激光在金属楔形板中激发超声导波传播规律的研究
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摘要
本文从理论方面对脉冲激光在楔形板中激发超声导波的规律和超声导波在楔形板中传播的频散特性进行了研究。
基于弹性力学的基本理论,建立了楔形板导波传播的理论模型,采用位移势函数法求解Navier-Stokes方程,并结合自由楔形板的零应力边界条件推导出楔形板的频散方程,通过数值方法求解频散方程得到频散曲线。比较并分析了几种不同角度楔形板的频散曲线,得到频散特性随楔形板角度变化的规律。小角度楔形板和大角度楔形板内导波的频散特性有较大区别,小角度楔形板厚度变化缓慢,导波频散曲线和平板中的情况相近；大角度楔形板厚度变化明显,导波频散特性较平板中有较大差异,随楔形结构角度不同频散特性也有明显变化。最后对楔形板内导波频散行为变化的原因给出了解释。
基于激光超声的热弹激发理论,考虑脉冲激光作用于楔形板表面激发超声导波,并忽略热扩散效应与光学穿透效应,将激光作用等效为表面脉冲点力源。将脉冲激光作用等效力视为边界条件,采用双积分变换法求解波动方程,并结合边界条件确定出积分变换解(?)(k,ω)的四个系数,再对(?)(k,ω)采用二维IFFT数值运算得到导波波形。编程求解了几种不同角度楔形板内导波波形,通过比较分析不同位置的波形,得到导波在楔形板中传播时波形的变化规律。导波在楔形板内传播时,波形随板厚度变化而变化,在板厚度小的位置波形有明显的Lamb波特征,随着导波传播波形逐渐发生改变,厚度大的位置波形出现Rayleigh波的特征,并且随楔形板角度增大,这种转变趋势越明显。最后通过实验研究了楔形板中导波波形的变化情况,和理论计算结果取得较好的符合。
本文的研究成果为金属楔形板和楔形结构材料的激光超声无损检测提供了理论依据。
Dispersion Properties of guided-wave and waveforms of guided-wave excited by pulsed laser in metal wedge are studied theoretically in this paper.
Established a theoretical model of guided wave propagation in metal wedge based on Elasticity. Using displacement potential function method for solving Navier-Stokes equations, derived dispersion equation of guided-wave in metal wedge combined with free stress boundary conditions. Using numerical method for solving the dispersion equation, and dispersion curves for different wedge angles are compared and analyzed. Small-angle wedge and wide-angle wedge dispersion properties of guided-wave are quite different. Guided-wave dispersion curves are similar to the case in flat in small-angle wedge with slowly linearly varying thickness. Dispersion characteristics of guided-waves in the wide-angle wedge have quite different than the flat, and waveform varies with the wedge angle. Finally, reasons for the changes of guided wave dispersion characteristics are given to explain.
Based on the thermoelastic mechanism of laser ultrasound, and ignore the thermal diffusion and optical penetration effect, consider the pulsed laser as a point force source excitation guided waves in surface of metal wedge. Solving wave equation in elastic media under the point force source boundary conditions using double Fourier transform method. Determine four coefficients of integral transform solution with the boundary condition, and out-of-plane displacement(waveform)is calculated using double IFFT method. Programming to solve guided-wave waveform with several different angles metal wedge, and waveforms on different positions are compared and analyzed. Guided-wave shape varies with the thickness of wedge, the Lamb wave wavform characteristics significantly in the small thickness position, and show the Rayleigh wave characteristics in the location of large thickness. And with the wedge angle increases, this change more obvious trend. Finally, changes of the waveform in aluminium wedge are studied experimentally, and consistent the theoretical calculation result.
This study result provide a theoretical basis for laser-ultrasonic nondestructive testing of metal wedge and wedge-shaped metal structure.
基于弹性力学的基本理论,建立了楔形板导波传播的理论模型,采用位移势函数法求解Navier-Stokes方程,并结合自由楔形板的零应力边界条件推导出楔形板的频散方程,通过数值方法求解频散方程得到频散曲线。比较并分析了几种不同角度楔形板的频散曲线,得到频散特性随楔形板角度变化的规律。小角度楔形板和大角度楔形板内导波的频散特性有较大区别,小角度楔形板厚度变化缓慢,导波频散曲线和平板中的情况相近；大角度楔形板厚度变化明显,导波频散特性较平板中有较大差异,随楔形结构角度不同频散特性也有明显变化。最后对楔形板内导波频散行为变化的原因给出了解释。
基于激光超声的热弹激发理论,考虑脉冲激光作用于楔形板表面激发超声导波,并忽略热扩散效应与光学穿透效应,将激光作用等效为表面脉冲点力源。将脉冲激光作用等效力视为边界条件,采用双积分变换法求解波动方程,并结合边界条件确定出积分变换解(?)(k,ω)的四个系数,再对(?)(k,ω)采用二维IFFT数值运算得到导波波形。编程求解了几种不同角度楔形板内导波波形,通过比较分析不同位置的波形,得到导波在楔形板中传播时波形的变化规律。导波在楔形板内传播时,波形随板厚度变化而变化,在板厚度小的位置波形有明显的Lamb波特征,随着导波传播波形逐渐发生改变,厚度大的位置波形出现Rayleigh波的特征,并且随楔形板角度增大,这种转变趋势越明显。最后通过实验研究了楔形板中导波波形的变化情况,和理论计算结果取得较好的符合。
本文的研究成果为金属楔形板和楔形结构材料的激光超声无损检测提供了理论依据。
Dispersion Properties of guided-wave and waveforms of guided-wave excited by pulsed laser in metal wedge are studied theoretically in this paper.
Established a theoretical model of guided wave propagation in metal wedge based on Elasticity. Using displacement potential function method for solving Navier-Stokes equations, derived dispersion equation of guided-wave in metal wedge combined with free stress boundary conditions. Using numerical method for solving the dispersion equation, and dispersion curves for different wedge angles are compared and analyzed. Small-angle wedge and wide-angle wedge dispersion properties of guided-wave are quite different. Guided-wave dispersion curves are similar to the case in flat in small-angle wedge with slowly linearly varying thickness. Dispersion characteristics of guided-waves in the wide-angle wedge have quite different than the flat, and waveform varies with the wedge angle. Finally, reasons for the changes of guided wave dispersion characteristics are given to explain.
Based on the thermoelastic mechanism of laser ultrasound, and ignore the thermal diffusion and optical penetration effect, consider the pulsed laser as a point force source excitation guided waves in surface of metal wedge. Solving wave equation in elastic media under the point force source boundary conditions using double Fourier transform method. Determine four coefficients of integral transform solution with the boundary condition, and out-of-plane displacement(waveform)is calculated using double IFFT method. Programming to solve guided-wave waveform with several different angles metal wedge, and waveforms on different positions are compared and analyzed. Guided-wave shape varies with the thickness of wedge, the Lamb wave wavform characteristics significantly in the small thickness position, and show the Rayleigh wave characteristics in the location of large thickness. And with the wedge angle increases, this change more obvious trend. Finally, changes of the waveform in aluminium wedge are studied experimentally, and consistent the theoretical calculation result.
This study result provide a theoretical basis for laser-ultrasonic nondestructive testing of metal wedge and wedge-shaped metal structure.
引文
[1]李喜孟,无损检测[M].第一版.北京：机械工业出版社,2001
[2]刘贵民,无损检测技术[M].北京：国防工业出版社,2006
[3]袁易全,陈思忠.近代超声原理与应用[M].第一版.南京：南京大学出版社,1996
[4]C.B.Scruby, L.E.Drain. Laser Ultrasonics:Techniques and Applications[M]. Bristol Adam Hilger,1990
[5]钱梦騄,激光超声检测技术及应用[J],上海计量测试,2003,30(1)：4-7
[6]钱梦騄,激光超声学的若干进展[J],声学技术,2002,21(1)：19-24
[7]张淑仪,超声无损检测高新技术[J],国际学术动态,1998,8,58-60
[8]张淑仪,激光超声与材料无损检测[J],应用声学,1992,11(4)：1-6
[9]R.M.White, Generation of elastic waves by transient surface heating[J], J.Appl.Phys. 1963,34(12):3559-3567
[10]A.Askaryan, A.M.Prolhorov, G.F.C.Hanturcy, M.P.S.Hipulo, The effects of a laser beam in a liquid[J], S.Sov.Phys.JETP.,1963,17(6):1463-1465
[11]C.B.Scruby, R.J.Dewhurst, S.B.Palmer, Quantitative studied of thermally generated elastic waves in laser-irradiated metal[J], J.Appl.Phys.,1980,51(12):6210-6216
[12]R.L.Weaver, Y.H.Pao, Axisymmetric Elastic Waves Excited by a Point Source in a Plate[J], J.Appl.Mech.,1982,49:821-836
[13]L.R.F.Rose, Point-Source representation for laser-generated ultrasound[J], J.Acoust.Soc.Am,1984,75(3):723-732
[14]J.D.Aussel, A.L.Brun, J.C.Baboux, Generating acoustic waves by lasentheoretical and experimental study of the emission source[J], Ultrasonics,1988,26,245
[15]L.F.Bresse, D.A.Hutchins, Transient generation by a wide thermoelastic source at a solid surface[J], J.Appl.Phys.,1989,65(4):1441-1446
[16]David.H.Hurley, James.B.Spicer, Point-source representation for laser-generated ultrasound in an elastic,transversely isotropic half-space[J], J.Appl.Phys.,1999,86(6): 3423-3427
[17]J.R.Bernstein, J.B.Spicer, Line source representation for laser-generated ultrasound in aluminum[J], J.Acoust.Soc.Am,2000,107(3):1352-1357
[18]Yijun Shi, Shi-Chang Wooh, Mark Orwat, Laser-ultrasonic generation of lamb waves in the reaction force range, Ultrasonics,2003,41:623-633
[19]P.A.Doyle, On epicentral waveforms for laser-generated ultrasound J.Phys.D:Appl.Phys.,1986,19:1613-1623
[20]F.Alan McDonald, On the precursor in laser-generated ultrasound waveforms in metals, Appl.Phys.Lett.,1990,56(3):230-232
[21]James.B.Spicer, A.D.W.Mckie, J.W.Wagner, Quantitative theory for laser ultrasonic waves in a thin plate, Appl.Phys.Lett.,1990,57(18):1882-1884
[22]T.Sanderson, C.Ume, J.Jarzynski, Longitudinal wave generation in laser ultrasonics, Ultrasonics,1998,35:553-561
[23]T.W.Murray, J.W.Wagner, Laser generation of acoustic waves in the ablative regime[J], J.Appl.Phys.,1999,85(4):2031-2040
[24]D.Royer, C.Chenu, Experimental and theoretical waveforms of Rayleigh waves generated by a thermoelastic laser line source[J], Ultrasonics,2000,38:891-895
[25]Irene Arias, Jan D.Achenbach, Thermoelastic generation of ultrasound by line-focused laser irradiation[J], Int.J.Solid.Struct.,2003,40:6917-6935
[26]Irene Arias, T.W.Murry, J.D.Achenbach, Near field analysis of laser-generated ultrasound:the effects of thermal diffusion and optical penetration[J], Review of Quantitative Nondestructive Evaluation,2002,615:324-331
[27]Lei Wu, Jian-Chun Cheng, Shu-Yi Zhang, Mechanisms of laser-generated ultrasound in plates[J], J.Phys.D:Appl.Phys.,1995,28:957-964
[28]J.C.Cheng, S.Y.Zhang, L.Wu, Excitations of thermoelastic waves in plates by a pulsed laser[J], Appl.Phys.A,1995,61:311-319
[29]Wu Lei, Cheng Jian-Chun, Zhang Shu-Yi, Laser-Generated Transient Lamb wave in thin plates[J], CHIN.PHYS.LETT.,1996,13(1):24-27
[30]J.C.Cheng, S.Y.Zhang, Quantitative theory for laser-generated Lamb waves in orthotropic thin plates, Appl.Phys.Lett.,1999,74(14):2087-2089
[31]CHENG Jian-chun, FU Tao, ZHANG Shu-yi, Thermoelastic Excitation of Transient Lamb Wave in an Orthotropic Thin Plate, CHIN.PHYS.LETT.,1999,16(3):187-189
[32]Zhong-hua SHEN, Shu-yi ZHANG, Jian-chun CHENG, Theoretical study on surface Acoustic Wave Generated by a Laser Pulse in solids[J], Analytical Science,2001,17: s204-207
[33]钱梦騄,张万春,吴田成,激光热弹激发超声脉冲的特性研究[J],声学学报,1995,20(1)：1-10
[34]胡文祥,钱梦騄,激光脉冲线源位移场的数值与实验研究[J],声学学报,2000,25(4)：345-350
[35]孟振庭,激光脉冲激发的超声脉冲波形的理论研究[J],科技通报,2001,17(5)：38-42
[36]孟振庭,激光超声的热弹机理研究[J],西安交通大学学报,2002,36(5)：548-550
[37]高会栋,沈中华,徐晓东,张淑仪,固体中脉冲激光激发声表面波的理论研究,应用声学,2002,21(5)：19-24
[38]苏琨,任大海,激光致声技术的研究[J],光电工程,2002,29(5)：68-72
[39]孔令剑,徐军,闫夷升,谷小飞,朱桂芳,侯洵,激光激发超声波的新方法研究[J],光子学报,2006,35(1)：20-23
[40]Baiqiang Xu, Zhonghua Shen, Xiaowu Ni, Jian Lu, Finite element model of Laser-generated surface acoustic waves in coating-substrate system[J], J.Appl.Phys.,2004, 95(4):2109-2115
[41]J.Gao, J.Yang, L.J.Cui, J.C.Cheng, M.L.Qian, Modeling laser-generated guided waves in bonded plates by the finite element method[J], ultrasonics,2006,44:e985-989
[42]Jijun Wang, Zhonghua Shen, Xiaowu Ni, Baiqiang Xu, Jianfei Guan, Jian Lu, Numerical simulation of laser-generated surface acoustic waves in the transparent coating on a substrate by the finite element method[J], Optics&Laser Technology,2007,39:21-28
[43]沈中华,关建飞,陆建,倪晓武,激光热弹激发超声的有限元数值模拟[J],声学技术,2005,24：9-10
[44]赵艳,沈中华,陆建,倪晓武,激光热弹激励流-固泄露Lamb波的有限元模拟[J],力学学报,2008,40(1)：35-39
[45]赵艳,沈中华,陆建,倪晓武,激光在管道中激发周向导波的有限元模拟[J],物理学报,2007,56：321-326
[46]袁玲,沈中华,倪晓武,陆建,激光在近表面弹性性质梯度变化的材料中激发超声波的数值分析[J],物理学报,2007,56：7058-7063
[47]H.Lamb, On Waves in an elastic plate[J], Proceedings of the Royal Society of London, 1917:293-312
[48]I.A.Victorov. Rayleigh and Lamb waves[M], New York:Plenum Press,1967
[49]D.C.Worlton, Experimental confirmation of Lamb waves at Megacycle Frequencies[J], J.Appl.Phys.,1961,32(6):967-971
[50]R.J.Dewhurst, C.Edwards, A.D.W.Micie, S.B.Palmer, Estimation of thickness of thin metal sheet using laser generated ultrasound[J], Appl.Phys.Lett.,1987,51(14):1066-1068
[51]H.Nakano, S.Nagai, Laser generation of antisymetric lamb waves in thin plates[J], Ultrasonics,1991,29:230-234
[52]R.Daniel Costley Jr., Yves H. Berthelota, Dispersion curve analysis of laser-generated Lamb waves[J], Ultrasonics,1994,32(4):249-253
[53]M.A.Johson, Y.H.Berthelot, P.H.Brodeur, L.A.Jacobs, Investigation of laser generation of Lamb waves in copy paper[J], Ultrasonics,1996,34:703-710
[54]Michael D.Seale, Barry T.Smith, W.H.Prosser, Lamb wave assessment of fatigue and thermal damage in composites[J], J.Acoust.Soc.Am,1998,103(5):2416-2424
[55]J.L.Rose. Ultrasonic Waves in Solid Media[M], Cambridge University Press,1999
[56]T.Hayashi, K.Kawashima, Mode extraction multi-modes of Lamb wave[J], Review of Quantitative Nondestructive Evaluation,2002,21:219-224
[57]刘镇清,无损检测中的超声兰姆波[J],无损检测,1999,21(9)：409-423
[58]刘镇清,他得安,用二维傅里叶变换识别兰姆波模式的研究[J],声学技术,2000,19(4)：212
[59]郑祥明,顾向华,史立峰,史耀武,超声兰姆波的时频分析[J],声学学报,2003,28(4)：368-374
[60]郑祥明,赵玉珍,史耀武,兰姆波频散曲线的计算[J],无损检测,2003,25(2)：66-69
[61]张海燕,吕东辉,刘镇清,二维傅里叶变换在Lamb波模式识别研究中的应用[J],振动、测试与诊断,2004,24(1)：23-26
[62]刘增华,何存富,吴斌,单层板频散曲线的矩阵表示及Matlab实现[J],无损检测,2005,27(5)：225-227
[63]王杜,郑祥明,兰姆波在薄钢板无损检测中的应用研究[J],无损检测,2007,29(4)：193-199
[64]冯占英,周正干,高羿飞,大型薄板中超声导波的产生与鉴别[J],无损探伤,2007,31(5)：1-7
[65]李富才,孟光,窄频带Lamb波频散特性研究[J],物理学报,2008,57：4265-4272
[66]朱金颖,陈龙珠,吴世明,层状板中Lamb波的频散特性研究[J],振动工程学报,1998,11(3)：366-372
[67]张海燕,刘镇清,马小松,界面层对层状各项异性复合结构中Lamb波的影响[J],物理学报,2003,52：2492-2499
[68]张海燕,刘镇清,吕东辉,全局矩阵法及其在层状各项异性复合板中Lamb波传播特性研究中的应用[J],复合材料学报,2004,21(2)：111-116
[69]A.Demcenko, L.Mazeika, Calculation of Lamb waves dispersion curves in multi-layered planar structures[J], ULTRAGARSAS,2002,3(44):15-17
[70]M.Ech-Cherif El-Kettani, F.Luppe, A.Guillet, Guided waves in a plate with linearly varying thickness:experimental and numerical results[J], Ultrasonics,2004,42:807-812
[71]P.Marical, M.Ech-Cherif El-Kettani, M.V.Predoi, Guided waves in elastic plates with Gaussian section variation:experimental and numerical results[J],Ultrasonics,2007,47:1-9
[72]F.Jenot, M.Ouaftouh, M.Ourak, M.Duquennoy, P.Poussot, Finite element modeling of guided waves propagation in plates with variable thickness[R], Proceedings of the international Congress on Ultrasonics,2007,1-4
[73]M.V.Predoi, M.Ech-Cherif El-Kettani, Z.Hamitouche, C.C.Petre, Guided waves in plates with linear variation of thickness[R], Acoustics 08 Paris,2008,5293-5297
[74]Sridhar Krishnaswamy, Theory and Applications of Laser-Ultrasonic Techniques[M], Ultrasonic nondestructive evaluation,2003,435-494
[75]T.W.Murry, J.B.Deaton, J.W.Wagner, Experimental Evaluation of enhanced generation of ultrasonic waves using an Array of Laser Sources[J], Ultrasonics,1996,34(1):69-77
[76]R.M.White, elastic wave generation by electron bombardment or electromaganetic wave absorpation[J], J.Appl.Phys.,1963,34:2123-2124
[77]R.D.Mindlin, Waves and vibrations in isotropic elastic plates, in:Structural Mechanics[M], NewYork:Pergamon Press,1960
[78]罗武德,楔形钢和楔形断面零件及其生产方法：中国,92108150.2[P],1993.5.19
[79]高娟,楔形板厚控系统及轧制工艺研究(硕士论文),燕山大学,2008
[80]杨桂通,弹性力学[M],北京：高等教育出版社,1998
[81]朗道、曹富新译,弹性理论[M],北京：高等教育出版社,2009,117-119
[82]陆建、倪晓武、贺安之,激光与材料相互作用物理学[M],北京：机械工业出版社,1996
[83]阿肯巴赫,徐植信、洪锦如译,弹性固体中波的传播[M],上海：同济大学出版社,1992
[2]刘贵民,无损检测技术[M].北京：国防工业出版社,2006
[3]袁易全,陈思忠.近代超声原理与应用[M].第一版.南京：南京大学出版社,1996
[4]C.B.Scruby, L.E.Drain. Laser Ultrasonics:Techniques and Applications[M]. Bristol Adam Hilger,1990
[5]钱梦騄,激光超声检测技术及应用[J],上海计量测试,2003,30(1)：4-7
[6]钱梦騄,激光超声学的若干进展[J],声学技术,2002,21(1)：19-24
[7]张淑仪,超声无损检测高新技术[J],国际学术动态,1998,8,58-60
[8]张淑仪,激光超声与材料无损检测[J],应用声学,1992,11(4)：1-6
[9]R.M.White, Generation of elastic waves by transient surface heating[J], J.Appl.Phys. 1963,34(12):3559-3567
[10]A.Askaryan, A.M.Prolhorov, G.F.C.Hanturcy, M.P.S.Hipulo, The effects of a laser beam in a liquid[J], S.Sov.Phys.JETP.,1963,17(6):1463-1465
[11]C.B.Scruby, R.J.Dewhurst, S.B.Palmer, Quantitative studied of thermally generated elastic waves in laser-irradiated metal[J], J.Appl.Phys.,1980,51(12):6210-6216
[12]R.L.Weaver, Y.H.Pao, Axisymmetric Elastic Waves Excited by a Point Source in a Plate[J], J.Appl.Mech.,1982,49:821-836
[13]L.R.F.Rose, Point-Source representation for laser-generated ultrasound[J], J.Acoust.Soc.Am,1984,75(3):723-732
[14]J.D.Aussel, A.L.Brun, J.C.Baboux, Generating acoustic waves by lasentheoretical and experimental study of the emission source[J], Ultrasonics,1988,26,245
[15]L.F.Bresse, D.A.Hutchins, Transient generation by a wide thermoelastic source at a solid surface[J], J.Appl.Phys.,1989,65(4):1441-1446
[16]David.H.Hurley, James.B.Spicer, Point-source representation for laser-generated ultrasound in an elastic,transversely isotropic half-space[J], J.Appl.Phys.,1999,86(6): 3423-3427
[17]J.R.Bernstein, J.B.Spicer, Line source representation for laser-generated ultrasound in aluminum[J], J.Acoust.Soc.Am,2000,107(3):1352-1357
[18]Yijun Shi, Shi-Chang Wooh, Mark Orwat, Laser-ultrasonic generation of lamb waves in the reaction force range, Ultrasonics,2003,41:623-633
[19]P.A.Doyle, On epicentral waveforms for laser-generated ultrasound J.Phys.D:Appl.Phys.,1986,19:1613-1623
[20]F.Alan McDonald, On the precursor in laser-generated ultrasound waveforms in metals, Appl.Phys.Lett.,1990,56(3):230-232
[21]James.B.Spicer, A.D.W.Mckie, J.W.Wagner, Quantitative theory for laser ultrasonic waves in a thin plate, Appl.Phys.Lett.,1990,57(18):1882-1884
[22]T.Sanderson, C.Ume, J.Jarzynski, Longitudinal wave generation in laser ultrasonics, Ultrasonics,1998,35:553-561
[23]T.W.Murray, J.W.Wagner, Laser generation of acoustic waves in the ablative regime[J], J.Appl.Phys.,1999,85(4):2031-2040
[24]D.Royer, C.Chenu, Experimental and theoretical waveforms of Rayleigh waves generated by a thermoelastic laser line source[J], Ultrasonics,2000,38:891-895
[25]Irene Arias, Jan D.Achenbach, Thermoelastic generation of ultrasound by line-focused laser irradiation[J], Int.J.Solid.Struct.,2003,40:6917-6935
[26]Irene Arias, T.W.Murry, J.D.Achenbach, Near field analysis of laser-generated ultrasound:the effects of thermal diffusion and optical penetration[J], Review of Quantitative Nondestructive Evaluation,2002,615:324-331
[27]Lei Wu, Jian-Chun Cheng, Shu-Yi Zhang, Mechanisms of laser-generated ultrasound in plates[J], J.Phys.D:Appl.Phys.,1995,28:957-964
[28]J.C.Cheng, S.Y.Zhang, L.Wu, Excitations of thermoelastic waves in plates by a pulsed laser[J], Appl.Phys.A,1995,61:311-319
[29]Wu Lei, Cheng Jian-Chun, Zhang Shu-Yi, Laser-Generated Transient Lamb wave in thin plates[J], CHIN.PHYS.LETT.,1996,13(1):24-27
[30]J.C.Cheng, S.Y.Zhang, Quantitative theory for laser-generated Lamb waves in orthotropic thin plates, Appl.Phys.Lett.,1999,74(14):2087-2089
[31]CHENG Jian-chun, FU Tao, ZHANG Shu-yi, Thermoelastic Excitation of Transient Lamb Wave in an Orthotropic Thin Plate, CHIN.PHYS.LETT.,1999,16(3):187-189
[32]Zhong-hua SHEN, Shu-yi ZHANG, Jian-chun CHENG, Theoretical study on surface Acoustic Wave Generated by a Laser Pulse in solids[J], Analytical Science,2001,17: s204-207
[33]钱梦騄,张万春,吴田成,激光热弹激发超声脉冲的特性研究[J],声学学报,1995,20(1)：1-10
[34]胡文祥,钱梦騄,激光脉冲线源位移场的数值与实验研究[J],声学学报,2000,25(4)：345-350
[35]孟振庭,激光脉冲激发的超声脉冲波形的理论研究[J],科技通报,2001,17(5)：38-42
[36]孟振庭,激光超声的热弹机理研究[J],西安交通大学学报,2002,36(5)：548-550
[37]高会栋,沈中华,徐晓东,张淑仪,固体中脉冲激光激发声表面波的理论研究,应用声学,2002,21(5)：19-24
[38]苏琨,任大海,激光致声技术的研究[J],光电工程,2002,29(5)：68-72
[39]孔令剑,徐军,闫夷升,谷小飞,朱桂芳,侯洵,激光激发超声波的新方法研究[J],光子学报,2006,35(1)：20-23
[40]Baiqiang Xu, Zhonghua Shen, Xiaowu Ni, Jian Lu, Finite element model of Laser-generated surface acoustic waves in coating-substrate system[J], J.Appl.Phys.,2004, 95(4):2109-2115
[41]J.Gao, J.Yang, L.J.Cui, J.C.Cheng, M.L.Qian, Modeling laser-generated guided waves in bonded plates by the finite element method[J], ultrasonics,2006,44:e985-989
[42]Jijun Wang, Zhonghua Shen, Xiaowu Ni, Baiqiang Xu, Jianfei Guan, Jian Lu, Numerical simulation of laser-generated surface acoustic waves in the transparent coating on a substrate by the finite element method[J], Optics&Laser Technology,2007,39:21-28
[43]沈中华,关建飞,陆建,倪晓武,激光热弹激发超声的有限元数值模拟[J],声学技术,2005,24：9-10
[44]赵艳,沈中华,陆建,倪晓武,激光热弹激励流-固泄露Lamb波的有限元模拟[J],力学学报,2008,40(1)：35-39
[45]赵艳,沈中华,陆建,倪晓武,激光在管道中激发周向导波的有限元模拟[J],物理学报,2007,56：321-326
[46]袁玲,沈中华,倪晓武,陆建,激光在近表面弹性性质梯度变化的材料中激发超声波的数值分析[J],物理学报,2007,56：7058-7063
[47]H.Lamb, On Waves in an elastic plate[J], Proceedings of the Royal Society of London, 1917:293-312
[48]I.A.Victorov. Rayleigh and Lamb waves[M], New York:Plenum Press,1967
[49]D.C.Worlton, Experimental confirmation of Lamb waves at Megacycle Frequencies[J], J.Appl.Phys.,1961,32(6):967-971
[50]R.J.Dewhurst, C.Edwards, A.D.W.Micie, S.B.Palmer, Estimation of thickness of thin metal sheet using laser generated ultrasound[J], Appl.Phys.Lett.,1987,51(14):1066-1068
[51]H.Nakano, S.Nagai, Laser generation of antisymetric lamb waves in thin plates[J], Ultrasonics,1991,29:230-234
[52]R.Daniel Costley Jr., Yves H. Berthelota, Dispersion curve analysis of laser-generated Lamb waves[J], Ultrasonics,1994,32(4):249-253
[53]M.A.Johson, Y.H.Berthelot, P.H.Brodeur, L.A.Jacobs, Investigation of laser generation of Lamb waves in copy paper[J], Ultrasonics,1996,34:703-710
[54]Michael D.Seale, Barry T.Smith, W.H.Prosser, Lamb wave assessment of fatigue and thermal damage in composites[J], J.Acoust.Soc.Am,1998,103(5):2416-2424
[55]J.L.Rose. Ultrasonic Waves in Solid Media[M], Cambridge University Press,1999
[56]T.Hayashi, K.Kawashima, Mode extraction multi-modes of Lamb wave[J], Review of Quantitative Nondestructive Evaluation,2002,21:219-224
[57]刘镇清,无损检测中的超声兰姆波[J],无损检测,1999,21(9)：409-423
[58]刘镇清,他得安,用二维傅里叶变换识别兰姆波模式的研究[J],声学技术,2000,19(4)：212
[59]郑祥明,顾向华,史立峰,史耀武,超声兰姆波的时频分析[J],声学学报,2003,28(4)：368-374
[60]郑祥明,赵玉珍,史耀武,兰姆波频散曲线的计算[J],无损检测,2003,25(2)：66-69
[61]张海燕,吕东辉,刘镇清,二维傅里叶变换在Lamb波模式识别研究中的应用[J],振动、测试与诊断,2004,24(1)：23-26
[62]刘增华,何存富,吴斌,单层板频散曲线的矩阵表示及Matlab实现[J],无损检测,2005,27(5)：225-227
[63]王杜,郑祥明,兰姆波在薄钢板无损检测中的应用研究[J],无损检测,2007,29(4)：193-199
[64]冯占英,周正干,高羿飞,大型薄板中超声导波的产生与鉴别[J],无损探伤,2007,31(5)：1-7
[65]李富才,孟光,窄频带Lamb波频散特性研究[J],物理学报,2008,57：4265-4272
[66]朱金颖,陈龙珠,吴世明,层状板中Lamb波的频散特性研究[J],振动工程学报,1998,11(3)：366-372
[67]张海燕,刘镇清,马小松,界面层对层状各项异性复合结构中Lamb波的影响[J],物理学报,2003,52：2492-2499
[68]张海燕,刘镇清,吕东辉,全局矩阵法及其在层状各项异性复合板中Lamb波传播特性研究中的应用[J],复合材料学报,2004,21(2)：111-116
[69]A.Demcenko, L.Mazeika, Calculation of Lamb waves dispersion curves in multi-layered planar structures[J], ULTRAGARSAS,2002,3(44):15-17
[70]M.Ech-Cherif El-Kettani, F.Luppe, A.Guillet, Guided waves in a plate with linearly varying thickness:experimental and numerical results[J], Ultrasonics,2004,42:807-812
[71]P.Marical, M.Ech-Cherif El-Kettani, M.V.Predoi, Guided waves in elastic plates with Gaussian section variation:experimental and numerical results[J],Ultrasonics,2007,47:1-9
[72]F.Jenot, M.Ouaftouh, M.Ourak, M.Duquennoy, P.Poussot, Finite element modeling of guided waves propagation in plates with variable thickness[R], Proceedings of the international Congress on Ultrasonics,2007,1-4
[73]M.V.Predoi, M.Ech-Cherif El-Kettani, Z.Hamitouche, C.C.Petre, Guided waves in plates with linear variation of thickness[R], Acoustics 08 Paris,2008,5293-5297
[74]Sridhar Krishnaswamy, Theory and Applications of Laser-Ultrasonic Techniques[M], Ultrasonic nondestructive evaluation,2003,435-494
[75]T.W.Murry, J.B.Deaton, J.W.Wagner, Experimental Evaluation of enhanced generation of ultrasonic waves using an Array of Laser Sources[J], Ultrasonics,1996,34(1):69-77
[76]R.M.White, elastic wave generation by electron bombardment or electromaganetic wave absorpation[J], J.Appl.Phys.,1963,34:2123-2124
[77]R.D.Mindlin, Waves and vibrations in isotropic elastic plates, in:Structural Mechanics[M], NewYork:Pergamon Press,1960
[78]罗武德,楔形钢和楔形断面零件及其生产方法：中国,92108150.2[P],1993.5.19
[79]高娟,楔形板厚控系统及轧制工艺研究(硕士论文),燕山大学,2008
[80]杨桂通,弹性力学[M],北京：高等教育出版社,1998
[81]朗道、曹富新译,弹性理论[M],北京：高等教育出版社,2009,117-119
[82]陆建、倪晓武、贺安之,激光与材料相互作用物理学[M],北京：机械工业出版社,1996
[83]阿肯巴赫,徐植信、洪锦如译,弹性固体中波的传播[M],上海：同济大学出版社,1992