时域有限差分法在超声波声场特性分析中的应用
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摘要
超声波无损检测结果与超声波换能器的声场特性密切相关,运用数值方法可以有效地进行超声波声场特性分析。介绍时域有限差分法(Finite difference time domain method,FDTD),分析二维流体运动方程并建立相关有限差分模型,使时域宽带超声波信号的分析更易于实现;应用完全匹配层(Perfect matched layer,PML)方法对FDTD计算的边界进行吸收处理,取得了理想的边界吸收效果;通过数值计算和仿真,研究超声波声场传播特性及圆盘声源声场分布特性,与相关文献的对比表明该算法有效可行;对脉冲波信号激励的聚焦超声波换能器分别进行有限差分法数值仿真和实际测量试验,声束轴向切面的声场分布试验结果表明两者的分布特性有很好的一致性。研究结果为超声波声场特性分析提供一种新方法。
Ultrasonic non-destructive testing result is correlative with ultrasonic transducer sound field characteristic,and numerical method can effectively analyze ultrasonic sound field characteristics. Finite difference time-domain method(FDTD) is used to analyses 2D fluid kinetic equation,FDTD model is described. Perfect matched layer method is used to achieve boundary condition and obtain desired absorbing effect. Ultrasonic sound field propagation and disc sound source characteristic is researched through numerical calculation and simulation,effectiveness and feasibility of the algorithm is confirmed in comparison with other research results. Numerical simulation and practical measurement test is accomplished in focal ultrasonic transducer with pulse stimulated. There is good consistency existing in experiment result of sound field characteristic in axial cross section.
Ultrasonic non-destructive testing result is correlative with ultrasonic transducer sound field characteristic,and numerical method can effectively analyze ultrasonic sound field characteristics. Finite difference time-domain method(FDTD) is used to analyses 2D fluid kinetic equation,FDTD model is described. Perfect matched layer method is used to achieve boundary condition and obtain desired absorbing effect. Ultrasonic sound field propagation and disc sound source characteristic is researched through numerical calculation and simulation,effectiveness and feasibility of the algorithm is confirmed in comparison with other research results. Numerical simulation and practical measurement test is accomplished in focal ultrasonic transducer with pulse stimulated. There is good consistency existing in experiment result of sound field characteristic in axial cross section.
引文
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[10]李景叶,陈小宏.TI介质地震波场数值模拟边界条件处理[J].西安石油大学学报,2006,21(4):20-23.LI Jingye,CHEN Xiaohong.Treatment of the boundary conditions in the numerical simulation of the seismic wave field in transversely isotropic(TI)medium[J].Journal of Xi’an Shiyou University,2006,21(4):20-23.
[11]BERENGER J P.A perfectly matched layer for the absorption of electromagnetic waves[J].Journal of Computational Physics,1994,114:185-200.
[12]COLLINO F,TSOGKA C.Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J].Geophy-sics,2001,66(1):294-307.
[2]彭应秋,郑初华,李坚,等.航空制件超声检测中的声场特性分析[J].航空学报,2003,24(4):301-305.PENG Yingqiu,ZHENG Chuhua,LI Jian,et al.Character analysis for acoustic field in ultrasonic testing of aeronautical products[J].Acta Aeronautica Et Astr-onautica Sinica,2003,24(4):301-305.
[3]沈建国.应用声学基础—实轴积分法及二维谱技术[M].天津:天津大学出版社,2004.SHEN Jianguo.Basic of applied acoustics-real axis integration and2-dimensions spectrum method[M].Tianjin:Tianjin University Press,2004.
[4]李太宝.计算声学-声场的方程和计算方法[M].北京:科学出版社,2003.LI Taibao.Computational acoustics-sound field equation and calculate method[M].Beijing:Science Press,2003.
[5]何存富,李隆涛,吴斌,等.空心圆柱体中的周向超声导波[J].机械工程学报,2004,40(8):7-12.HE Cunfu,LI Longtao,WU Bin,et al.Guided circumferential waves in hollow cylinders[J].Chinese Journal of Mechanical Engineering,2004,40(8):7-12.
[6]DU Sanhu,ZHANG Fuliang,LI Zailiang,et al.Detection of delamination in a composite plate by SEM[J].Chinese Journal of Mechanical Engineering,2001,14(4):289-292.
[7]YEE K S.Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media[J].IEEE Transactions on Antennas and Propagation,1966,14(3):302-307.
[8]MUR G.Absorbing boundary conditions for the finite-difference approximation of the time-domain electro-magnetic field equations[J].IEEE Transactions on Electromagnetic Compatibility,1981,EMC-23(4):377-382.
[9]杨丹,方剑,廖成,等.PML吸收边界条件在孔缝耦合模拟中的应用[J].西南交通大学学报,2005,40(1):108-112.YANG Dan,FANG Jian,LIAO Cheng,et al.Application of PML absorbing boundary condition in numerical simulation of pulses coupling into slot[J].Journal of Southwest Jiaotong University,2005,40(1):108-112.
[10]李景叶,陈小宏.TI介质地震波场数值模拟边界条件处理[J].西安石油大学学报,2006,21(4):20-23.LI Jingye,CHEN Xiaohong.Treatment of the boundary conditions in the numerical simulation of the seismic wave field in transversely isotropic(TI)medium[J].Journal of Xi’an Shiyou University,2006,21(4):20-23.
[11]BERENGER J P.A perfectly matched layer for the absorption of electromagnetic waves[J].Journal of Computational Physics,1994,114:185-200.
[12]COLLINO F,TSOGKA C.Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J].Geophy-sics,2001,66(1):294-307.
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