基于模态参数的梁结构多裂纹定位与程度识别

PDF(1396 KB)

振动与冲击 ›› 2020, Vol. 39 ›› Issue (23) : 271-279.

论文

郭帅平1，吴琪强1，李学军1,2，王钢1

作者信息 +

Multi-crack location and degree identification of beam structure based on modal parameters

GUO Shuaiping1, WU Qiqiang1, LI Xuejun1,2, WANG Gang1

Author information +

文章历史 +

摘要

针对梁结构多裂纹诊断的问题，基于梁结构的固有频率，提出了一种灵敏度方阵法与单元细分法相结合的多裂纹识别方法。首先，让选用的结构固有频率阶数与梁划分的单元个数相等，基于梁的各阶振型函数计算梁的灵敏度方阵；其次，测量的固有频率，求解灵敏度方阵方程，确定含裂纹单元，并结合单元细分法缩小裂纹所在区域；再次，针对多裂纹梁，基于归零逆求法，依次求得各裂纹单独存在时梁的固有频率参数，将多裂纹诊断问题转化为多个不相关的单裂纹诊断问题；最后，根据梁结构单裂纹定位与程度识别方法，在单元内进一步定位裂纹并识别裂纹程度，最终实现多裂纹的诊断。进行了数值仿真分析及试验，该多裂纹诊断方法精度较高，验证了其有效性，能为实际工程应用提供理论依据。

Abstract

Aiming at multi-crack diagnosis problems of beam structure, based on natural frequencies of beam structure, a multi-crack diagnosis method to combine the sensitivity square matrix with the element subdivision was proposed.Firstly, natural frequency orders of a selected beam structure were equal to the number of elements divided in the beam, and the sensitivity square matrix of the beam was calculated based on the beam’s various modal shapes.Secondly, measured natural frequencies of the beam were used to solve the sensitivity square matrix equation, and determine cracked elements.The element subdivision method was employed to reduce crack area.Thirdly, aiming at the multi-crack beam, based on the return to zero inverse method, the beam’s natural frequency parameters were solved in turn when each crack exists alone.The multi-crack diagnosis problem was converted into multiple uncorrelated single-crack diagnosis problems.Finally, according to the beam’s single crack location and degree recognition method, within an element, cracks were further located and their degrees were recognized to realize multi-crack diagnosis.Numerical simulation and tests were performed.Results showed that the proposed beam multi-crack diagnosis method has higher accuracy; its effectiveness is verified; it can provide a theoretical basis for practical engineering application.

导出引用

郭帅平1，吴琪强1，李学军1,2，王钢1. 基于模态参数的梁结构多裂纹定位与程度识别[J]. 振动与冲击, 2020, 39(23): 271-279

GUO Shuaiping1, WU Qiqiang1, LI Xuejun1,2, WANG Gang1. Multi-crack location and degree identification of beam structure based on modal parameters[J]. Journal of Vibration and Shock, 2020, 39(23): 271-279

参考文献

[1] Palmeri A, Cicirello A. Physically-based Dirac’s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams[J]. International Journal of Solids and Structures, 2011, 48(14-15): 2184-2195.
[2] Yan Y, Ren Q, Xia N, et al. A close-form solution applied to the free vibration of the Euler–Bernoulli beam with edge cracks[J]. Archive of Applied Mechanics, 2016, 86(9): 1633-1646.
[3] Jassim Z A, Ali N N, Mustapha F, et al. A review on the vibration analysis for a damage occurrence of a cantilever beam[J]. Engineering Failure Analysis, 2013, 31: 442-461.
[4] Zhou Y L, Hongyou C, Zhen N, et al. Review on structural damage assessment via transmissibility with vibration based measurements[C]//Journal of Physics: Conference Series. IOP Publishing, 2017, 842(1): 012016.
[5] Dahak M, Touat N, Benkedjouh T. Crack Detection through the Change in the Normalized Frequency Shape[J]. Vibration, 2018, 1(1): 56-68.
[6] 刘学坤,杨世锡,刘永强,池永为,何俊.圆柱类金属构件表面裂纹的激光超声识别方法研究[J].振动与冲击, 2020, 39(5): 10-17.
LIU Xuekun,YANG Shixi,LIU Yongqiang,CHI Yongwei, HE Jun. Laser ultrasonic identification method for surface cracks on cylindrical metal components. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(5): 10-17.
[7] Shuai Q, Tang J. Enhanced modeling of magnetic impedance sensing system for damage detection[J]. Smart materials and structures, 2013, 23(2): 025008.
[8] Lacidogna G, Piana G, Carpinteri A. Damage monitoring of three-point bending concrete specimens by acoustic emission and resonant frequency analysis[J]. Engineering Fracture Mechanics, 2019, 210: 203-211.
[9] Hanke R, Fuchs T, Uhlmann N. X-ray based methods for non-destructive testing and material characterization[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2008, 591(1): 14-18.
[10] 吴琪强，郭帅平，王钢，李学军. 基于固有频率的风力机叶片裂纹精确定位与程度识别[J]. 振动与冲击, 2019, 38(24): 18-27.
WU Qiqiang,GUO Shuaiping,WANG Gang,LI Xuejun. Accurate location and degree identification of wind turbine blade cracks based on natural frequency. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(24): 18-27.
[11] Cawley P, Adams R D. The location of defects in structures from measurements of natural frequencies[J]. The Journal of Strain Analysis for Engineering Design, 1979, 14(2): 49-57.
[12] Wu Q, Guo S, Li X, et al. Crack diagnosis method for a cantilevered beam structure based on modal parameters[J]. Measurement Science and Technology, 2019, 31(3): 035001.
[13] Liang R Y, Hu J, Choy F. Theoretical study of crack-induced eigenfrequency changes on beam structures[J]. Journal of Engineering Mechanics, 1992, 118(2): 384-396.
[14] Chen X F, Zi Y Y, Li B, et al. Identification of multiple cracks using a dynamic mesh-refinement method[J]. The Journal of Strain Analysis for Engineering Design, 2006, 41(1): 31-39.
[15] Zhang K, Yan X. Multi-cracks identification method for cantilever beam structure with variable cross-sections based on measured natural frequency changes[J]. Journal of Sound and Vibration, 2017, 387: 53-65.
[16] Maghsoodi A , Ghadami A , Mirdamadi H R . Multiple-crack damage detection in multi-step beams by a novel local flexibility-based damage index[J]. Journal of Sound and Vibration, 2013, 332(2):294-305.
[17] Babu K R P, Kumar B R, Narayana K L, et al. Multiple crack detection in beams from the differences in curvature mode shapes[J]. ARPN Journal of Engineering and Applied Sciences, 2015, 10(4).
[18] Yazdanpanah1a O, Seyedpoor S M. A new damage detection indicator for beams based on mode shape data[J]. Structural Engineering and Mechanics, 2015, 53(4): 725-744.
[19] 孟凡豪,于靖军,马文硕. 基于动态测量柔度矩阵的悬索桥吊索损伤检测[J].振动与冲击, 2019, 38(14): 267-275.
MENG Fanhao, YU Jingjun, MA Wenshuo. Cable damage detection of a suspension bridge in terms of dynamically measured flexibility matrix. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(14): 267-275.
[20] Liu X, Lieven N A J, Escamilla-Ambrosio P J. Frequency response function shape-based methods for structural damage localisation[J]. Mechanical systems and signal processing, 2009, 23(4): 1243-1259.
[21] Bandara R P, Chan T H T, Thambiratnam D P. Frequency response function based damage identification using principal component analysis and pattern recognition technique[J]. Engineering Structures, 2014, 66: 116-128.
[22] Yang D, Kang C, Hu Z, et al. On the study of element modal strain energy sensitivity for damage detection of functionally graded beams[J]. Composite Structures, 2019, 224: 110989.
[23] Kopsaftopoulos F P, Fassois S D. Vibration based health monitoring for a lightweight truss structure: experimental assessment of several statistical time series methods[J]. Mechanical Systems and Signal Processing, 2010, 24(7): 1977-1997.
[24] 谢峻;韩大建. 一种改进的基于频率测量的结构损伤识别方法[J]. 工程力学, 2004, 21(1): 21-25.
XIE Jun;HAN Da-jian. AN IMPROVED METHOD FOR STRUCTURE DAMAGE DETECTION BASED ON FREQUENCY MEASUREMENT[J]. Engineering Mechanics, 2004, 21(1): 21-25.
[25] Bahlous S E O, Smaoui H, El-Borgi S. Experimental validation of an ambient vibration-based multiple damage identification method using statistical modal filtering[J]. Journal of sound and vibration, 2009, 325(1-2): 49-68.
[26] Ercolani G D, Felix D H, Ortega N F. Crack detection in prestressed concrete structures by measuring their natural frequencies[J]. Journal of Civil Structural Health Monitoring, 2018, 8(4): 661-671.
[27] Hearn G, Testa R B. Modal analysis for damage detection in structures[J]. Journal of structural engineering, 1991, 117(10): 3042-3063.