粘接结构中垂直入射纵波的准静态模型解
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摘要
研究了板状粘接结构中垂直入射纵波的准静态模型解。在将粘接界面简化为准静态模型(QSM)的情况下,推导了界面为完好连接且上下基体为同种材料的板状粘接结构中垂直入射纵波的声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了比较以阐释准静态模型的适用条件;接着分析了法向刚度系数和界面相对质量的变化对纵波反射和透射特性的影响。结果表明,在特定频率下,随着刚度系数或界面相对质量的增加,纵波的反射和透射系数的幅值分别减小和增大至某一稳定值。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指导。
The Quasi-Static Model(QSM) solution of vertical incident longitudinal waves in plate-like adhesive structure was studied. Under the condition that the bonding interface was simplified as a Quasi-Static Model, the expressions of the reflection and transmission coefficients of vertical incident longitudinal waves in plate-like adhesive structure with perfectly connected interfaces and the same material for upper and lower substrates were derived. The Quasi-Static Model and the exact solutions of longitudinal waves were compared with each other to explain the applicable conditions of the Quasi-Static Model. The influences of the changes of the normal stiffness coefficient and relative mass of the interface on the reflection and transmission characteristics of longitudinal waves were analyzed. The results indicate that at certain frequencies, the reflection coefficient of longitudinal waves reduces to a stable value, while the transmission coefficient increases to a stable value with the increase of the stiffness coefficient or the relative mass of the interface. The research results could provide a theoretical guide for the detection of bonding structure by longitudinal wave vertical incident.
The Quasi-Static Model(QSM) solution of vertical incident longitudinal waves in plate-like adhesive structure was studied. Under the condition that the bonding interface was simplified as a Quasi-Static Model, the expressions of the reflection and transmission coefficients of vertical incident longitudinal waves in plate-like adhesive structure with perfectly connected interfaces and the same material for upper and lower substrates were derived. The Quasi-Static Model and the exact solutions of longitudinal waves were compared with each other to explain the applicable conditions of the Quasi-Static Model. The influences of the changes of the normal stiffness coefficient and relative mass of the interface on the reflection and transmission characteristics of longitudinal waves were analyzed. The results indicate that at certain frequencies, the reflection coefficient of longitudinal waves reduces to a stable value, while the transmission coefficient increases to a stable value with the increase of the stiffness coefficient or the relative mass of the interface. The research results could provide a theoretical guide for the detection of bonding structure by longitudinal wave vertical incident.
引文
[1]Pavlopoulou S,Grammatikos S A,Kordatos E Z,et al.Continuous debonding monitoring of a patch repaired helicopter stabilizer:damage assessment and analysis[J].Composite Structures,2015,127:231―244.
[2]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.
[3]陈颖璞,赵明,马书义,等.管道损伤处纵向导波模态转换对损伤识别的影响[J].工程力学,2016,33(6):215―221.Chen Yingpu,Zhao Ming,Ma Shuyi,et al.The effect of longitudinal modes waveguide conversion on the feature identification of defects in pipes[J].Engineering Mechanics,2016,33(6):215―221.(in Chinese)
[4]张小明,薛铜龙.具有初应力的多层空心圆柱体中的导波[J].工程力学,2014,31(8):223―229.Zhang Xiaoming,Xue Tonglong.Guided waves in initially stressed multilayered hollow cylinders[J].Engineering Mechanics,2014,31(8):223―229.(in Chinese)
[5]于保华,杨世锡,甘春标.一种多层圆管纵向导波频散特性分析方法研究[J].工程力学,2013,30(4):373―379.Yu Baohua,Yang Shixi,Gan Chunbiao.Research on frequency dispersion characteristics of longitudinal guided wave in multi-layer tube[J].Engineering Mechanics,2013,30(4):373―379.(in Chinese)
[6]齐辉,蔡立明,潘向南,等.带形介质内SH型导波对圆柱孔洞的动力分析[J].工程力学,2015,32(3):9―14.Qi Hui,Cai Liming,Pan Xiangnan,et al.Dynamic analyses of SH guided waves by circular cylindrical cavity in an elastic strip[J].Engineering Mechanics,2015,32(3):9―14.(in Chinese)
[7]Moreno M C S,Cela J J L,Vicente J L M,et al.Adhesively bonded joints as a dissipative energy mechanism under impact loading[J].Applied Mathematical Modelling,2015,39(12):3496―3505.
[8]Kundu S,Manna S,Gupta S.Propagation of SH-wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi-infinite media[J].Mathematical Methods in the Applied Sciences,2015,38(9):1926―1936.
[9]Singh A K,Chen B Y,Tan V B C,et al.Finite element modeling of nonlinear acoustics/ultrasonics for the detection of closed delaminations in composites[J].Ultrasonics,2017,74:89―98.
[10]Pilarski A,Rose J L.A transverse-wave ultrasonic obliquely-incident technique for interfacial weakness detection in adhesive bonds[J].Journal of Applied Physics,1988,62(2):300―307.
[11]Qiu Z G,Wu B,He C F.Research on adhesive layer depth and frequency in weak interface of bonded structures[J].Insight,2011,53(5):302―306.
[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]Ning W,Wang Y J.Lamb wave propagation in three-layered composites[J].Chinese Journal of Acoustics,1995,14(4):300―306.
[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]Thomson W T.Transmission of elastic waves through a stratified solid medium[J].Journal of Applied Physics,1950,21(2):88―93.
[17]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.
[18]Zhang H Y,Quan Z,Lv D H,et al.Ultrasonic Lamb wave tomography of through hole flaws in isotropic thin plates[J].Acta Acoustica,2007,32(1):83―70.
[19]Wang Y J.Sound reflection from layered solid medium with rigid and slip interfaces[J].Acta Acustica,1992,17(2):81―92.
[20]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.
[21]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.
[22]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.
[23]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.
[24]Kendall K,Tabor D.An ultrasonic study of the area of contact between stationary and sliding surfaces[C].London,England:Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences,1971,323(1554):321―340.
[25]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.
[26]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)
[27]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)
[28]Margetan F J,Thompson R B,Gray T A.Interfacial spring model for ultrasonic interactions with imperfect interfaces:theory of oblique incidence and application to diffusion-bonded butt joints[J].Journal of Nondestructive Evaluation,1988,7(3/4):131―152.
[29]丁俊才,吴斌,何存富.纵波在含有线性粘滞粘接层的粘接结构中的传播[J].复合材料学报,2017,34(8):1801―1809.Ding Juncai,Wu Bin,He Cunfu.Propagation of longitudinal wave in adhesive structure with linear viscous adhesive layer[J].Acta Materiae Compositae Sinica,2017,34(8):1801―1809.(in Chinese)
[30]Rose J L.Ultrasonic guided waves in solid media[M].Cambridge:Cambridge University Press,2014:53―66.
[2]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.
[3]陈颖璞,赵明,马书义,等.管道损伤处纵向导波模态转换对损伤识别的影响[J].工程力学,2016,33(6):215―221.Chen Yingpu,Zhao Ming,Ma Shuyi,et al.The effect of longitudinal modes waveguide conversion on the feature identification of defects in pipes[J].Engineering Mechanics,2016,33(6):215―221.(in Chinese)
[4]张小明,薛铜龙.具有初应力的多层空心圆柱体中的导波[J].工程力学,2014,31(8):223―229.Zhang Xiaoming,Xue Tonglong.Guided waves in initially stressed multilayered hollow cylinders[J].Engineering Mechanics,2014,31(8):223―229.(in Chinese)
[5]于保华,杨世锡,甘春标.一种多层圆管纵向导波频散特性分析方法研究[J].工程力学,2013,30(4):373―379.Yu Baohua,Yang Shixi,Gan Chunbiao.Research on frequency dispersion characteristics of longitudinal guided wave in multi-layer tube[J].Engineering Mechanics,2013,30(4):373―379.(in Chinese)
[6]齐辉,蔡立明,潘向南,等.带形介质内SH型导波对圆柱孔洞的动力分析[J].工程力学,2015,32(3):9―14.Qi Hui,Cai Liming,Pan Xiangnan,et al.Dynamic analyses of SH guided waves by circular cylindrical cavity in an elastic strip[J].Engineering Mechanics,2015,32(3):9―14.(in Chinese)
[7]Moreno M C S,Cela J J L,Vicente J L M,et al.Adhesively bonded joints as a dissipative energy mechanism under impact loading[J].Applied Mathematical Modelling,2015,39(12):3496―3505.
[8]Kundu S,Manna S,Gupta S.Propagation of SH-wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi-infinite media[J].Mathematical Methods in the Applied Sciences,2015,38(9):1926―1936.
[9]Singh A K,Chen B Y,Tan V B C,et al.Finite element modeling of nonlinear acoustics/ultrasonics for the detection of closed delaminations in composites[J].Ultrasonics,2017,74:89―98.
[10]Pilarski A,Rose J L.A transverse-wave ultrasonic obliquely-incident technique for interfacial weakness detection in adhesive bonds[J].Journal of Applied Physics,1988,62(2):300―307.
[11]Qiu Z G,Wu B,He C F.Research on adhesive layer depth and frequency in weak interface of bonded structures[J].Insight,2011,53(5):302―306.
[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]Ning W,Wang Y J.Lamb wave propagation in three-layered composites[J].Chinese Journal of Acoustics,1995,14(4):300―306.
[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]Thomson W T.Transmission of elastic waves through a stratified solid medium[J].Journal of Applied Physics,1950,21(2):88―93.
[17]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.
[18]Zhang H Y,Quan Z,Lv D H,et al.Ultrasonic Lamb wave tomography of through hole flaws in isotropic thin plates[J].Acta Acoustica,2007,32(1):83―70.
[19]Wang Y J.Sound reflection from layered solid medium with rigid and slip interfaces[J].Acta Acustica,1992,17(2):81―92.
[20]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.
[21]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.
[22]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.
[23]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.
[24]Kendall K,Tabor D.An ultrasonic study of the area of contact between stationary and sliding surfaces[C].London,England:Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences,1971,323(1554):321―340.
[25]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.
[26]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)
[27]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)
[28]Margetan F J,Thompson R B,Gray T A.Interfacial spring model for ultrasonic interactions with imperfect interfaces:theory of oblique incidence and application to diffusion-bonded butt joints[J].Journal of Nondestructive Evaluation,1988,7(3/4):131―152.
[29]丁俊才,吴斌,何存富.纵波在含有线性粘滞粘接层的粘接结构中的传播[J].复合材料学报,2017,34(8):1801―1809.Ding Juncai,Wu Bin,He Cunfu.Propagation of longitudinal wave in adhesive structure with linear viscous adhesive layer[J].Acta Materiae Compositae Sinica,2017,34(8):1801―1809.(in Chinese)
[30]Rose J L.Ultrasonic guided waves in solid media[M].Cambridge:Cambridge University Press,2014:53―66.