CN108595794A - A kind of pipeline structure oscillating load analysis method - Google Patents
A kind of pipeline structure oscillating load analysis method Download PDFInfo
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Abstract
The present invention relates to a kind of pipeline structure oscillating load analysis methods, include the following steps：1st step obtains pipeline structure dynamic characteristic；Measuring point is arranged at pipeline structure exemplary position, obtains the acceleration responsive power spectral density of measuring point for 2nd step；3rd step calculates modal acceleration root-mean-square value at each measuring point using equivalent white-noise excitation method；4th step is weighted each measuring point modal acceleration root-mean-square value in the 3rd step average, acquisition each rank modal acceleration root-mean-square value of pipeline structure using each point position Mode Shape value；5th step carries out the calculating of mode root mean square equivalent load under random vibration.The method is by the mode root mean square in the loading analysis method, providing equivalent white-noise excitation computing technique so that this method can achieve the effect that quickly to analyze.And with engineering simplification formula, the feature that quickly analysis calculates, pipeline structure dynamics load design can be instructed.
Description
Technical field
The present invention relates to a kind of pipeline structure oscillating load analysis methods, belong to Structural Dynamics simulation analysis field.
Background technology
The basic function of pipeline is that specified medium is transported to using position.For the dynamics intensity of pipeline structure,
Generally analysis of Fatigue-life means is taken to be assessed.This needs acquisition region of interest (to have more present connector, clip, welding etc.
Place) accurate dynamic stress and fatigue of materials performance parameter.But since structure type, processing technology, material property, modeling miss
The influence of the factors such as difference carries out accurate Stress Calculation analysis to above-mentioned weak part, test measurement is very difficult
's.
With the fast development of China's modern industry, it is complicated more that the pipeline in all kinds of mechanical systems shows structure type
The characteristics of sample, substantial amounts, the workload that this also causes the analysis of Fatigue-life of pipeline structure to calculate is excessive, is unfavorable for initially setting
The quick use in meter stage.
The seventies in last century,《NASA-TM-X-64669-Vibration Manual》Middle US National Aeronautics and Space Administration is just
It mentions and utilizes Miles formula, carrying out random and sinusoidal vibration Equivalent Static inertial load to pipeline structure analyzes, to obtain pipe
Section load at the low order resonant frequency key position of road, for design reference.
The purpose of load (including oscillating load) analysis is the type of load, numerical value and transfer route, energy in clear pipeline
Enough foundation is provided for pipeline structure Intensity Design.Currently, it is domestic in industrial circles such as space flight, for the initial designs of pipeline structure
Also the theory of loading analysis design is used gradually.It is generally appropriate by being multiplied by but due to lacking oscillating load quantitative analysis means
Safety coefficient consider the influence in actual working environment in terms of vibration, it is random larger.
Invention content
(1) technical problems to be solved
For demand in the prior art, the present invention proposes a kind of pipeline structure oscillating load analysis method, by right
Mode root mean square in the loading analysis method provides equivalent white-noise excitation computing technique so that this method can reach
The effect quickly analyzed.And with engineering simplification formula, the feature that quickly analysis calculates, pipeline structure dynamics can be instructed to carry
Lotus is designed.
(2) technical solution
The present invention proposes a kind of pipeline structure oscillating load analysis method, includes the following steps：
1st step obtains pipeline structure dynamic characteristic；
Measuring point is arranged at pipeline structure exemplary position, obtains the acceleration responsive power spectral density of measuring point for 2nd step；
3rd step calculates modal acceleration root-mean-square value at each measuring point using equivalent white-noise excitation method；
4th step, using each point position Mode Shape value, to each measuring point modal acceleration root-mean-square value in the 3rd step into
Row weighted average obtains each rank modal acceleration root-mean-square value of pipeline structure；
5th step carries out the calculating of mode root mean square equivalent load under random vibration.
(3) advantageous effect
The present invention proposes a kind of pipeline structure oscillating load analysis method, for the mode in the loading analysis method
Root mean square provides equivalent white-noise excitation computing technique so that this method can achieve the effect that quickly to analyze.This method has
There are engineering simplification formula, the feature that quickly analysis calculates, can be provided for quantitative dynamic load in pipeline structure Intensity Design
Foundation.
Description of the drawings
A kind of pipeline structure oscillating load analysis method flow charts of Fig. 1.
Fig. 2 spatial pipeline system structural finite element models.
The bases Fig. 3 arbitrary excitation acceleration spectrum.
Z-direction acceleration is accordingly composed at Fig. 4 exemplary positions.
The 1st rank modal regions equivalent load stress of Fig. 5 is compared with random vibration cumulative stress root-mean-square value.Wherein, left figure
For stress under the 1st rank mode equivalent load, right figure is frequency【10,200】Hz range internal stress root mean square.
The 5th rank modal regions equivalent load stress of Fig. 6 is compared with random vibration cumulative stress root-mean-square value.Wherein, left figure
For stress under the 5th rank mode equivalent load, right figure is frequency【650,1000】Hz range internal stress root mean square.
The 5th rank modal regions equivalent load stress of Fig. 7 with the sum of compared with random vibration cumulative stress root-mean-square value.Its
In, left figure is the sum of stress under the 5th rank mode equivalent load, and right figure is frequency【10,1000】Hz range internal stress root mean square.
Specific implementation mode
A kind of pipeline structure oscillating load analysis method of the present invention, includes the following steps：
1st step obtains pipeline structure dynamic characteristic.
The modal frequency of pipeline structure, Mode Shape are obtained by simulation calculation or test measurement, is obtained by test measurement
The modal damping for obtaining pipeline structure establishes structural finite element model according to the specific geometric dimension of pipeline structure, material properties,
The support end face at pipeline both ends is clamped, calculates the modal frequency f for obtaining pipeline structureiWith Mode Shape φi(x)。
The present embodiment takes the means of simulation analysis to be said by taking pipeline structure finite element model shown in Fig. 2 as an example
It is bright.Table 1 lists the preceding 10 rank modal frequency of the pipeline structure.
10 rank modal frequency before table 1
| Exponent number | f1 | f2 | f3 | f4 | f5 | f6 | f7 | f8 | f9 | f10 |
| Frequency (Hz) | 121.95 | 267.20 | 351.47 | 592.49 | 707.69 | 1115.9 | 1229.3 | 1734.2 | 1876.4 | 2611.0 |
Measuring point is arranged at pipeline structure exemplary position, obtains the acceleration responsive power spectral density of measuring point for 2nd step.
The acceleration responsive power spectrum at pipeline structure exemplary position is obtained by the means of simulation calculation or test measurement
Density, the Z-direction in the support end face at pipeline structure both ends applies acceleration power spectrum, and assumes that all rank modal dampings are certain
Value, amplification coefficient also mutually should be certain value, to carry out random vibration corresponding analysis；Choose several position conducts on pipeline structure
Experiment measuring point obtains the Z-direction acceleration corresponding power spectrum density curve of the experiment measuring point to simulate pipeline structure response.Its
In, Z-direction is in pipeline end face and the perpendicular direction of the both ends of the surface line of centres, as shown in Figure 2.
The means of simulation analysis are still taken to illustrate in the present embodiment, the acceleration power spectrum is used as in Fig. 3
Shown in acceleration power spectrum, all rank modal dampings are：
ζi=0.01,
I.e. amplification coefficient is：
Referring to Fig. 2, position at 9 is chosen on pipeline structure and is obtained described as experiment measuring point simulation pipeline structure response
The Z-direction acceleration corresponding power spectrum density curve of measuring point is tested, the curve is as shown in Figure 4.
3rd step calculates modal acceleration root-mean-square value at each measuring point using equivalent white-noise excitation method.
Pipeline structure meets small damping structure feature, i.e. each crest frequency of its PSD response is significantly separated, and peak value is rung
Should be approximately the resonance response of single-mode system, as shown in Figure 4.For the root-mean-square value of power spectral density plot isolated peak
It can be calculated by the corresponding single-mode system of white-noise excitation of respective magnitudes.
Assuming that power spectral density plot isolated peak frequency is fk, amplification coefficient Qk, it is assumed that power spectral density amplitude maximum
Value WkWith its equivalent white noise acoustic amplitude W0Ratio be α, then：
So whenWhen, root-mean-square value and the utilization amplitude in the power spectral density plot isolated peak region are W0It is white
The root-mean-square value that noise excitation single-mode system generates is equal, and the frequency of the single-mode system is f0=fk, the list is certainly
It is Q by the amplification coefficient of degree system0=Qk.Therefore, further it can estimate that power spectral density plot is isolated using Miles formula
The root-mean-square value of peak value.
It is assumed that j-th of measuring point x on pipeline structurejAcceleration power spectral density curve beSo, if i-th
Rank modal frequency is fi, amplification coefficient Qi, correspond to power spectral density plot peak region acceleration-root-mean square be：
The 1st rank and the 5th rank modal acceleration at each measuring point being calculated using formula (2) is set forth in table 2, table 3
Root-mean-square value.
The 1st rank modal frequency (f of table 2i=121.95Hz) region, measuring point acceleration responsive RMS
| Point position | 1st rank Mode Shape value | Frequency range chooses (Hz) | Q in formula (2)iValue | Formula 2 calculates RMS (g) |
| Node 6769 | 0.137562 | [10,200] | 50 | 2.539 |
| Node 9304 | 0.335238 | [10,200] | 50 | 6.140 |
| Node 11178 | 0.544263 | [10,200] | 50 | 9.959 |
| Node 14384 | 0.782450 | [10,200] | 50 | 14.312 |
| Node 17218 | 0.978226 | [10,200] | 50 | 17.891 |
| Node 17809 | 0.946763 | [10,200] | 50 | 17.316 |
| Node 22755 | 0.823882 | [10,200] | 50 | 15.069 |
| Node 27076 | 0.542858 | [10,200] | 50 | 9.933 |
| Node 28554 | 0.233324 | [10,200] | 50 | 4.281 |
The 5th rank modal frequency region (f of table 3i=707.69Hz) region, measuring point acceleration responsive RMS
4th step, using each point position Mode Shape value, to each measuring point modal acceleration root-mean-square value in the 3rd step into
Row weighted average obtains each rank modal acceleration root-mean-square value of pipeline structure.
The root-mean-square displacement of pipeline structure the i-th rank modeFor：
In formula (3), φi(x) it is the Mode Shape after the normalization of pipeline structure the i-th rank maximum value, φi(xj) it is xjMeasuring point
The i-th rank Mode Shape value.For xjResponse root-mean-square value corresponding to i-th rank mode of measuring point, n are experiment measuring point
Number.
Table 4 gives the preceding 5 rank modal acceleration root-mean-square value being calculated using formula (3).
5 rank mode root mean square acceleration before table 4
| Rank number of mode | Frequency (Hz) | Root mean square acceleration (g) |
| 1 | 121.95 | 19 |
| 2 | 267.20 | 5.96 |
| 3 | 351.47 | 1.89 |
| 4 | 592.49 | 132.7 |
| 5 | 707.69 | 73.6 |
5th step carries out the calculating of mode root mean square equivalent load under random vibration.
According to Modal Analysis Theory, for the i-th rank mode, if applying inertia force m (x on pipeline structurej)(2πfi)2
φi(xj), (j=1,2, L, N), wherein N is structural finite element model degree of freedom number, then corresponding structure static state deformation curve
For the i-th rank Mode Shape φi(x), wherein m (xj) it is xjThe lumped mass of point position.Correspondingly, if defining the i-th rank mode
The root-mean-square displacement of responseBy the i-th rank Mode Shape φi(x) maximum value normalizes, then, apply inertia on pipeline structure
PowerThen corresponding static deformation curve is the root-mean-square displacement of the i-th rank modal responseTherefore,
The root mean square equivalent load of i-th rank mode is represented by：
For pipeline structure PSD response, the acceleration power spectral density P of certain pointa(f), speed-power spectrum density
Pv(f), displacement power spectral density Pu(f) transformational relation between is：
The calculating of pipeline structure mode root mean square equivalent load can be obtained by formula (4), (5) and (6)：
F in formula (5), (6) is the frequency in power spectral density, the generally horizontal axis in power spectral density plot；In formula (7)For the i-th rank modal acceleration root mean square obtained in the 4th step.
It should be noted that when using finite element method, need the vibration shape value using corresponding node, lumped mass into
Row calculates.After obtaining the equivalent oscillating load distribution of pipeline structure the i-th rank mode root mean square by formula (7), and then structure can be obtained
Shearing, moment of flexure and stress.
Fig. 5, Fig. 6 are respectively to the 1st rank, the lower stress of the 5th rank mode root mean square equivalent load effect and corresponding modal regions
It is compared in random vibration cumulative stress root-mean-square value；Fig. 7 is to the stress under the effect of preceding 5 rank mode root mean square equivalent load
The sum of compared with random vibration cumulative stress root-mean-square value of the excited frequency under [10,1000].It is answered from pipeline structure
The correct validity of context of methods is fully verified and illustrated to force-responsive distribution angle result consistency.
Claims (7)
1. a kind of pipeline structure oscillating load analysis method, which is characterized in that include the following steps：1st step obtains pipeline structure
Dynamic characteristic；
Measuring point is arranged at pipeline structure exemplary position, obtains the acceleration responsive power spectral density of measuring point for 2nd step；
3rd step calculates modal acceleration root-mean-square value at each measuring point using equivalent white-noise excitation method；
4th step adds each measuring point modal acceleration root-mean-square value in the 3rd step using each point position Mode Shape value
Weight average obtains each rank modal acceleration root-mean-square value of pipeline structure；
5th step carries out the calculating of mode root mean square equivalent load under random vibration.
2. a kind of pipeline structure oscillating load analysis method as described in claim 1, which is characterized in that the 1st step is specific
Including：The modal frequency of pipeline structure, Mode Shape are obtained by simulation calculation or test measurement, is managed by test measurement
The modal damping of line structure establishes structural finite element model, in pipeline according to the specific geometric dimension of pipeline structure, material properties
The support end face at both ends is clamped, calculates the modal frequency f for obtaining pipeline structureiWith Mode Shape φi(x)。
3. a kind of pipeline structure oscillating load analysis method as claimed in claim 2, which is characterized in that the 2nd step is specific
Including：The acceleration responsive power spectrum at pipeline structure exemplary position is obtained by the means of simulation calculation or test measurement
Degree, the Z-direction in the support end face at pipeline structure both ends applies acceleration power spectrum, and assumes that all rank modal dampings are certain
Value, amplification coefficient also mutually should be certain value, to carry out Random vibration analysis；Choose several position conducts on pipeline structure
Experiment measuring point obtains the Z-direction acceleration corresponding power spectrum density curve of the experiment measuring point to simulate pipeline structure response,
In, Z-direction is in pipeline end face and the perpendicular direction of the both ends of the surface line of centres.
4. a kind of pipeline structure oscillating load analysis method as claimed in claim 3, which is characterized in that the 3rd step is specific
Including：Pipeline structure meets small damping structure feature, i.e. each crest frequency of its PSD response is significantly separated, and peak response is close
Like the resonance response for being single-mode system, respective magnitudes are passed through for the root-mean-square value of power spectral density plot isolated peak
White-noise excitation corresponding single-mode system calculates.
5. a kind of pipeline structure oscillating load analysis method as claimed in claim 4, which is characterized in that described for power spectrum
The root-mean-square value of density curve isolated peak calculates tool by the corresponding single-mode system of white-noise excitation of respective magnitudes
Body includes：
Assuming that power spectral density plot isolated peak frequency is fk, amplification coefficient Qk, it is assumed that power spectral density amplitude maximum Wk
With its equivalent white noise acoustic amplitude W0Ratio be α, then：
So whenWhen, root-mean-square value and the utilization amplitude in the power spectral density plot isolated peak region are W0White noise
Encourage the root-mean-square value that single-mode system generates equal, the frequency of the single-mode system is f0=fk, the single-degree-of-freedom
The amplification coefficient of system is Q0=Qk；Therefore, further power spectral density plot isolated peak can be estimated using Miles formula
Root-mean-square value；
It is assumed that j-th of measuring point x on pipeline structurejAcceleration power spectral density curve beSo, if the i-th rank mode
Frequency is fi, amplification coefficient Qi, correspond to power spectral density plot peak region acceleration-root-mean square be：
6. a kind of pipeline structure oscillating load analysis method as claimed in claim 5, which is characterized in that the 4th step is specific
Including：
The root-mean-square displacement of pipeline structure the i-th rank modeFor：
In formula (3), φi(x) it is the Mode Shape after the normalization of pipeline structure the i-th rank maximum value, φi(xj) it is xjThe i-th of measuring point
Rank Mode Shape value；For xjResponse root-mean-square value corresponding to i-th rank mode of measuring point, n are experiment measuring point number.
7. a kind of pipeline structure oscillating load analysis method as claimed in claim 6, which is characterized in that the 5th step is specific
Including：
According to Modal Analysis Theory, for the i-th rank mode, if applying inertia force m (x on pipeline structurej)(2πfi)2φi
(xj), (j=1,2, L, N), wherein N is structural finite element model degree of freedom number, then corresponding structure static state deformation curve is
I-th rank Mode Shape φi(x), wherein m (xj) it is xjThe lumped mass of point position；Correspondingly, it is rung if defining the i-th rank mode
The root-mean-square displacement answeredBy the i-th rank Mode Shape φi(x) maximum value normalizes, then, apply inertia force on pipeline structureThen corresponding static deformation curve is the root-mean-square displacement of the i-th rank modal responseTherefore,
The root mean square equivalent load of i rank mode is represented by：
For pipeline structure PSD response, the acceleration power spectral density P of certain pointa(f), speed-power spectrum density Pv
(f), displacement power spectral density Pu(f) transformational relation between is：
The calculating of pipeline structure mode root mean square equivalent load can be obtained by formula (4), (5) and (6)：
F in formula (5), (6) is the frequency in power spectral density；In formula (7)The i-th rank mode to be obtained in the 4th step accelerates
Spend root mean square.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111597722A (en) * | 2020-05-20 | 2020-08-28 | 北京航空航天大学 | Method for predicting equipment precision retention time by using running state information |
| CN112464537A (en) * | 2020-12-15 | 2021-03-09 | 四川长虹空调有限公司 | Air conditioner pipeline structure noise radiation rapid calculation method |
| CN113148231A (en) * | 2021-05-14 | 2021-07-23 | 北京宇航系统工程研究所 | Catheter dynamic strength modular structure based on staggered frequency design |
| CN116432335A (en) * | 2023-03-03 | 2023-07-14 | 江阴市南方管件制造有限公司 | Preparation process of non-standard pipe fitting for chemical industry based on finite element analysis |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102223327A (en) * | 2011-07-18 | 2011-10-19 | 西安电子科技大学 | SAGE (Space-alternating Generalized Expectation-maximization) based channel estimation method in CoMP multi-user system |
| CN106096119A (en) * | 2016-06-07 | 2016-11-09 | 西北工业大学 | The lower Structural Topology Optimization Design method of casual acceleration based on large-mass method excitation |
-
2018
- 2018-04-11 CN CN201810318880.5A patent/CN108595794A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102223327A (en) * | 2011-07-18 | 2011-10-19 | 西安电子科技大学 | SAGE (Space-alternating Generalized Expectation-maximization) based channel estimation method in CoMP multi-user system |
| CN106096119A (en) * | 2016-06-07 | 2016-11-09 | 西北工业大学 | The lower Structural Topology Optimization Design method of casual acceleration based on large-mass method excitation |
Non-Patent Citations (1)
| Title |
|---|
| 王帅 等: "管路结构振动载荷设计与评估技术", 《强度与环境》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111597722A (en) * | 2020-05-20 | 2020-08-28 | 北京航空航天大学 | Method for predicting equipment precision retention time by using running state information |
| CN111597722B (en) * | 2020-05-20 | 2023-11-10 | 北京航空航天大学 | Method for predicting equipment precision holding time by using running state information |
| CN112464537A (en) * | 2020-12-15 | 2021-03-09 | 四川长虹空调有限公司 | Air conditioner pipeline structure noise radiation rapid calculation method |
| CN112464537B (en) * | 2020-12-15 | 2022-06-21 | 四川长虹空调有限公司 | Air conditioner pipeline structure noise radiation rapid calculation method |
| CN113148231A (en) * | 2021-05-14 | 2021-07-23 | 北京宇航系统工程研究所 | Catheter dynamic strength modular structure based on staggered frequency design |
| CN116432335A (en) * | 2023-03-03 | 2023-07-14 | 江阴市南方管件制造有限公司 | Preparation process of non-standard pipe fitting for chemical industry based on finite element analysis |
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