基于时频转换的管路时域随机振动分析方法

王彤晖; 王延荣; 魏大盛

doi:10.13700/j.bh.1001-5965.2022.0859

基于时频转换的管路时域随机振动分析方法

doi: 10.13700/j.bh.1001-5965.2022.0859

北京航空航天大学能源与动力工程学院，北京 100191

基金项目: 国家科技重大专项(J2019-Ⅳ-0012-0080)

详细信息

通讯作者:
E-mail：weidasheng@buaa.edu.cn

中图分类号: V214.1；TB123
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出版历程
- 收稿日期: 2022-10-30
- 录用日期: 2023-03-31
- 网络出版日期: 2023-04-12
- 整期出版日期: 2024-11-30

Time-domain random vibration analysis method of pipeline based on time-frequency conversion

School of Energy and Power Engineering，Beihang University，Beijing 100191，China

Funds: National Science and Technology Major Project (J2019-Ⅳ-0012-0080)

More Information

Corresponding author: E-mail：weidasheng@buaa.edu.cn

摘要

摘要:
减振结构的阻尼效果是管路振动设计的重点，传统频域随机振动计算方法考虑阻尼卡箍非线性因素较为困难。基于时频转换理论，提出了利用时域随机化方法将随机振动载荷谱转换为满足高斯分布的时域振动信号后进行动态计算的管路时域振动分析方法。利用简支梁模型计算了频域随机振动结果与时域随机振动结果，验证了时域随机振动分析方法的可行性，采样位置振动应力均方根值与频域结果误差在5%以内。针对实际管路结构分析了时域方法与频域方法的结果差异，并通过等效阻尼比的计算证明了时域方法在实际设计中的应用优势，采用时域方法分析了阻尼卡箍的摩擦系数、预紧力和不同卡箍构型对管路振动应力均方根值的影响，结果表明，构型和预紧力对振动影响较大，而摩擦系数影响较小，时域随机振动分析方法的参数设定更加灵活，能够差异化研究各类结构参数对管路振动的影响，提高管路减振结构设计效率。
- 管路 /
- 随机振动 /
- 减振结构 /
- 时域随机化 /
- 非线性因素
Abstract:
Characteristics of damping structures are essential for pipeline vibration design. In traditional random vibration analysis, it is currently challenging to take nonlinear variables caused by damping structure into account. Based on the theory of time-frequency conversion, this paper proposes a time-domain dynamic analysis method that converts random vibration load spectrum into a time-domain vibration signal satisfying Gaussian distribution by using the time-domain randomization method. First, using a simple beam model, the reliability of the time-domain analysis method was demonstrated by comparing random vibration results in frequency-domain and time-domain analysis. Notably, there is a 5% discrepancy in the stress root mean square error between the two approaches. In addition, the difference between the time-domain method and the frequency-domain method is analyzed for the actual pipeline structure, and the advantage of the time-domain method in practical design is proved by calculating the equivalent damping ratio. Thereafter, it was analyzed that the influence of friction coefficient, preload of damping clamp and different clamp configurations on pipeline vibration by applying the time-domain analysis method. The results indicate that the configuration and preload have a greater influence on vibration, but the friction coefficient has a smaller influence. It is evident from the aforementioned analysis that the time-domain random vibration analysis method's parameter setting is more adaptable, allowing for a more thorough investigation of the effects of different structural parameters on pipeline vibration and an improvement in the damping structure's design efficiency.
- pipeline /
- random vibration /
- damping structure /
- time domain randomization /
- nonlinear factor

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图 1 加窗、搭接过程示意图^[13]

Figure 1. Schematic diagram of windowing and superposition process^[13]

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图 2 随机振动信号的时频转换过程^[12]

Figure 2. Time-frequency conversion process of random vibration signal^[12]

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图 3 时域随机化生成的振动信号

Figure 3. Vibration signals generated by time domain randomization

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图 4 功率谱密度曲线对比

Figure 4. Comparison of power spectral density curves

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图 5 时域随机振动分析流程

Figure 5. Process of random vibration analysis in time domain

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图 6 简支梁有限元模型示意图

Figure 6. Schematic diagram of finite element model of simply supported beam

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图 7 输出单元z方向应力PSD曲线

Figure 7. z direction stress PSD curves of the output element

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图 8 2 032号单元应力时域和频域响应曲线

Figure 8. Time domain and frequency domain stress response curves of element 2 032

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图 9 管路有限元模型

Figure 9. Finite element model of pipeline

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图 10 频域随机振动分析的应力均方根值分布

Figure 10. Stress RMS distribution for random vibration analysis in frequency domain

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图 11 选定的应力输出单元

Figure 11. Selected stress output element

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图 12 选定3个输出单元的频域随机振动响应

Figure 12. Random vibration responses of three selected output elements in frequency domain

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图 13 时长0.2 s的随机信号

Figure 13. Random signal of 0.2 s duration

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图 14 3个不同位置单元的时域随机振动计算结果

Figure 14. Computational results of time domain random vibration for three differently positioned elements

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图 15 管路阻尼卡箍结构

Figure 15. Damping clamp structure of pipeline

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图 16 摩擦系数对随机振动应力的影响

Figure 16. The influence of friction coefficient on random vibration stress

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图 17 216 478号单元的应力PSD曲线瀑布图

Figure 17. Waterfall diagram of stress PSD curve for element 216 478

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图 18 预紧力加载示意图

Figure 18. Schematic diagram of clamping load

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图 19 阻尼块内外表面接触压力随预紧力的变化

Figure 19. The contact pressure varies with the clamping load at internal and external surface of damping block

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图 20 预紧力对随机振动应力的影响

Figure 20. The influence of clamping load on random vibration stress

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图 21 215 740号单元的应力PSD曲线瀑布图

Figure 21. Waterfall diagram of stress PSD curve for element 215 740

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图 22 216 478号单元的摩擦系数与预紧力耦合影响

Figure 22. Coupling effect of friction coefficient and clamping load on element 216 478

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图 23 215 740号单元的摩擦系数与预紧力耦合影响

Figure 23. Coupling effect of friction coefficient and clamping load on element 215 740

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图 24 3种不同管路卡箍构型

Figure 24. Three types of clamp configuration at pipeline

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图 25 216 478号单元的应力谱密度曲线对比

Figure 25. Comparison of stress PSD curves for element 216 478

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表 1 随机振动功率谱密度

Table 1. Random vibration power spectral density

频率/Hz	PSD/ (g²·Hz⁻¹)
10	0.008
100	0.08
1 000	0.08
2 000	0.02

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表 2 频域随机振动计算结果

Table 2. Calculation results of random vibration in frequency domain

单元号	z方向应力均方根值/MPa	特征频率/Hz
2 032	19.93	554.7/1114
2 100	13.61	554.7/1114

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表 3 时域随机振动计算结果

Table 3. Calculation results of random vibration in time domain

时域信号时长/s	单元号	z方向应力均方根值/MPa
时域信号时长/s	单元号	第1次	第2次	第3次	第4次	第5次	第6次	均值	标准差
0.2	2 032	21.73	15.82	19.82	22.18	14.69	22.27	19.42	3.07
0.2	2 100	14.86	10.82	13.55	15.17	10.13	15.24	13.30	2.07
1	2 032	22.96	18.09	17.28	20.57	17.46	21.02	19.56	2.10
1	2 100	15.72	12.36	11.81	14.07	11.93	14.37	13.38	1.45

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表 4 时域分析与ABAQUS频域分析的应力均方根值对比

Table 4. Comparison of stress RMS values in time domain and ABAQUS frequency domain analysis

时域信号时长/s	单元号	时域应力均方根值/MPa	ABAQUS频域计算均方根值/MPa	误差/%
0.2	2 032	19.42	19.93	−2.57
0.2	2 100	13.30	13.61	−2.31
1	2 032	19.56	19.93	−1.84
1	2 100	13.37	13.61	−1.71

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表 5 管路频域与时域分析的应力均方根值对比

Table 5. Comparison of stress RMS values for pipeline in time domain and frequency domain analysis

单元号	时域计算S11 均方根值/MPa	频域计算S11均方根值/MPa
单元号	时域计算S11 均方根值/MPa	模态阻尼比0.004	模态阻尼比0.006	模态阻尼比0.008	模态阻尼比0.01	模态阻尼比0.012	模态阻尼比0.014
216 478	4.37	8.53	6.97	6.04	5.41	4.94	4.57
215 740	7.13	11.28	9.2	7.96	7.12	6.5	6.01
217 038	2.59	6.08	4.97	4.31	3.86	3.53	3.26

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表 6 3种构型的应力均方根值结果

Table 6. Stress RMS values of three configurations

单元号	S11应力均方根值/MPa
单元号	构型A	构型B	构型C
216 478	7.58	5.86	4.90
215 740	6.33	5.74	4.43
217 038	5.98	4.42	3.92

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