共振条件下的裂纹梁振动与裂纹扩展耦合分析 *

推进技术 ›› 2014, Vol. 35 ›› Issue (10): 1404-1411.

共振条件下的裂纹梁振动与裂纹扩展耦合分析 *

崔　韦,王建军

北京航空航天大学能源与动力工程学院，北京 100191;北京航空航天大学能源与动力工程学院，北京 100191

发布日期:2021-08-15
作者简介:崔　韦(1985—)，男，博士生，研究领域为航空发动机结构强度振动。

Coupling Analysis of Vibration and Crack Propagation for a Cracked Beam at Resonant State

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

Published:2021-08-15

摘要/Abstract

摘要： 为了对裂纹静子叶片在共振激励下的损伤容限寿命潜力进行初步探索，采用接触有限元法研究了共振状态下裂纹梁的振动与疲劳裂纹扩展的耦合问题。裂纹梁采用二维平面应力单元离散，接触模型模拟呼吸裂纹开合过程中的弯曲刚度变化。振动分析中，分别使用解析法预估和瞬态响应扫频计算得到系统一阶共振频率。断裂力学参量在有限元法中使用线弹性断裂力学方法进行求解。耦合分析中，模拟了耦合现象中的两个典型问题——裂纹止裂和失稳扩展，通过在共振激励下扫描裂纹长度计算应力强度因子曲线，通过该曲线与断裂韧度、裂纹扩展门槛值对比判断裂纹扩展的稳定性、计算裂纹扩展寿命。最后使用耦合分析结论基于Campbell图对假设静子叶片进行了定性的共振分析。

关键词: 呼吸裂纹；耦合分析；共振响应；接触有限元；裂纹扩展；Campbell图

Abstract: As an exploration of damage tolerance lifetime analysis for a cracked stator blade，coupling effect of vibration and fatigue crack propagation for a cracked beam was studied by using contact FEM. Cracked beam is discretized by 2-D plane elements and stiffness changes of breathing crack during opening and closing process are described by contact model. The first resonant frequency was calculated by analytical method and transient response frequency sweeping. Linear fracture mechanics theory was used to calculate the stress intensity factor in vibration analysis. Two numerical examples were calculated to investigate coupling effects at resonant state: crack arrest problem and crack unstable propagation problem. The stability of crack propagation was predicted and crack propagation lifetime was calculated. Based on the Campbell diagram，the judgment of resonance was analyzed according to the conclusions from the numerical tests.

Key words: Breathing crack；Coupling analysis；Resonant response；Contact FEM；Crack propagation；Campbell diagram

崔　韦,王建军. 共振条件下的裂纹梁振动与裂纹扩展耦合分析 *[J]. 推进技术, 2014, 35(10): 1404-1411.

CUI Wei,WANG Jian-jun. Coupling Analysis of Vibration and Crack Propagation for a Cracked Beam at Resonant State[J]. Journal of Propulsion Technology, 2014, 35(10): 1404-1411.

参考文献

[1] 李其汉, 王延荣, 王建军. 航空发动机叶片高循环疲劳失效研究[J]. 航空发动机, 2003, 29(4): 16-18.
[2] 宋兆泓. 航空发动机典型故障分析[M]. 北京:北京航空航天大学出版社, 1993.
[3] 吴大观. 航空发动机研制工作论文集[M]. 北京:航空工业出版社, 1999.
[4] 尹泽勇. 航空发动机设计手册第18册: 叶片轮盘及主轴强度分析[M]. 北京: 航空工业出版社, 1999.
[5] Volovoi V V, Hodges D H, Cesnik C E S, et al. Assessment of Beam Modeling Methods for Rotor Blade Applications [J]. Mathematical and Computer Modelling, 2001, 33(10-11): 1099-1112.
[6] Rao S S, Gupta R S. Finite Element Vibration Analysis of Rotating Timoshenko Beams [J]. Journal of Sound and Vibration, 2001, 242(1): 103-124.
[7] Wang G, Wereley N. Free Vibration Analysis of Rotating Blades with Uniform Tapers [J]. AIAA Journal, 2004, 42(12): 2429-2437.
[8] Arvin H, Bakhtiari-Nejad F. Non-Linear Modal Analysis of a Rotating Beam [J]. International Journal of Non-linear Mechanics, 2011, 46(6): 877-897.
[9] Dimarogonas A D. Vibration of Cracked Structures:a State of the Art Review [J]. Engineering Fracture Mechanics, 1996, 55(5):831-875.
[10] Chondros T G, Dimarogonas A D, Yao J. A Continuous Cracked Beam Vibration Theory [J]. Journal of Sound and Vibration, 1998, 215(1): 17-24.
[11] Chondros T G, Dimarogonas A D, Yao J. Vibration of a Beam with a Breathing Crack [J]. Journal of Sound and Vibration, 2001, 239(1): 57-67.
[12] Cheng S M, Wu X J, Wallace W. Vibrational Response of a Beam with a Breathing Crack [J]. Journal of Sound and Vibration, 1999, 225(1): 201-208.
[13] ZHONG Zhen-Yuan. Coupling Analysis of Vibration and Fatigue Crack Growth of a Four-Bar Mechanism [D]. Taiwan:Chung Yuan Christian University, Master Thesis, 2002.
[14] CHEN Sheng-Zhi. Coupling Analysis of Vibration and Fatigue Crack Growth for a Crank-Slider Mechanism [D]. Taiwan:Chung Yuan Christian University, Master Thesis, 2003.
[15] Andreaus U, Casini P, Vestroni F. Non-Linear Dynamics of a Cracked Cantilever Beam Under Harmonic Excitation [J]. International Journal of Non-Linear Mechanics, 2007, 42(3): 566-575.
[16] 胡家顺, 冯新, 周晶. 呼吸裂纹梁非线性动力特性研究[J]. 振动与冲击, 2009, 28 (1) 76-80.
[17] 刘文光, 陈国平. 呼吸式裂纹梁的振动疲劳裂纹扩展耦合分析[J]. 中国机械工程, 2010, 21(23): 2798-2802.
[18] Bathe KJ. Finite Element Procedures [M].London: Prentice-Hall, Upper Saddle River, NJ, 1996.
[19] Chu Y C, Shen M H H. Analysis of Forced Bilinear Oscillators and the Application to Cracked Beam Dynamics [J]. AIAA Journal, 1992, 30 (10): 2512-2519.
[20] Henshell R D, Shaw K G. Crack Tip Finite Elements are Unnecessary [J]. International Journal for Numerical Methods in Engineering, 1975, (9): 495-507.
[21] Barsoum R S. On the Use of Isoparametric Finite Elements in Linear Fracture Mechanics [J]. International Journal for Numerical Methods in Engineering, 1976, (10): 25-37.
[22] 马德林. 常用黑色金属材料断裂力学性能参数手册[M]. 北京:兵器工业出版社, 1994.(编辑:张荣莉)　　　　　　　　　　　　　*　收稿日期:2013-10-09；修订日期:2013-12-09。作者简介:崔韦(1985—),男,博士生,研究领域为航空发动机结构强度振动。E-mail:cuiwei@sjp.buaa.edu.cn