 15 segments according to an embodiment of the present invention;

[0041] Figure 7 This is a time-series displacement diagram of the tube bundle flow-induced vibration displacement calculated by the accelerometer in an embodiment of the present invention;

[0042] Figure 8 In this embodiment of the invention, the root mean square displacement calculated by dividing the tube bundle into 15 segments is compared with the root mean square displacement of the tube bundle flow-induced vibration calculated by the accelerometer. Detailed Implementation

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0044] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0045] Example 1

[0046] like Figure 1 As shown, a structural vibration displacement prediction method based on segmented power spectrum conversion of tube bundles includes the following steps:

[0047] Step S1: Measure the circumferential pressure of the tube bundle, integrate the circumferential pressure to obtain the force, and then perform a Fourier transform and dimensionless transformation on the force to obtain the dimensionless power spectral density.

[0048] Step S2: Divide the tube bundle length into multiple segments at equal intervals, such as... Figure 3 As shown. Then, the self-spectral density Φ of each tube segment is calculated using the dimensionless power spectral density. F (f).

[0049] The specific content is as follows:

[0050] Step S201: Divide the tube bundle length L = 0.237m into 15 equally spaced segments. The specific expression is:

[0051]

[0052] Where Δx represents the integration length; L represents the tube bundle length; and N represents the number of tube bundle segments.

[0053] In this embodiment, the tube bundle is an elastic tube bundle, and its structure is as follows: Figure 2 As shown. Assuming each tube segment is sufficiently short and is a rigid segment, its mode shapes are... This simplifies the calculation of force and vibration models.

[0054] The principle for simplifying each tube bundle into a rigid segment is as follows:

[0055]

[0056] Δx << λ;

[0057] Where v represents the propagation velocity of the bending wave in the tube bundle, which can be approximated as the characteristic velocity of wave propagation in the structure; f1 represents the first-order mode frequency of the tube bundle; and λ represents the wavelength of the bending wave.

[0058] In this embodiment, And Δx = 0.0158, which satisfies Δx << λ.

[0059] Step S202: Calculate the autospectral density Φ of each tube segment. F (f) provides a frequency domain basis for subsequent time-domain force synthesis.

[0060] The specific expression is:

[0061]

[0062] Where a represents the modal correlation coefficient; L0 represents the tube bundle reference length; D represents the tube bundle diameter; D0 represents the reference diameter; p0 and f0 represent the two-phase flow normalization factors; and f represents the frequency. This represents the dimensionless power spectral density.

[0063] In this embodiment, a = 2; L0 = 1m; D0 = 0.2m.

[0064] Step S3: Calculate the autospectral density Φ of each tube segment. F (f) Perform inverse Fourier transform to generate time-domain force F i (t).

[0065] The specific content of step S3 is as follows:

[0066] Step S301: Calculate the autospectral density Φ of each tube segment. F (f) Perform an inverse Fourier transform to generate several segments of uncorrelated time-domain forces F. i (t), the specific expression is:

[0067]

[0068] Among them, f k Φ represents the k-th frequency; F (f k ) represents frequency f k The autospectral density at a given location; Δf represents the frequency interval, Δf = f k+1 -f k t represents time; θ ik This indicates that the i-th segment of the tube bundle is at frequency f k The random phase at point follows a uniform distribution in [0, 2π].

[0069] like Figure 4 As shown, one of the 15 generated time-domain force time history plots is displayed.

[0070] Step S302: Calculate the correlation coefficient C between the temporal forces of each tube segment. ij To verify whether there is a correlation between the time-domain forces of different tube segments, the specific expression is as follows:

[0071]

[0072] Among them, F i (t) represents the temporal force of the i-th segment of the bundle; F j (t) represents the temporal force of the j-th segment of the control; E <F i (t)F j (t)> represents the covariance between the temporal force of the i-th segment and the temporal force of the j-th segment of the bundle; E <F i (t)F i (t)> represents the value of the autocorrelation function of the time-domain force of the i-th segment of the bundle at zero time delay, i.e., the mean square value of the time-domain force of the i-th segment of the bundle; E <F j (t)F j(t)> represents the value of the autocorrelation function of the time-domain force of the j-th segment of the bundle at zero time delay, that is, the mean square value of the time-domain force of the j-th segment of the bundle.

[0073] In this embodiment, the correlation coefficients between the temporal forces of the 15 tube bundle segments are calculated, and the results are as follows: Figure 5 As shown, it can be seen that only the diagonal lines show obvious autocorrelation, while the rest do not exhibit any correlation.

[0074] Step S4: Use the MATLAB program and the transient integration method to generate the displacement response of the tube bundle.

[0075] The displacement response of the tube bundle includes the displacement response curve X(t) and the root mean square displacement X. RMS The result is as follows Figure 6 As shown.

[0076] Specifically, the expression for this process is:

[0077]

[0078] Where X(t) represents the displacement response at time t; dτ represents the integral variable; h(t-τ) represents the impulse response function of the system; and Q(τ) represents the generalized force at time τ.

[0079] The specific expression for the generalized force Q(t) at time τ=t is:

[0080] Q(t)=φ T F i (t);

[0081] Where φ represents the mode shape vector; T represents the transpose.

[0082] The specific expression for the root mean square of displacement is:

[0083]

[0084] Among them, X RMS Represents the root mean square of the displacement; X(t) represents the displacement response at time t; N t This represents the total number of time steps.

[0085] For the same tube bundle structure, the vibration acceleration signal of the tube bundle is collected in real time by an accelerometer. After bandpass filtering and double integration, the displacement response of the tube bundle is finally output, namely the displacement response curve Y(t) and the root mean square displacement Yt. RMS The result is as follows Figure 7 As shown.

[0086] like Figure 8As shown, the root mean square (RMS) displacement of the tube bundle calculated by the method of this invention is compared with the RMS displacement of the tube bundle obtained by experimental measurement using an accelerometer. It can be seen that within the flow velocity test range of 0.65 m / s to 1.8 m / s, the maximum relative error between the two methods does not exceed 23%, and the obtained tube bundle vibration displacements accurately correspond to the measured values. This further demonstrates the reliability and feasibility of the method of this invention, which can accurately calculate the vibration displacement of the tube bundle in the turbulent buffeting region.

[0087] Therefore, the present invention adopts the above-mentioned structural vibration displacement prediction method based on tube bundle segmented power spectrum conversion, which solves the key problem of the difficulty in unifying measurement accuracy and engineering applicability in the prior art, realizes accurate calculation of tube bundle vibration displacement, significantly improves the accuracy and calculation stability of structural vibration displacement prediction, and provides a reliable technical means for the flow-induced vibration analysis of tube bundles in complex industrial scenarios.

[0088] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting structural vibration displacement based on segmented power spectrum conversion of tube bundles, characterized in that, Includes the following steps: Step S1: Obtain the dimensionless power spectral density; Step S2: Divide the tube bundle length into equal intervals and calculate the autospectral density of each tube bundle segment using dimensionless power spectral density; Step S3: Perform an inverse Fourier transform on the autospectral density of each tube segment to generate time-domain forces; Step S4: Using the MATLAB program and the transient integration method, generate the displacement response of the tube bundle; The specific content of step S2 is as follows: Step S201: Divide the tube bundle length into several segments at equal intervals. Assuming each segment is a rigid segment, the specific expression is as follows: ； in, Indicates the integration length; Indicates the length of the tube bundle; Indicates the number of tube segments; Step S202: Calculate the autospectral density of each tube segment. The specific expression is: ； in, Represents the modal correlation coefficient; Indicates the reference length of the tube bundle; Indicates the diameter of the tube bundle; Indicates the reference diameter; , This represents the normalization factor for two-phase flow; Indicates frequency; This represents the dimensionless power spectral density.

2. The structural vibration displacement prediction method based on segmented power spectrum conversion of tube bundles according to claim 1, characterized in that, The specific content of step S3 is as follows: Step S301: Calculate the autospectral density of each tube segment. Perform an inverse Fourier transform to generate several segments of uncorrelated time-domain forces. The specific expression is: ； in, Indicates the first One frequency; Represents frequency Autospectral density at the location; Indicates frequency interval, ; Indicates time; Indicates the first Segment bundle at frequency Random phase at the location; Step S302: Calculate the correlation coefficient between the temporal forces of each tube segment. To verify whether there is a correlation between the time-domain forces of different tube segments, the specific expression is as follows: ； in, Indicates the first Temporal force of segmented tubes; Indicates the first Temporal force of segmented tubes; Indicates the first Segmented tube time domain force and the first Covariance between temporal forces in the tube segment bundle; Indicates the first The value of the autocorrelation function of the time-domain force of the segmented tube at zero time delay, i.e., the value of the first segment... Mean square value of temporal force of segmented tube bundle; Indicates the first The value of the autocorrelation function of the time-domain force of the segmented tube at zero time delay, i.e., the value of the first segment... Mean square value of the time-domain force of the tube bundle.

3. The structural vibration displacement prediction method based on segmented power spectrum conversion of tube bundles according to claim 1, characterized in that, In step S4, the displacement response of the tube bundle includes the displacement response curve and the root mean square displacement of the tube bundle.

4. The structural vibration displacement prediction method based on segmented power spectrum conversion of tube bundles according to claim 1, characterized in that, In step S4, the specific expression for the root mean square of the displacement is: ； in, Indicates the root mean square of the displacement; express The displacement response value at time t; This represents the total number of time steps.

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