随机疲劳评估的反应谱法及工程应用

doi:10.7527/S1000-6893.2025.31473

Abstract

Abstract: To address efficient prediction of structural fatigue life under random excitation, the fatigue response spectrum method (FRSM), a high-efficiency algorithm, is established and organized. In the proposed method, a fatigue damage response spectrum (FDRS) is constructed to quantify the contribution of modal response to the total fatigue damage of the structure, and an explicit relationship is deduced to connect the fatigue life of the structure and structural characteristics, such as the natural frequency and the stress mode shape. Firstly, based on the theory of random vibration, the establishment of the FRSM is discussed in terms of the single moment method and the power spectral density (PSD) decomposition strategy of the fatigue life assessment in the frequency domain, and three calculation formats of the FRSM is provided. Then, the dimensionless FDRS is constructed, with the spatial characteristics of the structure (the stress mode and the modal participation coefficient) separated from the modal contribution to the total fatigue damage, and a feasible database establishment strategy is proposed. Finally, numerical examples are carried out based on the engineering application of the FRSM to vibration and acoustic fatigue problems, demonstrating its advancement in dealing with large-scale engineering problems. The result shows that the accuracy of the FRSM is consistent with that of classical methods such as the rainflow counting method, Dirlik method, and T-B method, and the efficiency can be improved by 2-3 orders of magnitude due to the avoidance of the PSD functions as well as the spectral moments.

Key words: High-cycle fatigue, Random vibration, Frequency domain method, Fatigue response spectrum method, Fatigue damage response spectrum

CLC Number:

V21
O324

Guohao Sui. Response spectrum method and its engineering application for random fatigue assessment[J]. Acta Aeronautica et Astronautica Sinica, doi: 10.7527/S1000-6893.2025.31473.

References

[1] 顾孟奇, 朱家才, 郭万林, 薛松. 可重复使用运载火箭结构疲劳耐久性与可靠性展望[J]. 航空学报, 2023, 44(23): 34-57.
GU M Q, ZHU J C, GUO W L, XUE S. Prospects for fatigue durability and reliability of reusable rocket struc-tures[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(23): 34-57.（in Chinese）
[2] Zhao B F, Xie L Y, Song J X, Ren J G, Wang B W, Zhang S J. Fatigue life prediction of aero-engine com-pressor disk based on a new stress field intensity ap-proach[J]. International Journal of Mechanical Sciences, 2020, 165: 105190.
[3] Kim H J, Jang B S, Du Kim J. Fatigue-damage predic-tion for ship and offshore structures under wide-banded non-Gaussian random loadings part I: Approximation of cycle distribution in wide-banded gaussian random pro-cesses[J]. Applied Ocean Research, 2020, 101: 102294.
[4] 姚卫星. 结构疲劳寿命分析[M]. 北京: 科学出版社, 2019.
[5] Miner M A. Cumulative damage in fatigue[J]. Journal of Applied Mechanics, 1945, 12(3): 159-164.
[6] Zorman A, Slavi? J, Bolte?ar M. Vibration fatigue by spectral methods-A review with open-source support evaluation of mechanical components[J]. Mechanical Systems and Signal Processing, 2023, 190: 110149.
[7] Bendat J S. Probability functions for random responses: prediction of peaks, fatigue damage, and catastrophic failures[R]. Report NASA-CR-33, 1964.
[8] Lutes L D, Larsen C E. Improved spectral method for variable amplitude fatigue prediction[J]. Journal of Struc-tural Engineering, 1990, 116(4): 1149-1164.
[9] Larsen C E, Lutes L D. Predicting the fatigue life of off-shore structures by the single-moment spectral method[J]. Probabilistic Engineering Mechanics, 1991, 6(2): 96-108.
[10] Dirlik T. Application of computers in fatigue analysis[D]. The University of Warwick, 1985.
[11] Tovo R. Cycle distribution and fatigue damage under broad-band random loading[J]. International Journal of Fatigue, 2002, 24(11): 1137-1147.
[12] Benasciutti D, Tovo R. Spectral methods for lifetime prediction under wide-band stationary random process[J]. International Journal of Fatigue, 2005, 27(8): 867-877.
[13] 郑向远, 高山, 李炜. 一种新的高斯多模态随机疲劳损伤频域分析方法[J]. 哈尔滨工业大学学报, 2020, 52(10): 85-93.
ZHENG X Y, GAO S, LI W. A new frequency-domain method for analysis of Gaussian multi-modal random fa-tigue damage[J]. Journal of Harbin Institute of Technolo-gy, 2020, 52(10): 85-93.（in Chinese）
[14] 袁奎霖, 靳宏义. 一种新的高斯双模态随机疲劳损伤分析方法[J]. 哈尔滨工业大学学报, 2023, 55(8): 135-142.
YUAN K L, JIN H Y. Development of a new frequency-domain method for fatigue damage assessment in bimod-al Gaussian random processes[J]. Journal of Harbin In-stitute of Technology, 2023, 55(8): 135-142.（in Chinese）
[15] 周敏亮, 陈忠明, 邓吉宏, 施荣明. 飞机结构振动疲劳寿命频域预估方法研究[J].飞机设计, 2017, 37(3): 25-30.
ZHOU M L, CHEN Z M，DENG J H，SHI R M. Re-search on vibration fatigue life frequency-domain estima-tion method of aircraft structure [J]. Aircraft Design, 2017, 37(3): 25-30. （in Chinese）
[16] 吴光强, 李超, 丁丰, 章蕾. 基于频域和时域法的电池包随机振动疲劳计算对比研究[J]. 湖南大学学报(自然科学版), 2024, 51(2): 208-218.
WU G Q, LI C, DING F, ZHANG L. A comparing study on battery pack random vibration fatigue calcula-tion based on frequency domain and time domain ap-proaches[J]. Journal of Hunan University (Natural Sci-ences), 2024, 51(2): 208-218.（in Chinese）
[17] Martinez-Puente E, Zarketa-Astigarraga A, Martinez-Agirre M, Zabala A, Esnaola JA, Mu?iz-Calvente M, Llavori I, Penalba M. Benchmarking of spectral methods for fatigue assessment ofmooring systems and dynamic cables in offshore renewable energy technologies[J]. Ocean Engineering, 2024, 308: 118311.
[18] 袁盛铭, 吴兴文, 赵明花, 池茂儒. 随机振动疲劳寿命评估频域法模型适用性研究[J]. 噪声与振动控制, 2023, 43(2): 28-34.
YUAN S M, WU X W, ZHAO M H, CHI M R. Re-search on applicability of frequency domain model for random vibration fatigue lifespan assessment[J]. Noise and Vibration Control, 2023, 43(2): 28-34.（in Chinese）
[19] 邓康清, 朱雯娟, 王相宇, 余小波, 郭春亮, 刘梦珂, 张峰涛, 向进, 王鹍鹏, 张琪敏. 特种结构固体火箭发动机燃烧室随机振动疲劳分析[J]. 固体火箭技术，2023, 46(2): 263-271.
DENG K Q, ZHU W J, WANG X Y, YU X B, GUO C L, LIU M K, ZHANG F T, XIANG J, WANG K P, ZHANG Q M. Fatigue analysis on chamber of a special structure SRM under random vibration[J]. Journal of Solid Rocket Technology, 2023, 46(2): 263-271.（in Chinese）
[20] 许卓, 徐鹤松, 李晖, 王相平, 张海洋, 刘洋, 孙伟, 马辉, 赵丙峰, 韩清凯, 贾璞, 周晋, 闻邦椿. 基础随机激励下纤维增强复合薄板振动疲劳寿命预报[J]. 航空动力学报，2023, 38(1): 47-54.
XU Z, XU H S, LI H, WANG X P, ZHANG H Y, LIU Y, SUN W, MA H, ZHAO B F, HAN Q K, JIA P, ZHOU J, WEN B C. Vibration fatigue life prediction of fiber reinforced composite thin plate under basic random excitation[J]. Journal of Aerospace Power, 2023, 46(1): 263-271. （in Chinese）
[21] 赵旭升, 陈果, 张旭, 钱进. 装配应力对飞机管道随机疲劳寿命的影响分析与试验验证[J]. 机械强度, 2024, 46(1): 208-215.
ZHAO X S, CHEN G, ZHANG X, QIAN J. Analysis and experimental verification of the effect of assembly stress on the random fatigue life of aircraft pipeline[J]. Journal of Mechanical Strength, 2024, 46(1): 208-215.（in Chinese）
[22] 李孔娟, 陈海波. 加筋板中频声振疲劳分析方法研究[J]. 空天技术, 2023, (2): 75-83+96.
LI K J, CHEN H B. A mid-frequency vibro-acoustic fatigue analysis method for stiffened panels[J]. Aerospace Technology, 2023, (2): 75-83+96. （in Chinese）
[23] Wang Y Y, Chen H B, Zhou H W. A fatigue life estimation algorithm based on Statistical Energy Analysis in high-frequency random processes[J]. International Journal of Fatigue, 2016, 83: 221-229.
[24] 牟彬杰, 蒋劲松, 杨堃, 付焕兵, 孟德虹, 金伟. 战斗机进气道结构声疲劳设计方法[J]. 航空学报, 2024, 45(14): 229603.
MOU B J, JIANG J S, YANG K, FU Hu B, MENG D H, JIN W. Acoustic fatigue design method for fighter in-let structure[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(14): 229603.（in Chinese）
[25] 林家浩, 张亚辉, 赵岩. 虚拟激励法在国内外工程界的应用回顾与展望[J].应用数学和力学, 2017, 38(1): 1-32.
Lin J H, Zhang Y H, Zhao Y. The pseudo-excitation method and its industrial applications in China and abroad[J]. Applied Mathematics and Mechanics, 2017, 38(1): 1-31. （in Chinese）
[26] Braccesi C, Cianetti F, Tomassini L. An innovative modal approach for frequency domain stress recovery and fa-tigue damage evaluation[J]. International Journal of Fa-tigue, 2016, 91: 382-396.
[27] Braccesi C, Cianetti F, Tomassini L. Fast evaluation of stress state spectral moments[J]. International Journal of Mechanical Sciences, 2017, 127: 4-9.
[28] Mr?nik M, Slavi? J, Bolte?ar M. Vibration fatigue using modal decomposition[J]. Mechanical Systems and Signal Processing, 2018, 98: 548-556.
[29] Zhou Y D, Tao J Y. Theoretical and numerical investiga-tion of stress mode shapes in multi-axial random fa-tigue[J]. Mechanical Systems and Signal Processing, 2019, 127: 499-512.
[30] Der Kiureghian A. Structural response to stationary exci-tation[J]. Journal of the Engineering Mechanics Division, 1980, 106(6): 1195-1213.
[31] Der Kiureghian A, Nakamura Y. CQC modal combina-tion rule for high-frequency modes[J]. Earthquake Engi-neering and Structural Dynamics, 1993, 22(11): 943-956.
[32] Sui G H, Zhang Y H. Response spectrum method for fatigue damage assessment of mechanical systems[J]. In-ternational Journal of Fatigue, 2023, 166: 107278.
[33] Sui G H, Jin X Y, Cui H Y, Zhang Y H. Improvement and test verification of the fatigue response spectrum method[J]. Mechanical Systems and Signal Processing, 2024, 217: 111519.
[34] Sui G H, Zhang Y H. A complete SRSS format for the response spectrum method of high-cycle fatigue life as-sessment considering modal truncation error correc-tion[J]. International Journal of Fatigue, 2023, 175: 107834.
[35] Yang Y B, Sui G H, Zhang Y H. Response spectrum method for fatigue damage assessment of aero-hydraulic pipeline systems[J]. Computers and Structures, 2023, 287: 107119.
[36] Cook R D, Malkus D S, Plesha M E, Witt R J. Concepts and Applications of Finite Element Analysis (5th ed)[M]. New York: Wiley, 2002.
[37] Heredia-Zavoni E. The complete SRSS modal combination rule[J]. Earthquake Engineering and Structural Dynamics, 2011, 40(11): 1181-1196.
[38] Heredia-Zavoni E, Santa-Cruz S, Silva-González FL. Modal response analysis of multi-support structures using a random vibration approach[J]. Earthquake Engineering and Structural Dynamics, 2015, 44(13): 2241-2260.
[39] Preumont A, Piéfort V. Predicting random high-cycle fatigue life with finite elements[J]. Journal of Vibration and Acoustics, 1994, 116(2): 245-248.
[40] Benasciutti D, Cristofori A, Tovo R. Analogies between spectral methods and multiaxial criteria in fatigue damage evaluation[J]. Probabilistic Engineering Mechanics, 2013, 31: 39-45.
[41] Cristofori A, Benasciutti D, Tovo R. A stress invariant based spectral method to estimate fatigue life under multiaxial random loading[J]. International Journal of Fatigue, 2011, 33(7): 887-899.
[42] Braccesi C, Cianetti F, Tomassini L. Random fatigue. A new frequency domain criterion for the damage evaluation of mechanical components[J]. International Journal of Fatigue, 2015, 70: 417-427.
[43] Benasciutti D, Braccesi C, Cianetti F, Cristofori A, Tovo R. Fatigue damage assessment in wide-band uniaxial random loadings by PSD decomposition: outcomes from recent research[J]. International Journal of Fatigue, 2016, 91: 248-250.
[44] Wijker J. Miles’ Equation in Random Vibrations[M]. Cham: Springer, 2018.

Response spectrum method and its engineering application for random fatigue assessment

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