含裂纹损伤充液圆柱壳的振动响应求解方法
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摘要
薄壁圆柱壳流体冲击振动响应是一个复杂的流固耦合(FSI)动力学问题,对于薄壳状态监测与缺陷识别具有重要意义.基于Flügge壳体应力理论,得到壳体运动的高阶偏微分方程组(PDE),利用波传播方法获得圆柱壳系统振动响应.将壳体周围流体定义为理想声学介质,通过亥姆霍兹方程描述声压场,得到流固耦合条件下的薄壁圆柱壳受迫振动响应演变规律.针对薄壳裂纹损伤识别问题,基于断裂力学理论建立局部柔度矩阵,结合呼吸型线弹簧模型(LSM),构造裂纹附近应力及位移连续条件,获得含裂纹损伤充液圆柱壳的振动响应,进而给出一种基于振动能量流的裂纹损伤识别方法.研究结果表明:充液圆柱壳耦合系统在非线性激励下,位移响应在沿轴向、周向和径向的传播特性差异明显;裂纹的存在会导致结构局部柔度的降低和耦合系统固有频率下降;归一化输入功率流能够有效地对充液圆柱壳耦合系统进行结构裂纹损伤识别.研究结果可为充液薄壳振动响应方面的研究提供有益参考,也可为流固耦合条件下的结构裂纹损伤识别方面提供技术支持.
The vibration responses of thin cylindrical shells subjected to shock waves from fluid is a complex fluid-structure interaction(FSI)issue,and is of important significance to the state monitoring and damage recognition for thin shells.Based on the Flügge shell stress theory,the high-order partial differential equations(PDEs)of thin-shell motion are set up,and the vibration responses of the system are obtained by the wave propagation method.The peripheral fluid is defined as an ideal acoustic medium,and the acoustic pressure field is described by the Helmholtz equation.According to the above hypothesis,the forced vibration response and evolution regularities for thin cylindrical shells considering the fluid-structure interaction are acquired.For crack damage recognition of thin shells,the partial flexibility matrix is constructed based on fracture mechanics principles,and in combination with the breathing linear spring model(LSM),the adjacent stress and displacement conditions are built.Consequently,the forced vibration responses of thin liquid-filled cylindrical shells with cracks are obtained,and a vibration-power-flow-based crack damage recognition method is presented.The results show that under nonlinear excitations,the displacement responses in the radial,axial and circumferential directions of a thin liquid-filled cylindrical shell are apparently different.Hysteresis is observed for the peak values of radial and axial displacements.The radial displacement contains more peak values,and is more closely related with the impulse excitation from fluid.The crack can decrease the partial flexibility and the natural frequency of the system,and change the power flow characteristics of the FSI system.The transmission coefficient of vibration wave decreases with the increase of crack depth.The normalized input power flow can recognize the crack damage of thin liquidfilled cylindrical shells.This research can not only provide useful references to the modeling of vibration responses for thin liquid-filled shells,but also offer potential solution schemes for the recognition of structural cracks under the fluid-solid coupling condition.
The vibration responses of thin cylindrical shells subjected to shock waves from fluid is a complex fluid-structure interaction(FSI)issue,and is of important significance to the state monitoring and damage recognition for thin shells.Based on the Flügge shell stress theory,the high-order partial differential equations(PDEs)of thin-shell motion are set up,and the vibration responses of the system are obtained by the wave propagation method.The peripheral fluid is defined as an ideal acoustic medium,and the acoustic pressure field is described by the Helmholtz equation.According to the above hypothesis,the forced vibration response and evolution regularities for thin cylindrical shells considering the fluid-structure interaction are acquired.For crack damage recognition of thin shells,the partial flexibility matrix is constructed based on fracture mechanics principles,and in combination with the breathing linear spring model(LSM),the adjacent stress and displacement conditions are built.Consequently,the forced vibration responses of thin liquid-filled cylindrical shells with cracks are obtained,and a vibration-power-flow-based crack damage recognition method is presented.The results show that under nonlinear excitations,the displacement responses in the radial,axial and circumferential directions of a thin liquid-filled cylindrical shell are apparently different.Hysteresis is observed for the peak values of radial and axial displacements.The radial displacement contains more peak values,and is more closely related with the impulse excitation from fluid.The crack can decrease the partial flexibility and the natural frequency of the system,and change the power flow characteristics of the FSI system.The transmission coefficient of vibration wave decreases with the increase of crack depth.The normalized input power flow can recognize the crack damage of thin liquidfilled cylindrical shells.This research can not only provide useful references to the modeling of vibration responses for thin liquid-filled shells,but also offer potential solution schemes for the recognition of structural cracks under the fluid-solid coupling condition.
引文
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[14]郭文杰,李天匀,朱翔,屈凯旸.部分浸没圆柱壳声固耦合计算的半解析法研究[J].物理学报,2018,67(08):140-151.(Guo W J,Li T Y,Zhu X,Qu K Y.Semi-analytical research on acoustic-structure coupling calculation of partially submerged cylindrical shell[J].Acta Physica Sinica,2018,67(08):140-151.(in Chinese))
[15] Maria S,Danny V H,Patrick G,Dimitrios G,Aggelis.Acoustic emission monitoring of crack propagation in additively manufactured and conventional titanium components[J].Mechanics Research Communications,2017,84:8-13.
[16] Linda C H,Jiji G W.Crack detection in X-ray images using fuzzy index measure[J].Applied Soft Computing,2011,11(4):3571-3579.
[17] Broberg P.Surface crack detection in welds using thermography[J].NDT&E International,2013,57:69-73.
[18]胡宁,刘瑶璐,赵友选,章俊,刘许旸.基于低频动态信息和超声导波的复杂结构损伤的在线诊断技术[J].固体力学学报,2017,38(04):312-347.(Hu N,Liu Y L,Zhao Y X,Zhang J,Liu X Y.On-line monitoring technologies for complex structural damage identification based on low-frequency structural dynamic signals ultrasonic guided waves[J].Chinese Journal of Solid Mechanics,2017,38(04):312-347.(in Chinese))
[19] Moazzez K,Googarchin H S,Sharifi S.Natural frequency analysis of a cylindrical shell containing a variably oriented surface crack utilizing Line-Spring model[J].Thin-Walled Structures,2018,125:63-75.
[20] Xiang J,Matsumoto T,Wang Y,Jiang Z.Detect damages in conical shells using curvature mode shape and wavelet finite element method[J].International Journal of Mechanical Sciences,2013,66:83-93.
[21] Shi Z Y,Law S S,Zhang L M.Improved damage quantification from elemental modal strain energy change[J].J Eng Mech,2002,128(5):521-529.
[22] Shi Z Y,Law S S,Zhang L M.Structural damage detection from modal strain energy change[J].J Eng Mech,2000,126(12):1216-1223.
[23] Huh Y C,Chung T Y,Moon S J,Kil H G,Kim J K.Damage detection in beams using vibratory power estimated from the measured accelerations[J].Journal of Sound and Vibration,2011,330(15):3645-3665.
[24] Huh Y C,Chung T Y,Lee J W,Kim J K.Damage identification in plates using vibratory power estimated from measured accelerations[J].Journal of Sound and Vibration,2015,336:106-131.
[25] Li X B.Study on free vibration analysis of circular cylindrical shells using wave propagation[J].Journal of Sound and Vibration,2008,311(3):667-682.
[26]陈正翔,金咸定,张维衡.充液圆柱管壳中振动波的频散特性[J].船舶力学,2000,(05):60-67.(Chen Z X,Jin X D,Zhang W H.Frequency dispersion of vibrational waves in cylindrical shells filled with fluid[J].Journal of Ship Mechanics,2000,(05):60-67.(in Chinese))
[27]胡家顺,冯新,周晶.圆周非贯穿裂纹管局部柔度的理论和试验研究[J].工程力学,2010,27(04):37-43.(Hu J S,Feng X,Zhou J.Theoretical and experimental study on local flexibility of pipe with a partthrough circumferential crack[J].Engineering Mechanics,2010,27(04):37-43.(in Chinese))
[28]徐慕冰,张小铭,张维衡.充液圆柱壳的波传播和功率流特性研究[J].振动工程学报,1997,02:114-119.(Xu M B,Zhang X M,Zhang W H.Characteristics of wave propagation and vibrational power flow in a fluid-filled cylindrical shell[J].Journal of Vibration Engineering,1997,02:114-119.(in Chinese))
[29]刘延安.流固耦合管道固有频率及参数灵敏度分析[J].机械科学与技术,2012,31(03):498-501+506.(Liu Y A.Analysis of natural frequency and parameter sensitivity for a fluid-structure interaction pipe[J].Mechanical Science and Technology for Aerospace Engineering,2012,31(03):498-501+506.(in Chinese))
[30]朱翔.裂纹损伤结构的振动功率流特性与损伤识别[D].湖北:华中科技大学,2007.(Zhu X.Vibration Power Flow Characteristics and Damage Identification of Crack Damage Structures[D].Hubei:Huazhong University of Science and Technology,2007.(in Chinese))
[2]任建亭,姜节胜.输流管道系统振动研究进展[J].力学进展,2003,(03):313-324.(Ren J T,Jiang J S.Advances and trends on vibration of pipes conveying fluid[J].Advances in Mechanics,2003,(03):313-324.(in Chinese))
[3]鲁华平,贾普荣,刘永寿,孙波,李宝辉.基于模态测试的航空管道动力学响应实验与分析[J].中国机械工程,2012,23(16):1925-1929.(Lu H P,Jia P R,Liu Y S,Sun B,Li B H.Dynamics response experience and analysis of aviation pipeline based on modal test[J].China Mechanical Engineering,2012,23(16):1925-1929.(in Chinese))
[4]韩文.“中石化石油管道爆炸”报道中新闻与宣传的失衡[J].新闻世界,2014,08:397-398.(Han W.The imbalance between news and propaganda in the report of"Sinopec Oil Pipeline Explosion"[J]. News World,2014,08:397-398.(in Chinese))
[5]Amabili M A.Comparison of shell theories for largeamplitude vibrations of circular cylindrical shells:Lagrangian approach[J].Journal of Sound and Vibration,2003,264(5):1091-1125.
[6]Fuller C R.The input mobility of an infinite circular cylindrical elastic shell filled with liquid[J].Journal of Sound and Vibration,1983,87(3):409-427.
[7]Lakis A A,Bursuc G,Toorani M H.Sloshing effect on the dynamic behaviour of horizontal cylindrical shells[J].Nuclear Eng Design,2009,239(7):1193-1206.
[8]Tran I T,Manh C N.Dynamic stiffness method for free vibration of composite cylindrical shells containing fluid[J].Appl Math Modelling,2016,40(21-22):9286-9301.
[9]Xu M B.Three methods for analyzing forced vibration of a fluid-filled cylindrical shell[J].Applied Acoustics,2003,64(7):731-752.
[10]刘志忠,李天匀,刘敬喜.考虑流体静压时充液圆柱壳的频散特性分析[J].船舶力学,2009,13(04):635-640.(Liu Z Z,Li T Y,Liu J X.Characteristics of the frequency dispersion in cylindrical shells filled with fluid considering hydrostatic pressure[J].Journal of Ship Mechanics,2009,13(04):635-640.(in Chinese))
[11]李天匀,王露,郭文杰,杨国栋,朱翔.有限长半充液圆柱壳振动特性分析[J].中国舰船研究,2016,11(02):106-110.(Li T Y,Wang L,Guo W J,Yang G D,Zhu X.Vibration characteristics analysis of finite cylindrical shells semi-filled with liquid[J].Chinese Journal of Ship Research,2016,11(02):106-110.(in Chinese))
[12]路中磊,魏英杰,王聪,孙钊.基于高速摄像实验的开放腔体圆柱壳入水空泡流动研究[J].物理学报,2016,65(01):309-323(Lu Z L,Wei Y J,Wang C,Sun Z.An experimental study of water-entry cavitating flows of an end-closed cylindrical shell based on the high-speed imaging technology[J].Acta Physica Sinica,2016,65(01):309-323.(in Chinese))
[13]王家维,田晓耕.水中爆炸载荷下夹芯圆柱壳的结构优化[J].固体力学学报,2015,36(S1):1-8.(Wang J W,Tian X G.Structure optimization of aluminum foam-cored sandwich shell subjected to underwated expllosion[J].Chinese Journal of Solid Mechanics,2015,36(S1):1-8.(in Chinese))
[14]郭文杰,李天匀,朱翔,屈凯旸.部分浸没圆柱壳声固耦合计算的半解析法研究[J].物理学报,2018,67(08):140-151.(Guo W J,Li T Y,Zhu X,Qu K Y.Semi-analytical research on acoustic-structure coupling calculation of partially submerged cylindrical shell[J].Acta Physica Sinica,2018,67(08):140-151.(in Chinese))
[15] Maria S,Danny V H,Patrick G,Dimitrios G,Aggelis.Acoustic emission monitoring of crack propagation in additively manufactured and conventional titanium components[J].Mechanics Research Communications,2017,84:8-13.
[16] Linda C H,Jiji G W.Crack detection in X-ray images using fuzzy index measure[J].Applied Soft Computing,2011,11(4):3571-3579.
[17] Broberg P.Surface crack detection in welds using thermography[J].NDT&E International,2013,57:69-73.
[18]胡宁,刘瑶璐,赵友选,章俊,刘许旸.基于低频动态信息和超声导波的复杂结构损伤的在线诊断技术[J].固体力学学报,2017,38(04):312-347.(Hu N,Liu Y L,Zhao Y X,Zhang J,Liu X Y.On-line monitoring technologies for complex structural damage identification based on low-frequency structural dynamic signals ultrasonic guided waves[J].Chinese Journal of Solid Mechanics,2017,38(04):312-347.(in Chinese))
[19] Moazzez K,Googarchin H S,Sharifi S.Natural frequency analysis of a cylindrical shell containing a variably oriented surface crack utilizing Line-Spring model[J].Thin-Walled Structures,2018,125:63-75.
[20] Xiang J,Matsumoto T,Wang Y,Jiang Z.Detect damages in conical shells using curvature mode shape and wavelet finite element method[J].International Journal of Mechanical Sciences,2013,66:83-93.
[21] Shi Z Y,Law S S,Zhang L M.Improved damage quantification from elemental modal strain energy change[J].J Eng Mech,2002,128(5):521-529.
[22] Shi Z Y,Law S S,Zhang L M.Structural damage detection from modal strain energy change[J].J Eng Mech,2000,126(12):1216-1223.
[23] Huh Y C,Chung T Y,Moon S J,Kil H G,Kim J K.Damage detection in beams using vibratory power estimated from the measured accelerations[J].Journal of Sound and Vibration,2011,330(15):3645-3665.
[24] Huh Y C,Chung T Y,Lee J W,Kim J K.Damage identification in plates using vibratory power estimated from measured accelerations[J].Journal of Sound and Vibration,2015,336:106-131.
[25] Li X B.Study on free vibration analysis of circular cylindrical shells using wave propagation[J].Journal of Sound and Vibration,2008,311(3):667-682.
[26]陈正翔,金咸定,张维衡.充液圆柱管壳中振动波的频散特性[J].船舶力学,2000,(05):60-67.(Chen Z X,Jin X D,Zhang W H.Frequency dispersion of vibrational waves in cylindrical shells filled with fluid[J].Journal of Ship Mechanics,2000,(05):60-67.(in Chinese))
[27]胡家顺,冯新,周晶.圆周非贯穿裂纹管局部柔度的理论和试验研究[J].工程力学,2010,27(04):37-43.(Hu J S,Feng X,Zhou J.Theoretical and experimental study on local flexibility of pipe with a partthrough circumferential crack[J].Engineering Mechanics,2010,27(04):37-43.(in Chinese))
[28]徐慕冰,张小铭,张维衡.充液圆柱壳的波传播和功率流特性研究[J].振动工程学报,1997,02:114-119.(Xu M B,Zhang X M,Zhang W H.Characteristics of wave propagation and vibrational power flow in a fluid-filled cylindrical shell[J].Journal of Vibration Engineering,1997,02:114-119.(in Chinese))
[29]刘延安.流固耦合管道固有频率及参数灵敏度分析[J].机械科学与技术,2012,31(03):498-501+506.(Liu Y A.Analysis of natural frequency and parameter sensitivity for a fluid-structure interaction pipe[J].Mechanical Science and Technology for Aerospace Engineering,2012,31(03):498-501+506.(in Chinese))
[30]朱翔.裂纹损伤结构的振动功率流特性与损伤识别[D].湖北:华中科技大学,2007.(Zhu X.Vibration Power Flow Characteristics and Damage Identification of Crack Damage Structures[D].Hubei:Huazhong University of Science and Technology,2007.(in Chinese))