基于连续抗弯刚度模型的裂纹梁动力指纹损伤识别
|
摘要
基于断裂力学的应变能概念,建立裂纹简支梁连续抗弯刚度模型,提出基于连续抗弯刚度模型的裂纹梁动力指纹损伤识别方法。借助有限差分方法、Mathematica软件编程求解裂纹梁动力指纹(固有频率、振型、振型曲率),通过与铰接法及FEM法对不同裂纹工况下裂纹梁固有频率的数值计算比较及误差分析,成功验证了方法的有效性,并探讨了裂纹参数对动力指纹的影响。算例分析表明:连续抗弯刚度模型对裂纹参数变化敏感,裂纹梁抗弯刚度在裂纹处呈现最小值,邻近区域抗弯刚度受裂纹影响明显;裂纹简支梁的动力指纹随裂纹参数的变化呈跨中对称变化;裂纹梁结构的固有频率与振型曲率耦合的识别方法可以较好地识别出梁结构裂纹参数,识别误差为2.23%,证实了基于动力指纹检测裂纹损伤的可行性。本文结果为梁结构裂纹的检测提供了重要的理论依据,有广泛的实用与理论研究前景。
Based on the strain energy in fracture mechanics, a continuous bending stiffness model of a cracked simple supported beam is established, and a new damage identification method based on dynamic fingerprint for cracked beams is presented in this paper. Based on the finite difference method, the dynamic fingerprints of cracked beams(including natural frequencies, mode shapes, and curvature of vibration modes) are solved by programming calculation through Mathematica software. The calculated results of natural frequencies are compared with the results of the previous equivalent torsion spring method and the finite element method. The error analysis shows that the numerical results are in good agreement, and the validity of the method is verified successfully. The effects of crack parameters on dynamic fingerprint are discussed in this paper. The example analysis shows that the continuous bending stiffness model is sensitive to the change of the crack parameters, and the bending stiffness of the crack beam shows a minimum at the crack, which obviously affects the bending stiffness in the vicinity of the crack. The dynamic fingerprint of the cracked simple supported beam changes symmetrically with the change of the crack parameters. The identification method of the coupling of the natural frequency and the mode curvature of the cracked beam structure can identify the beam structure crack parameters better, and the identification error is within 2.23%.This paper proves the feasibility of detecting crack damage based on dynamic fingerprints, and provides an important theoretical basis for the detection of cracks in beam structures, which has a wide range of practical and theoretical research perspectives.
Based on the strain energy in fracture mechanics, a continuous bending stiffness model of a cracked simple supported beam is established, and a new damage identification method based on dynamic fingerprint for cracked beams is presented in this paper. Based on the finite difference method, the dynamic fingerprints of cracked beams(including natural frequencies, mode shapes, and curvature of vibration modes) are solved by programming calculation through Mathematica software. The calculated results of natural frequencies are compared with the results of the previous equivalent torsion spring method and the finite element method. The error analysis shows that the numerical results are in good agreement, and the validity of the method is verified successfully. The effects of crack parameters on dynamic fingerprint are discussed in this paper. The example analysis shows that the continuous bending stiffness model is sensitive to the change of the crack parameters, and the bending stiffness of the crack beam shows a minimum at the crack, which obviously affects the bending stiffness in the vicinity of the crack. The dynamic fingerprint of the cracked simple supported beam changes symmetrically with the change of the crack parameters. The identification method of the coupling of the natural frequency and the mode curvature of the cracked beam structure can identify the beam structure crack parameters better, and the identification error is within 2.23%.This paper proves the feasibility of detecting crack damage based on dynamic fingerprints, and provides an important theoretical basis for the detection of cracks in beam structures, which has a wide range of practical and theoretical research perspectives.
引文
[1]VESTRONI F,CAPECCHI D.Damage detection in beams structures based on frequency measurements[J].Journal of engineering mechanics,2000,126(7):761-768.
[2]胡家顺,冯新,李昕,等.裂纹梁振动分析和裂纹识别方法研究进展[J].振动与冲击,2007,26(11):146-152,189.(HU Jiashun,FENG Xin,LI Xin,et al.State-of-art of vibration analysis and crack identification of cracked beams[J].Journal of vibration and shock,2007,26(11):146-152,189(in Chinese)).
[3]胡家顺,孙文勇,周晶.含圆周非贯穿裂纹悬臂管道的振动分析与裂纹识别[J].振动与冲击,2011,30(5):18-22.(HU Jiashun,SUN Wenyong,ZHOU Jing.Vibration analysis and crack identification of a cantilever pipe with a circumferential part-through crack[J].Journal of vibration and shock,2011,30(5):18-22(in Chinese)).
[4]CHANDRASHEKHAR M,GANGGULI R.Damage assessment of sturctures with uncertainty by using mode-shape curvatures and fuzzy logic[J].Journal of sound and vibration,2009,326(3):939-957.
[5]PAPADOPOULOS C A,DIMAROGOUS A.Coupled longitudinal and bending vibrations of a rotating shaft with all open crack[J].Journal of sound and vibration,1987,117(1):81-83.
[6]王璋奇,贾建援.悬臂梁裂纹参数的识别方法[J].机械强度,2002,24(2):225-227.(WANG Zhangqi,JIA Jianyuan.Crack identification in a cantilever beam[J].Journal of mechanical strength,2002,24(2):225-227(in Chinese)).
[7]ZHENG Dingyang,FAN S C.Vibration and stability of cracked hollow-sectional beams[J].Journal of sound and vibration,2003,267(4):933-954.
[8]LIN Yanli,GUO Xinglin.Characteristics of vibrational power flow of a cracked periodically supported infinite beam[J].Journal of Dalian university of technology,2004,44(2):184-185.
[9]SWAMIDAS A S J,SESHADFI R,YANG Xinfeng.Identification of cracking in beam structures using Timoshenko and Euler formulations[J].Journal of engineering mechanics,2004,130(11):1297-1308.
[10]YANG E C,LI Y H,ZHAO X,et al.Vibration characteristics analysis of cracked beams based on energy method[J].Water resources research,2014,50(11):8845-8867.
[11]QIAN Bo,YUE Huaying.Numerical calculation of natural frequency of transverse vibration of non-uniform beams[J].Mechanics in engineering,2011,33(6):45-49.
[12]刘鹏,刘红军,林坤,等.基于样条有限点法的变截面Euler梁横向自由振动分析[J].振动与冲击,2016,35(11):66-73.(LIUPeng,LIU Hongjun,LIN Kun,et al.Free transverse vibration analysis of tapered Bernoulli-Euler beams based on spline finite point method[J].Journal of vibration and shock,2016,35(11):66-73(in Chinese)).
[13]李群,欧卓成,陈宜亨.高等断裂力学[M].北京:科学出版社,2017.(LI Qun,OU Zhuocheng,CHEN Yiheng.Advanced fracture mechanics[M].Beijing:Science Press,2017(in Chinese)).
[14]中国航空研究院.应力强度因子手册[M].北京:科学出版社,1993.(Chinese Aeronautical Establishment.Handbook of stress intensity factors[M].Beijing:Science Press,1993(in Chinese)).
[15]YANG Xinfeng,SWAMIDAS A S J,SESHADRI R.Crack identification in vibration beams using energy method[J].Journal of sound and vibration,2001,244(2):339-357.
[2]胡家顺,冯新,李昕,等.裂纹梁振动分析和裂纹识别方法研究进展[J].振动与冲击,2007,26(11):146-152,189.(HU Jiashun,FENG Xin,LI Xin,et al.State-of-art of vibration analysis and crack identification of cracked beams[J].Journal of vibration and shock,2007,26(11):146-152,189(in Chinese)).
[3]胡家顺,孙文勇,周晶.含圆周非贯穿裂纹悬臂管道的振动分析与裂纹识别[J].振动与冲击,2011,30(5):18-22.(HU Jiashun,SUN Wenyong,ZHOU Jing.Vibration analysis and crack identification of a cantilever pipe with a circumferential part-through crack[J].Journal of vibration and shock,2011,30(5):18-22(in Chinese)).
[4]CHANDRASHEKHAR M,GANGGULI R.Damage assessment of sturctures with uncertainty by using mode-shape curvatures and fuzzy logic[J].Journal of sound and vibration,2009,326(3):939-957.
[5]PAPADOPOULOS C A,DIMAROGOUS A.Coupled longitudinal and bending vibrations of a rotating shaft with all open crack[J].Journal of sound and vibration,1987,117(1):81-83.
[6]王璋奇,贾建援.悬臂梁裂纹参数的识别方法[J].机械强度,2002,24(2):225-227.(WANG Zhangqi,JIA Jianyuan.Crack identification in a cantilever beam[J].Journal of mechanical strength,2002,24(2):225-227(in Chinese)).
[7]ZHENG Dingyang,FAN S C.Vibration and stability of cracked hollow-sectional beams[J].Journal of sound and vibration,2003,267(4):933-954.
[8]LIN Yanli,GUO Xinglin.Characteristics of vibrational power flow of a cracked periodically supported infinite beam[J].Journal of Dalian university of technology,2004,44(2):184-185.
[9]SWAMIDAS A S J,SESHADFI R,YANG Xinfeng.Identification of cracking in beam structures using Timoshenko and Euler formulations[J].Journal of engineering mechanics,2004,130(11):1297-1308.
[10]YANG E C,LI Y H,ZHAO X,et al.Vibration characteristics analysis of cracked beams based on energy method[J].Water resources research,2014,50(11):8845-8867.
[11]QIAN Bo,YUE Huaying.Numerical calculation of natural frequency of transverse vibration of non-uniform beams[J].Mechanics in engineering,2011,33(6):45-49.
[12]刘鹏,刘红军,林坤,等.基于样条有限点法的变截面Euler梁横向自由振动分析[J].振动与冲击,2016,35(11):66-73.(LIUPeng,LIU Hongjun,LIN Kun,et al.Free transverse vibration analysis of tapered Bernoulli-Euler beams based on spline finite point method[J].Journal of vibration and shock,2016,35(11):66-73(in Chinese)).
[13]李群,欧卓成,陈宜亨.高等断裂力学[M].北京:科学出版社,2017.(LI Qun,OU Zhuocheng,CHEN Yiheng.Advanced fracture mechanics[M].Beijing:Science Press,2017(in Chinese)).
[14]中国航空研究院.应力强度因子手册[M].北京:科学出版社,1993.(Chinese Aeronautical Establishment.Handbook of stress intensity factors[M].Beijing:Science Press,1993(in Chinese)).
[15]YANG Xinfeng,SWAMIDAS A S J,SESHADRI R.Crack identification in vibration beams using energy method[J].Journal of sound and vibration,2001,244(2):339-357.