基于非线性弹簧模型的振动声调制机理研究
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摘要
飞机结构裂纹的在线监测是保证飞行器安全的重要举措,针对目前常规的无损检测方法无法实现在线及原位监测的不足,根据裂纹引起的超声非线性,基于振动声调制效应对结构裂纹进行监测是一种可行的方法。采用非线性弹簧模型对裂纹进行模拟,建立了两列一维简谐波在含接触界面的结构中的传播模型,通过公式推导,得到了透射信号的基波、调制边频谐波和高次谐波等信号成分的近似表达式,分析了各谐波成分幅值与激励信号参数间的对应关系,推导了边频调制谐波与两低频基波幅值乘积之比R与刚度系数间的关系。通过板中的振动声调制试验,分析了响应信号的谐波成分及各谐波成分随低频振动幅值的变化关系,探讨了指标R随外力变化情况,试验结果基本符合模型推导的结论,为采用基于振动声调制的方法进行裂纹监测提供了理论指导。
On-line Fatigue Crack Monitoring is an important initiative to ensure the safety of aircrafts. Aiming at the deficiency of the conventional non destructive test method that cannot be achieved on-line and in situ,the vibroacoustic modulation( VAM) provides an effective method for crack monitoring based on the ultrasonic nonlinearity caused by cracks. A nonlinear spring model was used to simulate the crack and a 1-D harmonic wave propagation model in structures with cracks interfaces was established. Approximate expressions of fundamental waves,modulation side-band harmonics and higher harmonics were obtained,and the corresponding relationship between the amplitude of harmonic components and the excitation signal parameters was analyzed. The relationship between the stiffness coefficent and the ratio R of the amplitude of harmonic components to the multiplication of two fundamental waves amplitudes was derived.Through the VAM test on a plate,the relationship between the harmonic components amplitudes and the low frequency vibration amplitudes was analyzed,and the change of index R along with the change of external force was discussed. The experimental results are in good agreement with the results derived from the model. The theoretical guidance was provided for the crack detection using the method of VAM.
On-line Fatigue Crack Monitoring is an important initiative to ensure the safety of aircrafts. Aiming at the deficiency of the conventional non destructive test method that cannot be achieved on-line and in situ,the vibroacoustic modulation( VAM) provides an effective method for crack monitoring based on the ultrasonic nonlinearity caused by cracks. A nonlinear spring model was used to simulate the crack and a 1-D harmonic wave propagation model in structures with cracks interfaces was established. Approximate expressions of fundamental waves,modulation side-band harmonics and higher harmonics were obtained,and the corresponding relationship between the amplitude of harmonic components and the excitation signal parameters was analyzed. The relationship between the stiffness coefficent and the ratio R of the amplitude of harmonic components to the multiplication of two fundamental waves amplitudes was derived.Through the VAM test on a plate,the relationship between the harmonic components amplitudes and the low frequency vibration amplitudes was analyzed,and the change of index R along with the change of external force was discussed. The experimental results are in good agreement with the results derived from the model. The theoretical guidance was provided for the crack detection using the method of VAM.
引文
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[13]PIECZONKA L,KLEPKA A,STASZEWSKI W J.Nonlinear vibroacoustic wave modulations for structural damage detection:an overview[J].Optical Engineering,2016,55(1):011005.
[14]CHEN B Y,TAY T E.Recent developments in modelling of progressive damage in fibre-reinforced composites[J].Applied Mechanics&Materials,2015,784:274-283.
[15]KIM S,ADAMS D E,SOHN H,et al.Crack detection technique for operating wind turbine blades using VibroAcoustic Modulation[J].Structural Health Monitoring,2014,13(6):660-670.
[16]焦敬品,何存富,吴斌.接触缺陷的振动调制超声导波检测技术研究[J].声学学报(中文版),2009,34(3):242-248.JIAO Jingpin,HE Cunfu,WU Bin.Vibro-modulation and guided wave techniques for contact defect detection in plate[J].Acta acustica,2009,34(3):242-248.
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[18]KLEPKA A,STASZEWSKI W J,JENAL R B,et al.Nonlinear acoustics for fatigue crack detection-experimental investigations of vibro-acoustic wave modulations[J].Structural Health Monitoring,2012,11(2):197-211.
[19]DONSKOY D,SUTIN A,EKIMOV A.Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing[J].Ndt&E International,2001,34(4):231-238.
[20]胡海峰.板状金属结构健康监测的非线性超声理论与关键技术研究[D].长沙:国防科学技术大学,2011:45-50.
[21]PIECZONKA,KLEPKA A,STASZEWSKI W J,et al.Analysis of vibro-acoustic modulations in nonlinear acoustics used for impact damage detection-numerical and experimental study[J].Key Engineering Materials,2013,558:341-348.
[22]BIWA S,ISHII Y.Second-harmonic generation in an infinite layered structure with nonlinear spring-type interfaces[J].Wave Motion,2016,63:55-67.
[23]KORSHAK,B.A,SOLODOV I Y,BALLAD E M.DC effects,sub-harmonics,stochasticity and“memory”for contact acoustic non-lineartiy[J].Ultrasonics,2002,40:707-713.
[24]NAKAJIMA S.On the acoustic nonlinearity of solid-solid contact with pressure-dependent interface stiffness[J].Journal of Applied Mechanics,2004,71(4):508-515.
[25]杨晓华,刘学君,张玎,等.基于振动声调制的板类结构裂纹定位成像[J/OL].北京航空航天大学学报,http://www.cnki.net/kcms/detail/11.2625.V.20161017.0955.007.html YANG Xiaohua,LIU Xuejun,ZHANG Ding,et al.Localization and imaging of crack damage in plate-like structures based on vibro-acousic modulation[J/OL].Journal of Beijing University of Aeronautics and Astronautics,http://www.cnki.net/kcms/detail/11.2625.V.20161017.0955.007.html
[2]陈军,李志浩,林莉,等.铝板中Lamb波检测的实验研究[J].应用声学,2011,30(2):98-104.CHEN Jun,LI Zhihao,LIN Li,et al.Experiment investigations of Lamb waves in an aluminum plate[J].Applied Acoustics,2011,30(2):98-104.
[3]孙虎,周丽.基于谱元法的裂Lamb纹梁波传播特性研究[J].工程力学,2012,29(9):50-55.SUN Hu,ZHOU Li.Lamb wave propagation in a cracked beam using spectral finite element method[M].Engineering mechanics,2012,29(9):50-55.
[4]张正罡,刘丹,他得安.多通道超声兰姆波检测板状结构中的裂纹[J].应用声学,2015,34(3):189-194.ZHANG Zhenggang,LIU Dan,TA Dean.Detection of crack in plate structural using multi-channel ultrasonic Lamb waves[J].Applied Acoustics,2015,34(3):189-194.
[5]SU Z Q,ZHOU L M,YE L,et al.Lamb wave based monitoring of fatigue crack growth using principal component analysis[J].Key Engineering Materials,2013,558:260-267.
[6]YUN D S,CHOI S H,KIM C S,et al.Imaging of harmonic wave generated by contact acoustic nonlinearity in obliquely incident ultrasonic wave[J].Journal of the Korean Society for Nondestructive Testing,2012,32(4):362-368.
[7]KEE S H,ZHU J.Surface wave transmission across a partially closed surface-breaking crack in concrete[J].Aci Materials Journal,2014,111(1):35-46.
[8]郑阳,周进节.兰姆波在裂纹处的模态转换及散射特性研究[J].工程力学,2014,31(6):21-29.ZHENG Yang,ZHOU Jinjie.Mode conversion and scattering properties of Lamb waves near localized cracking[J].Engineering mechanics,2014,31(6):21-29.
[9]WAN X,TSE P W,XU G,et al.FEM simulation of nonlinear lamb waves for detecting a micro-crack in a metallic plate[C]∥Engineering Asset Management-Systems,Professional Practices and Certification.Springer International Publishing,2015:1561-1569.
[10]ROH Y,KIM B,LEE S,et al.The reflection and transmission of Lamb waves across a rectangular crack as a function of the crack geometry[C]∥Ultrasonics Symposium,2008.Ius.IEEE,2008:1912-1915.
[11]MISHRA S,KUMAR A,MISHRA R K,et al.Structural health monitoring and Propagation of Lamb waves to identification of crack[J].Fordham Envtl.l.rep,2015,126(4):873-875.
[12]BRODA D,STASZEWSKI W J,MARTOWICZ A,et al.Modelling of nonlinear crack-wave interactions for damage detection based on ultrasound—A review[J].Journal of Sound&Vibration,2014,333(4):1097-1118.
[13]PIECZONKA L,KLEPKA A,STASZEWSKI W J.Nonlinear vibroacoustic wave modulations for structural damage detection:an overview[J].Optical Engineering,2016,55(1):011005.
[14]CHEN B Y,TAY T E.Recent developments in modelling of progressive damage in fibre-reinforced composites[J].Applied Mechanics&Materials,2015,784:274-283.
[15]KIM S,ADAMS D E,SOHN H,et al.Crack detection technique for operating wind turbine blades using VibroAcoustic Modulation[J].Structural Health Monitoring,2014,13(6):660-670.
[16]焦敬品,何存富,吴斌.接触缺陷的振动调制超声导波检测技术研究[J].声学学报(中文版),2009,34(3):242-248.JIAO Jingpin,HE Cunfu,WU Bin.Vibro-modulation and guided wave techniques for contact defect detection in plate[J].Acta acustica,2009,34(3):242-248.
[17]SOHN H,LIM H J,DESIMIO M P,et al.Nonlinear ultrasonic wave modulation for online fatigue crack detection[J].Journal of Sound&Vibration,2014,333(5):1473-1484.
[18]KLEPKA A,STASZEWSKI W J,JENAL R B,et al.Nonlinear acoustics for fatigue crack detection-experimental investigations of vibro-acoustic wave modulations[J].Structural Health Monitoring,2012,11(2):197-211.
[19]DONSKOY D,SUTIN A,EKIMOV A.Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing[J].Ndt&E International,2001,34(4):231-238.
[20]胡海峰.板状金属结构健康监测的非线性超声理论与关键技术研究[D].长沙:国防科学技术大学,2011:45-50.
[21]PIECZONKA,KLEPKA A,STASZEWSKI W J,et al.Analysis of vibro-acoustic modulations in nonlinear acoustics used for impact damage detection-numerical and experimental study[J].Key Engineering Materials,2013,558:341-348.
[22]BIWA S,ISHII Y.Second-harmonic generation in an infinite layered structure with nonlinear spring-type interfaces[J].Wave Motion,2016,63:55-67.
[23]KORSHAK,B.A,SOLODOV I Y,BALLAD E M.DC effects,sub-harmonics,stochasticity and“memory”for contact acoustic non-lineartiy[J].Ultrasonics,2002,40:707-713.
[24]NAKAJIMA S.On the acoustic nonlinearity of solid-solid contact with pressure-dependent interface stiffness[J].Journal of Applied Mechanics,2004,71(4):508-515.
[25]杨晓华,刘学君,张玎,等.基于振动声调制的板类结构裂纹定位成像[J/OL].北京航空航天大学学报,http://www.cnki.net/kcms/detail/11.2625.V.20161017.0955.007.html YANG Xiaohua,LIU Xuejun,ZHANG Ding,et al.Localization and imaging of crack damage in plate-like structures based on vibro-acousic modulation[J/OL].Journal of Beijing University of Aeronautics and Astronautics,http://www.cnki.net/kcms/detail/11.2625.V.20161017.0955.007.html