含各向异性层的多层结构中的横波传播
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摘要
对含有各向异性层的多层结构中波传播问题的数学描述非常复杂,这一复杂性源于界面的多样性和各向异性介质物理性质的特殊性.针对此问题,基于传递矩阵方法,以界面为刚性连接的各向同性/正交各向异性/各向同性3层结构为例,导出了此类结构中SV波和最低阶模态SH波(即SH0)的反射与透射系数表达式.利用数值模拟研究了入射角度、频厚积和中间层介质对横波传播特性的影响.结果表明:SV波入射多层结构会有临界角存在,SH波入射无此现象.当声波垂直入射,随着频厚积的增大,多层结构中SV和SH波的反射和透射系数曲线会产生多阶谐振.研究结果为实际实验中采用横波入射检测类似于各向同性/正交各向异性/各向同性的多层结构提供了理论依据.
The formulation for the wave propagation in a multilayered structure with an anisotropic layer is very complex,which results from the diversity of interfaces and the specifieness of physical properties of anisotropic medium. To solve this issue,based on the transfer matrix method,the expressions of reflection and transmission coefficients for SV wave and SH wave of the lowest-order mode( SH0) are deduced under the assumption of rigid connection,considering a three-layer structure with only orthotropic middle layer. The influences of incident angle,product of frequency-thickness and medium of intermediate layer on the shear wave propagation characteristics are investigated by using numerical simulation method. The results show that the critical angle will appear if SV wave is incident into a multilayered structure,but it is not the case of SH wave. When the sound is vertical incidence,with the increase of the product of frequency-thickness,the phenomenon of the multi-order resonance will occur with respect to the curves of reflection and transmission coefficients for SV wave and SH wave. The results provide a theoretical basis for the experimental detection of multilayered structure which is similar to the isotropic/orthotropic/isotropic case by shear waves.
The formulation for the wave propagation in a multilayered structure with an anisotropic layer is very complex,which results from the diversity of interfaces and the specifieness of physical properties of anisotropic medium. To solve this issue,based on the transfer matrix method,the expressions of reflection and transmission coefficients for SV wave and SH wave of the lowest-order mode( SH0) are deduced under the assumption of rigid connection,considering a three-layer structure with only orthotropic middle layer. The influences of incident angle,product of frequency-thickness and medium of intermediate layer on the shear wave propagation characteristics are investigated by using numerical simulation method. The results show that the critical angle will appear if SV wave is incident into a multilayered structure,but it is not the case of SH wave. When the sound is vertical incidence,with the increase of the product of frequency-thickness,the phenomenon of the multi-order resonance will occur with respect to the curves of reflection and transmission coefficients for SV wave and SH wave. The results provide a theoretical basis for the experimental detection of multilayered structure which is similar to the isotropic/orthotropic/isotropic case by shear waves.
引文
[1]Tatyana S,Vyacheslav M,Alexander A,et al.Structure and properties of multilayered composite materials“Nickel Nickel Aluminide”obtained using SPS method[J].High Technology:Research and Applications,2014,1040:161-165
[2]沈浩杰,姚卫星,吴富强.复合材料刚度性能表征的协同损伤力学模型[J].力学学报,2014,46(2):255-263Shen Haojie,Yao Weixing,Wu Fuqiang.Synergistic damage mechanic model for stiffness properties of composite laminates[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(2):255-263
[3]Cao X,Shi J,Jin F.Cut-off frequencies of Lamb waves in various functionally graded thin films[J].Applied Physics Letters,2011,99(12):121907-1-3
[4]何存富,刘宏业,刘增华,等.正交各向异性板中非主轴方向的Lamb波[J].固体力学学报,2013,34(1):55-62He Cunfu,Liu Hongye,Liu Zenghua,et al.Lamb waves propagation along non-principal directions in orthotropic plate[J].Chinese Journal of Solid Mechanics,2013,34(1):55-62
[5]Zhou W,Lu Z H,Wang Y R,et al.Acoustic response and micro-damage mechanism of fiber composite materials under mode-II delamination[J].Chinese Physics Letters,2015,32(4):046201-1-4
[6]Deng P,Zhu J T.Anisotropy of unsaturated layered soils:Impact of layer composition and domain size[J].Soil Science Society of America Journal,2015,79(2):487-494
[7]Shenderov E L.Sound transmission through a transversely isotropic plate[J].Soviet Physics Acoustics-Ussr,1984,30(1):69-73
[8]王耀俊,许明翔.层状各向异性固体媒质的声反射和声透射[J].声学学报,1995,20(3):161-169Wang Yaojun,Xu Mingxiang.Sound reflection and transmission on layered anisotropic solid media[J].Acta Acustica,1995,20(3):161-169
[9]王耀俊.铝合金粘接件界面层超声检测的进展[J].应用声学,1991,10(6):1-7Wang Yaojun.The ultrasonic testing progress of aluminum alloy interface layer[J].Applied Acoustics,1991,10(6):1-7
[10]邵继红,吴昆裕.各向异性固体层的声反射和透射谱[J].中国科学技术大学学报,2004,34(1):55-59Shao Jihong,Wu Kunyu.Reflection and transmission spectrum of sound at anisotropic solid layer[J].Journal of University of Science and Technology of China,2004,34(1):55-59
[11]Rokhlin S I,Bolland T K,Adler L.Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media[J].Journal of the Acoustical Society of America,1986,79(4):906-918
[12]Rokhlin S I,Huang W.Ultrasonic wave interaction with a thin anisotropic layer between two anisotropic solids:Exact and asymptotic-boundary-condition methods[J].Journal of the Acoustical Society of America,1992,92(3):1729-1742
[13]Chattopadhyay A.Wave reflection in triclinic crystalline medium[J].Archive of Applied Mechanics,2006,76(1/2):65-74
[14]Chattopadhyay A,Venkateswarlu R L K,Saha S.Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium[J].Sadhana,2002,27(6):613-630
[15]Chattopadhyay A,Gupta S,Kumari P,et al.Torsional wave propagation in non-homogeneous layer between nonhomogeneous half-spaces[J].International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(10):1280-1291
[16]Chattopadhyay A,Gupta S,Sahu S A,et al.Dispersion of horizontally polarized shear waves in an irregular non homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium[J].Journal of Vibration and Control,2013,19(1):109-119
[17]Baljeet S.Wave propagation in thermally conducting linear fibre-reinforced composite materials[J].Archive of Applied Mechanics,2006,75(8-9):513-520
[18]Tomar S K,Kaur J.Reflection and transmission of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic solid half-spaces[J].Earth Planets Space,2003,55(9):531-547
[19]Bostrm A,Golub M V.Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions[J].Quarterly Journal of Mechanics and Applied Mathematics,2009,62(1):39-52
[20]Golub M V,Bostrm A.Interface damage modeled by spring boundary conditions for in-plane elastic waves[J].Wave Motion,2011,48:105-115
[21]Mirzade F.Plane wave propagation in transversely isotropic laser-excited solids[J].Physica B:Condensed Matter,2014,461:17-22
[22]Grechka V.Shear wave group velocity surfaces in low-symmetry anisotropic media[J].Geophysics,2015,80(1):C1-C7
[23]Gupta S,Kundu S,Verma A K,et al.Propagation of S waves in a non-homogeneous anisotropic incompressible and initially stressed medium[J].International Journal of Engineering,Science and Technology,2010,2(2):31-42
[24]Son M S,Kang Y J.Propagation of shear waves in a poroelastic layer constrained between two elastic layers[J].Applied Mathematical Modelling,2011,36(8):3685-3695
[25]Kumar R,Rajeev K.Analysis of wave motion at the boundary surface of orthotropic thermoelastic material with voids and isotropic elastic half-space[J].Journal of Engineering Physics and Thermophysics,2011,84(2):463-478
[26]Maghsoodi A,Ohadi A,Sadighi M.Calculation of wave dispersion curves in multilayered composite-metal plates[J].Shock and Vibration,2014,DOI:10.1155/2014/410514
[27]Lin Y H,MA C C.Transient analysis of elastic wave propagation in multilayered structures[J].Computers Materials&Continua,2011,24(1):15-42
[28]刘欣欣,印兴耀,张峰,等.双相各向异性介质地震波传播特征[J].石油地球物理勘探,2014,49(1):132-142Liu Xinxin,Yin Xingyao,Zhang Feng,et al.Propagation characteristics of the seismic wave in bipolar anisotropic medium[J].Oil Geophysical Prospecting,2014,49(1):132-142
[29]孙宏祥,许伯强,徐晨光,等.横观各向同性材料中激光超声谱有限元数值模拟[J].光子学报,2009,38(5):1041-1046Sun Hongxiang,Xu Boqiang,Xu Chenguang,et al.Numerical simulation of laser-generated ultrasound by spectral finite element method in transverse isotropic material[J].Acta Photonica Sinica,2009,38(5):1041-1046
[30]张剑锋,刘铁林.各向异性介质中弹性波的数值模拟[J].固体力学学报,2000,21(3):234-242Zhang Jianfeng,Liu Tielin.Numerical simulation of elastic wave propagation in anisotropic media[J].Acta Mechanica Solid Sinica,2000,21(3):234-242
[31]秦飞,吴斌.弹性与塑性理论基础[M].北京:科学出版社,2011Qin Fei,Wu Bin.The theory foundation of elastic and plastic[M].Beijing:Science Press,2011
[32]Achenbach J D.Wave propagation in elastic solids[M].New York:North Holland,1976
[33]Rose J L.Ultrasonic waves in solid media[M].Beijing:Science Press,2004
[34]邵继红,吴昆裕.超声在流体和一般各向异性固体界面上的反射[J].声学技术,2002,21(1-2):10-14Shao Jihong,Wu Kunyu.Reflection of ultrasonic waves at the interface between fluid and generally anisotropic solid[J].Technical Acoustics,2002,21(1/2):10-14
[35]益小苏,杜善义,张立同.复合材料手册[M].北京:化学工业出版社,2009Yi Xiaosu,Du Shanyi,Zhang Litong.Handbook of composite materials[M].Beijing:Chemical Industry Press,2009
[36]Rose J L.Ultrasonic Guided waves in solid media[M].Cambridge:Cambridge University Press,2014
[37]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):81-92Wang Yaojun.Sound reflection from layered solid medium with rigid and slip interface[J].Acta Acoustica,1992,17(2):81-92
[2]沈浩杰,姚卫星,吴富强.复合材料刚度性能表征的协同损伤力学模型[J].力学学报,2014,46(2):255-263Shen Haojie,Yao Weixing,Wu Fuqiang.Synergistic damage mechanic model for stiffness properties of composite laminates[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(2):255-263
[3]Cao X,Shi J,Jin F.Cut-off frequencies of Lamb waves in various functionally graded thin films[J].Applied Physics Letters,2011,99(12):121907-1-3
[4]何存富,刘宏业,刘增华,等.正交各向异性板中非主轴方向的Lamb波[J].固体力学学报,2013,34(1):55-62He Cunfu,Liu Hongye,Liu Zenghua,et al.Lamb waves propagation along non-principal directions in orthotropic plate[J].Chinese Journal of Solid Mechanics,2013,34(1):55-62
[5]Zhou W,Lu Z H,Wang Y R,et al.Acoustic response and micro-damage mechanism of fiber composite materials under mode-II delamination[J].Chinese Physics Letters,2015,32(4):046201-1-4
[6]Deng P,Zhu J T.Anisotropy of unsaturated layered soils:Impact of layer composition and domain size[J].Soil Science Society of America Journal,2015,79(2):487-494
[7]Shenderov E L.Sound transmission through a transversely isotropic plate[J].Soviet Physics Acoustics-Ussr,1984,30(1):69-73
[8]王耀俊,许明翔.层状各向异性固体媒质的声反射和声透射[J].声学学报,1995,20(3):161-169Wang Yaojun,Xu Mingxiang.Sound reflection and transmission on layered anisotropic solid media[J].Acta Acustica,1995,20(3):161-169
[9]王耀俊.铝合金粘接件界面层超声检测的进展[J].应用声学,1991,10(6):1-7Wang Yaojun.The ultrasonic testing progress of aluminum alloy interface layer[J].Applied Acoustics,1991,10(6):1-7
[10]邵继红,吴昆裕.各向异性固体层的声反射和透射谱[J].中国科学技术大学学报,2004,34(1):55-59Shao Jihong,Wu Kunyu.Reflection and transmission spectrum of sound at anisotropic solid layer[J].Journal of University of Science and Technology of China,2004,34(1):55-59
[11]Rokhlin S I,Bolland T K,Adler L.Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media[J].Journal of the Acoustical Society of America,1986,79(4):906-918
[12]Rokhlin S I,Huang W.Ultrasonic wave interaction with a thin anisotropic layer between two anisotropic solids:Exact and asymptotic-boundary-condition methods[J].Journal of the Acoustical Society of America,1992,92(3):1729-1742
[13]Chattopadhyay A.Wave reflection in triclinic crystalline medium[J].Archive of Applied Mechanics,2006,76(1/2):65-74
[14]Chattopadhyay A,Venkateswarlu R L K,Saha S.Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium[J].Sadhana,2002,27(6):613-630
[15]Chattopadhyay A,Gupta S,Kumari P,et al.Torsional wave propagation in non-homogeneous layer between nonhomogeneous half-spaces[J].International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(10):1280-1291
[16]Chattopadhyay A,Gupta S,Sahu S A,et al.Dispersion of horizontally polarized shear waves in an irregular non homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium[J].Journal of Vibration and Control,2013,19(1):109-119
[17]Baljeet S.Wave propagation in thermally conducting linear fibre-reinforced composite materials[J].Archive of Applied Mechanics,2006,75(8-9):513-520
[18]Tomar S K,Kaur J.Reflection and transmission of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic solid half-spaces[J].Earth Planets Space,2003,55(9):531-547
[19]Bostrm A,Golub M V.Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions[J].Quarterly Journal of Mechanics and Applied Mathematics,2009,62(1):39-52
[20]Golub M V,Bostrm A.Interface damage modeled by spring boundary conditions for in-plane elastic waves[J].Wave Motion,2011,48:105-115
[21]Mirzade F.Plane wave propagation in transversely isotropic laser-excited solids[J].Physica B:Condensed Matter,2014,461:17-22
[22]Grechka V.Shear wave group velocity surfaces in low-symmetry anisotropic media[J].Geophysics,2015,80(1):C1-C7
[23]Gupta S,Kundu S,Verma A K,et al.Propagation of S waves in a non-homogeneous anisotropic incompressible and initially stressed medium[J].International Journal of Engineering,Science and Technology,2010,2(2):31-42
[24]Son M S,Kang Y J.Propagation of shear waves in a poroelastic layer constrained between two elastic layers[J].Applied Mathematical Modelling,2011,36(8):3685-3695
[25]Kumar R,Rajeev K.Analysis of wave motion at the boundary surface of orthotropic thermoelastic material with voids and isotropic elastic half-space[J].Journal of Engineering Physics and Thermophysics,2011,84(2):463-478
[26]Maghsoodi A,Ohadi A,Sadighi M.Calculation of wave dispersion curves in multilayered composite-metal plates[J].Shock and Vibration,2014,DOI:10.1155/2014/410514
[27]Lin Y H,MA C C.Transient analysis of elastic wave propagation in multilayered structures[J].Computers Materials&Continua,2011,24(1):15-42
[28]刘欣欣,印兴耀,张峰,等.双相各向异性介质地震波传播特征[J].石油地球物理勘探,2014,49(1):132-142Liu Xinxin,Yin Xingyao,Zhang Feng,et al.Propagation characteristics of the seismic wave in bipolar anisotropic medium[J].Oil Geophysical Prospecting,2014,49(1):132-142
[29]孙宏祥,许伯强,徐晨光,等.横观各向同性材料中激光超声谱有限元数值模拟[J].光子学报,2009,38(5):1041-1046Sun Hongxiang,Xu Boqiang,Xu Chenguang,et al.Numerical simulation of laser-generated ultrasound by spectral finite element method in transverse isotropic material[J].Acta Photonica Sinica,2009,38(5):1041-1046
[30]张剑锋,刘铁林.各向异性介质中弹性波的数值模拟[J].固体力学学报,2000,21(3):234-242Zhang Jianfeng,Liu Tielin.Numerical simulation of elastic wave propagation in anisotropic media[J].Acta Mechanica Solid Sinica,2000,21(3):234-242
[31]秦飞,吴斌.弹性与塑性理论基础[M].北京:科学出版社,2011Qin Fei,Wu Bin.The theory foundation of elastic and plastic[M].Beijing:Science Press,2011
[32]Achenbach J D.Wave propagation in elastic solids[M].New York:North Holland,1976
[33]Rose J L.Ultrasonic waves in solid media[M].Beijing:Science Press,2004
[34]邵继红,吴昆裕.超声在流体和一般各向异性固体界面上的反射[J].声学技术,2002,21(1-2):10-14Shao Jihong,Wu Kunyu.Reflection of ultrasonic waves at the interface between fluid and generally anisotropic solid[J].Technical Acoustics,2002,21(1/2):10-14
[35]益小苏,杜善义,张立同.复合材料手册[M].北京:化学工业出版社,2009Yi Xiaosu,Du Shanyi,Zhang Litong.Handbook of composite materials[M].Beijing:Chemical Industry Press,2009
[36]Rose J L.Ultrasonic Guided waves in solid media[M].Cambridge:Cambridge University Press,2014
[37]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):81-92Wang Yaojun.Sound reflection from layered solid medium with rigid and slip interface[J].Acta Acoustica,1992,17(2):81-92