纵波在含有线性粘滞粘接层的粘接结构中的传播
|
摘要
研究了纵波垂直入射上下基体为同种介质且含有线性粘滞粘接层的三层板状粘接结构时声波的反射和透射特性,基于粘接界面的准静态模型(QSM)并结合各向同性线性粘滞体的本构方程,导出了含有粘滞系数和体积弹性模量的纵波反射和透射系数表达式。首先将纵波的准静态模型解和精确解进行对比,研究了准静态模型的适用条件。其次在界面处于不同接触形式(完好连接和粘滞型弱粘接)的情况下,分别讨论了考虑和不考虑界面相对质量对声反射和透射特性的影响。接着分析了粘滞粘接层参数的变化对纵波反射和透射特性的影响。最后在不大于0.1 MHz-mm的较小频厚积范围内简要阐述了如何鉴别界面形式。结果表明,准静态模型适用于较小频厚积的检测;是否考虑界面的相对质量对纵波的反射和透射特性影响不大;在特定的频厚积下,利用纵波的反射或透射系数方法结合准静态模型可有效辨别界面形式。研究成果可为实验时采用纵波垂直入射检测粘接结构提供一定的理论参考。
The reflection and transmission properties of acoustic wave in the trilaminar plate-like adhesive structure with a linear viscous adhesive layer and the upper and lower substrates were the same kind of material were studied when longitudinal wave vertical incident.Based on the quasi-static model(QSM)of the adhesive interface and the constitutive equation of the isotropic linear viscous body,the expressions of the longitudinal wave reflection and transmission coefficients with the coefficient of viscosity and bulk modulus were derived.Firstly,the QSM and the exact solutions of the longitudinal wave were compared with each other to explain the applicable conditions of the QSM.Secondly,the effects of relative quality of interface on acoustic wave reflection and transmission coefficients were considered,by taking and not taking the fore-mentioned factor into consideration,under the condition of different interface contact forms(perfect connection and viscous weak bonding).Then,the influence of parameters changes of viscous adhesive layer on the reflection and transmission properties of the longitudinal wave was analyzed.Finally,the method of identifying the interface form in smaller frequency-thickness product range which was less than 0.1 MHz-mm was briefly interpreted.The results show that the QSM is suitable for the detection of smaller frequency-thickness product.Whether the relative mass of the interface is considered has little effect on the reflection and transmission characteristics of the longitudinal wave.The interface forms could be effectively identified by using the method of reflection or transmission coefficient of longitudinal wave combined with QSM at specific frequencythickness product.The research results could provide a theoretical reference for the detection of the adhesive structure by longitudinal wave vertical incident.
The reflection and transmission properties of acoustic wave in the trilaminar plate-like adhesive structure with a linear viscous adhesive layer and the upper and lower substrates were the same kind of material were studied when longitudinal wave vertical incident.Based on the quasi-static model(QSM)of the adhesive interface and the constitutive equation of the isotropic linear viscous body,the expressions of the longitudinal wave reflection and transmission coefficients with the coefficient of viscosity and bulk modulus were derived.Firstly,the QSM and the exact solutions of the longitudinal wave were compared with each other to explain the applicable conditions of the QSM.Secondly,the effects of relative quality of interface on acoustic wave reflection and transmission coefficients were considered,by taking and not taking the fore-mentioned factor into consideration,under the condition of different interface contact forms(perfect connection and viscous weak bonding).Then,the influence of parameters changes of viscous adhesive layer on the reflection and transmission properties of the longitudinal wave was analyzed.Finally,the method of identifying the interface form in smaller frequency-thickness product range which was less than 0.1 MHz-mm was briefly interpreted.The results show that the QSM is suitable for the detection of smaller frequency-thickness product.Whether the relative mass of the interface is considered has little effect on the reflection and transmission characteristics of the longitudinal wave.The interface forms could be effectively identified by using the method of reflection or transmission coefficient of longitudinal wave combined with QSM at specific frequencythickness product.The research results could provide a theoretical reference for the detection of the adhesive structure by longitudinal wave vertical incident.
引文
[1]ZHANG K S,ZHOU Z G,ZHOU J H,et al.Characteristics of laser ultrasound interaction with multi-layered dissimilar metals adhesive interface by numerical simulation[J].Applied Surface Science,2015,353:284-290.
[2]刘增华,樊军伟,何存富,等.基于概率损伤算法的复合材料板空气耦合Lamb波扫描成像[J].复合材料学报,2015,32(1):227-235.LIU Zenghua,FAN Junwei,HE Cunfu,et al.Scanning imaging of composite plate using air-coupled Lamb waves based on probabilistic damage algorithm[J].Acta Materiae Compositae Sinica,2015,32(1):227-235(in Chinese).
[3]温泉,郭东明,高航,等.碳纤维/环氧树脂复合材料制孔损伤综合评价方法[J].复合材料学报,2015,33(2):265-272.WEN Quan,GUO Dongming,GAO Hang,et al.Comprehensive evaluation method for carbon/epoxy composite holemaking damages[J].Acta Materiae Compositae Sinica,2015,33(2):265-272(in Chinese).
[4]THOMSON W T.Transmission of elastic waves through a stratified solid medium[J].Journal of Applied Physics,1950,21(2):88-93.
[5]ROKHLIN S I,WANG Y J.Analysis of boundary conditions for elastic wave interaction with an interface between two solids[J].Journal of the Acoustical Society of America,1991,89(2):503-515.
[6]王耀俊.具有刚性联接界面和滑移界面的层状固体媒质的声反射[J].声学学报,1992,17(2):81-92.WANG Yaojun.Sound reflection from layered solid medium with rigid and slip interfaces[J].Acta Acustica,1992,17(2):81-92(in Chinese).
[7]张海燕,刘镇清,吕东辉.全局矩阵法及其在层状各向异性复合板中Lamb波传播特性研究中的应用[J].复合材料学报,2004,21(2):111-116.ZHANG Haiyan,LIU Zhenqing,LV Donghui.Global matrix and its application to study on Lamb wave propagation in layered anisotropic composite plates[J].Acta Materiae Compositae Sinica,2004,21(2):111-116(in Chinese).
[8]TOHMYOH H,SUZUKI M.Measurement of the coating thickness on the back side of double-sided coated structures by means of acoustic resonant spectroscopy[J].Surface&Coatings Technology,2009,42(16):546-550.
[9]WU B,DING J C,HE C F,et al.Wave propagation in water-immersed adhesive structure with the substrates of finite thickness[J].NDT&E International,2016,80:35-47.
[10]丁俊才,吴斌,何存富,等.不同界面形式的粘接结构中纵波的反射与透射[J].华中科技大学学报(自然科学版),2016,44(6):84-90.DING Juncai,WU Bin,HE Cunfu,et al.Reflection and transmission of longitudinal wave in the adhesive structure with different interface forms[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2016,44(6):84-90(in Chinese).
[11]QIU Z G,WU B,HU C F.Ultrasonic beam steering using neumann boundary condition in multiplysics[J].Acta Mechanica Sinica,2012,28(1):146-150.
[12]邱兆国,吴斌,何存富.弱粘接结构中谐振频率与刚度比的数值研究[J].工程力学,2012,29(6):32-38.QIU Zhaoguo,WU Bin,HE Cunfu.Numerical analysis of resonance frequency and stiffness ratio in weak bonded structures[J].Engineering Mechanics,2012,29(6):32-38(in Chinese).
[13]吴斌,张婧,邱兆国,等.浸水斜入射条件下黏接结构的透射特性研究[J].机械工程学报,2012,49(10):45-52.WU Bin,ZHANG Jing,QIU Zhaoguo,et al.Research on the transmission characteristics of underwater bonding structure in oblique incidence[J].Journal of Mechanical Engineering,2012,49(10):45-52(in Chinese).
[14]李明轩,王小民,安志武.粘接界面特性的超声检测与评价[J].应用声学,2013,32(3):190-198.LI Mingxuan,WANG Xiaoming,AN Zhiwu.Ultrasonic testing and evaluation of bonding interface propertis[J].Applied Acoustics,2013,32(3):190-198(in Chinese).
[15]DING J C,WU B,HE C F.Reflection and transmission coefficients of the SH0 mode in the adhesive structures with imperfect interface[J].Ultrasonics,2016,70:248-257.
[16]BAIK J M,THOMPSON R B.Ultrasonic scattering from imperfect interfaces:A Quasi-Static model[J].Journal of Nondestructive Evaluation,1984,4(3):177-196.
[17]MARGETAN F J,THOMPSON R B,ROSE J H,et al.The interaction of ultrasound with imperfect interfaces:Experimental studies of model structures[J].Journal of Nondestructive Evaluation,1992,11(3-4):109-126.
[18]廉国选,李明轩.粘滞固体滑移界面层的超声测量[J].声学技术,2003(增刊):258-260.LIAN Guoxuan,LI Mingxuan.Ultrasonic measurement for the viscous interfacial fluid between two solids[J].Technical Acoustics,2003(Suppl):258-260(in Chinese).
[19]廉国选,李明轩.固体滑移界面的超声评价[J].声学学报,2005,30(1):21-25.LIAN Guoxuan,LI Mingxuan.Ultrasonic evaluation for the slip interface between two solids[J].Acta Acustica,2005,30(1):21-25(in Chinese).
[20]廉国选,李明轩.超声在粘接界面的反射和透射[J].应用声学,2004,23(4):34-42.LIAN Guoxuan,LI Mingxuan.Ultrasonic reflection and transmission at an adhesion interface[J].Applied Acoustics,2004,23(4):34-42(in Chinese).
[21]王小民,李明轩,毛捷,等.单层与衬底胶接结构超声反射波谱的低频特征[J].声学学报,2004,29(4):337-342.WANG Xiaoming,LI Mingxuan,MAO Jie,et al.Low-frequency features of the ultrasound echo from an adhesively bonded layer/substrate structure[J].Acta Acustica,2004,29(4):337-342(in Chinese).
[22]ZHOU C Z,LI M X,MAO J,et al.Determination of thickness of an inaccessible thin film under a multilayered system from natural frequencies[J].Chinese Physics Letters,2008,25(4):1336-1339.
[23]安志武,王小民,毛捷,等.粘接件拉伸强度的超声检测实验研究[J].声学学报,2011,36(4):384-388.AN Zhiwu,WANG Xiaoming,MAO Jie,et al.Experimental research on tensile strength of bonding structure by ultrasonics[J].Acta Acustica,2011,36(4):384-388(in Chinese).
[24]KENDALL K,TABOR D.An ultrasonic study of the area of contact between stationary and sliding surfaces[J].Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences,1971,323(1554):321-340.
[25]HAINES N F,LANGSTON D B.The reflection of ultrasonic pulses from surfaces[J].Journal of the Acoustical Society of America,1980,67(5):1443-1454.
[26]MOOSHABAD I Y,MARGETAN F J,GRAY T A,et al.Reflection of ultrasonic waves from imperfect interfaces:A combined boundary element method and independent scattering model approach[J].Journal of Nondestructive Evaluation,1992,11(3-4):141-149.
[27]YU J G,DING J C,MA Z J.On dispersion relations of waves in multilayered magneto/electro/elastic plates[J].Applied Mathematical Modelling,2012,36(12):5780-5791.
[28]冯元桢.连续介质力学导论[M].北京:科学出版社,1984:166-167.FENG Yuanzhen.An introduction to continuum mechanics[M].Beijing:Science Press,1984:166-167(in Chinese).
[29]李家伟.无损检测手册[M].北京:机械工业出版社,2011:323-325.LI Jiawei.Nondestructive testing manual[M].Beijing:Machinery Industry Press,2011:323-325(in Chinese).
[30]陈懋章.粘性流体动力学基础[M].北京:高等教育出版社,2002:412-415.CHEN Maozhang.Fundamentals of viscous fluid dynamics[M].Beijing:Higher Education Press,2002:412-415(in Chinese).
[31]ROSE J L.Ultrasonic guided waves in solid media[M].Cambridge:Cambridge University Press,2014:53-66.
[2]刘增华,樊军伟,何存富,等.基于概率损伤算法的复合材料板空气耦合Lamb波扫描成像[J].复合材料学报,2015,32(1):227-235.LIU Zenghua,FAN Junwei,HE Cunfu,et al.Scanning imaging of composite plate using air-coupled Lamb waves based on probabilistic damage algorithm[J].Acta Materiae Compositae Sinica,2015,32(1):227-235(in Chinese).
[3]温泉,郭东明,高航,等.碳纤维/环氧树脂复合材料制孔损伤综合评价方法[J].复合材料学报,2015,33(2):265-272.WEN Quan,GUO Dongming,GAO Hang,et al.Comprehensive evaluation method for carbon/epoxy composite holemaking damages[J].Acta Materiae Compositae Sinica,2015,33(2):265-272(in Chinese).
[4]THOMSON W T.Transmission of elastic waves through a stratified solid medium[J].Journal of Applied Physics,1950,21(2):88-93.
[5]ROKHLIN S I,WANG Y J.Analysis of boundary conditions for elastic wave interaction with an interface between two solids[J].Journal of the Acoustical Society of America,1991,89(2):503-515.
[6]王耀俊.具有刚性联接界面和滑移界面的层状固体媒质的声反射[J].声学学报,1992,17(2):81-92.WANG Yaojun.Sound reflection from layered solid medium with rigid and slip interfaces[J].Acta Acustica,1992,17(2):81-92(in Chinese).
[7]张海燕,刘镇清,吕东辉.全局矩阵法及其在层状各向异性复合板中Lamb波传播特性研究中的应用[J].复合材料学报,2004,21(2):111-116.ZHANG Haiyan,LIU Zhenqing,LV Donghui.Global matrix and its application to study on Lamb wave propagation in layered anisotropic composite plates[J].Acta Materiae Compositae Sinica,2004,21(2):111-116(in Chinese).
[8]TOHMYOH H,SUZUKI M.Measurement of the coating thickness on the back side of double-sided coated structures by means of acoustic resonant spectroscopy[J].Surface&Coatings Technology,2009,42(16):546-550.
[9]WU B,DING J C,HE C F,et al.Wave propagation in water-immersed adhesive structure with the substrates of finite thickness[J].NDT&E International,2016,80:35-47.
[10]丁俊才,吴斌,何存富,等.不同界面形式的粘接结构中纵波的反射与透射[J].华中科技大学学报(自然科学版),2016,44(6):84-90.DING Juncai,WU Bin,HE Cunfu,et al.Reflection and transmission of longitudinal wave in the adhesive structure with different interface forms[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2016,44(6):84-90(in Chinese).
[11]QIU Z G,WU B,HU C F.Ultrasonic beam steering using neumann boundary condition in multiplysics[J].Acta Mechanica Sinica,2012,28(1):146-150.
[12]邱兆国,吴斌,何存富.弱粘接结构中谐振频率与刚度比的数值研究[J].工程力学,2012,29(6):32-38.QIU Zhaoguo,WU Bin,HE Cunfu.Numerical analysis of resonance frequency and stiffness ratio in weak bonded structures[J].Engineering Mechanics,2012,29(6):32-38(in Chinese).
[13]吴斌,张婧,邱兆国,等.浸水斜入射条件下黏接结构的透射特性研究[J].机械工程学报,2012,49(10):45-52.WU Bin,ZHANG Jing,QIU Zhaoguo,et al.Research on the transmission characteristics of underwater bonding structure in oblique incidence[J].Journal of Mechanical Engineering,2012,49(10):45-52(in Chinese).
[14]李明轩,王小民,安志武.粘接界面特性的超声检测与评价[J].应用声学,2013,32(3):190-198.LI Mingxuan,WANG Xiaoming,AN Zhiwu.Ultrasonic testing and evaluation of bonding interface propertis[J].Applied Acoustics,2013,32(3):190-198(in Chinese).
[15]DING J C,WU B,HE C F.Reflection and transmission coefficients of the SH0 mode in the adhesive structures with imperfect interface[J].Ultrasonics,2016,70:248-257.
[16]BAIK J M,THOMPSON R B.Ultrasonic scattering from imperfect interfaces:A Quasi-Static model[J].Journal of Nondestructive Evaluation,1984,4(3):177-196.
[17]MARGETAN F J,THOMPSON R B,ROSE J H,et al.The interaction of ultrasound with imperfect interfaces:Experimental studies of model structures[J].Journal of Nondestructive Evaluation,1992,11(3-4):109-126.
[18]廉国选,李明轩.粘滞固体滑移界面层的超声测量[J].声学技术,2003(增刊):258-260.LIAN Guoxuan,LI Mingxuan.Ultrasonic measurement for the viscous interfacial fluid between two solids[J].Technical Acoustics,2003(Suppl):258-260(in Chinese).
[19]廉国选,李明轩.固体滑移界面的超声评价[J].声学学报,2005,30(1):21-25.LIAN Guoxuan,LI Mingxuan.Ultrasonic evaluation for the slip interface between two solids[J].Acta Acustica,2005,30(1):21-25(in Chinese).
[20]廉国选,李明轩.超声在粘接界面的反射和透射[J].应用声学,2004,23(4):34-42.LIAN Guoxuan,LI Mingxuan.Ultrasonic reflection and transmission at an adhesion interface[J].Applied Acoustics,2004,23(4):34-42(in Chinese).
[21]王小民,李明轩,毛捷,等.单层与衬底胶接结构超声反射波谱的低频特征[J].声学学报,2004,29(4):337-342.WANG Xiaoming,LI Mingxuan,MAO Jie,et al.Low-frequency features of the ultrasound echo from an adhesively bonded layer/substrate structure[J].Acta Acustica,2004,29(4):337-342(in Chinese).
[22]ZHOU C Z,LI M X,MAO J,et al.Determination of thickness of an inaccessible thin film under a multilayered system from natural frequencies[J].Chinese Physics Letters,2008,25(4):1336-1339.
[23]安志武,王小民,毛捷,等.粘接件拉伸强度的超声检测实验研究[J].声学学报,2011,36(4):384-388.AN Zhiwu,WANG Xiaoming,MAO Jie,et al.Experimental research on tensile strength of bonding structure by ultrasonics[J].Acta Acustica,2011,36(4):384-388(in Chinese).
[24]KENDALL K,TABOR D.An ultrasonic study of the area of contact between stationary and sliding surfaces[J].Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences,1971,323(1554):321-340.
[25]HAINES N F,LANGSTON D B.The reflection of ultrasonic pulses from surfaces[J].Journal of the Acoustical Society of America,1980,67(5):1443-1454.
[26]MOOSHABAD I Y,MARGETAN F J,GRAY T A,et al.Reflection of ultrasonic waves from imperfect interfaces:A combined boundary element method and independent scattering model approach[J].Journal of Nondestructive Evaluation,1992,11(3-4):141-149.
[27]YU J G,DING J C,MA Z J.On dispersion relations of waves in multilayered magneto/electro/elastic plates[J].Applied Mathematical Modelling,2012,36(12):5780-5791.
[28]冯元桢.连续介质力学导论[M].北京:科学出版社,1984:166-167.FENG Yuanzhen.An introduction to continuum mechanics[M].Beijing:Science Press,1984:166-167(in Chinese).
[29]李家伟.无损检测手册[M].北京:机械工业出版社,2011:323-325.LI Jiawei.Nondestructive testing manual[M].Beijing:Machinery Industry Press,2011:323-325(in Chinese).
[30]陈懋章.粘性流体动力学基础[M].北京:高等教育出版社,2002:412-415.CHEN Maozhang.Fundamentals of viscous fluid dynamics[M].Beijing:Higher Education Press,2002:412-415(in Chinese).
[31]ROSE J L.Ultrasonic guided waves in solid media[M].Cambridge:Cambridge University Press,2014:53-66.