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姓名	陳士欽(Sh-Qing Cheng )  查詢紙本館藏	畢業系所	機械工程研究所
論文名稱	人體耳道之有限元素與邊界元素分析
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摘要(中)	為了瞭解鼓膜所承受聲壓與頻率的關係，因此，使用數值方法來分析人體耳道聲場。 在生物聲學上，利用數值方法分析聲場主要是利用在聽覺系統和發音系統。而數值方法中，較常用來分析複雜的物體為有限元素法和邊界元素法。為了同時取得這兩種數值方法的優點，並避開其缺點，於是將這兩種數值方法作耦合。使用此耦合方法，可以避開兩種計算上的困難： (一)有限元素法對無限空間中元素分割的複雜性，且需要大量的記憶體來做運算。 (二)邊界積分式中，源點與場點重合所產生的奇異性問題。最後，比較本研究所做的數值解與Shaw所做的實驗結果，兩者相當一致。顯示在生物聲學的領域上，本研究採用的方法，相當有效且可靠。
關鍵字(中)	★ 有限元素 ★  邊界元素	關鍵字(英)
論文目次	中文摘要 I 英文摘要 II 目錄 III 圖表總覽 V 符號說明 VI 一、緒論 1 1.1 研究動機 1 1.2 文獻回顧 2 1.3 本文架構 4 二、二維聲場的有限元素公式 6 2.1 有限元素公式推導 6 2.2 數值解法 10 三、二維聲場的邊界積分公式 14 3.1 Helmholtz積分式 14 3.2 非唯一性問題 15 3.3 公式轉換 16 3.4 數值演算 20 四、耦合有限元素法和邊界積分式 23 4.1 耦合公式 23 4.2 非唯一性 28 4.3 聲波散射 30 五、實例測試與討論 33 5.1 圓形和長方形振動體的聲場放射 33 5.2 人體耳道的聲場放射 36 5.3 人體耳道的聲場散射 39 5.4 人體耳道模型的未來發展 44 5.5 耦合方法在生物力學上的未來發展 44 六、結論 45 參考文獻 47
參考文獻	1.Gladwell, G. M. L. (1966) ``A Variational Formula of Damped Acousto-Structural Vibration Problems," Journal of Sound and Vibration, Vol. 4, No. 2, pp. 172-186. 2.Hunt, J. T., Knittel, M. R., and Barach, D. (1974) ``Finite Element Approach to Acoustic Radiation from Elastic Structures, The Journal of Acoustical Society of America Vol. 55, No. 2, pp. 269--280. 3.Hunt, J. T., Knittel, M. R., Nichols, C. S., and Barach, D. (1975) ``Finite Element Approach to Acoustic Scattering from Elastic Structures, The Journal of Acoustical Society of America, Vol. 57, No. 2, pp. 287--299. 4.Kandidov, V. P. and Khristochevskii, S. A. (1978) ``Determination of the Pressure of a Fluid on a Cylinder by the Finite Element Method, Soviet Physics-Acoustics Vol. 24, No. 3, pp. 392--395. 5.Petyl, M. (1982) ``Finite Element Techniques for Acoustics,", in: R. G. White and J. G. Walker,eds., Noise and Vibration, Ellis Horwood Limited, Chichester, West Sussex. 6.Copley, L. G. (1967) ``Integral Equation Method for Radiation from Vibrating Bodies," The Journal of Acoustical Society of America, Vol. 41, No. 4, pp. 807-816. 7.Schenck, H. A. (1968) ``Improved Integral Formulation for Acoustic Radiation Problems," The Journal of Acoustical Society of America, Vol. 44, No. 1, pp. 41-58. 8.Burton, A. J. and Miller, G. F. (1971) ``The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems," Proceedings of the Royal Society, London A, Vol. 323, pp. 201-210. 9.Mathews, I. C. (1986) ``Numerical Techniques for Three-Dimensional Steady- State Fluid-Structure Interaction," The Journal of Acoustical Society of America}, Vol. 79, No. 5, pp. 1317-1325. 10.Zienkiewicz, O. C., Kelly, D. W., and Bettess, P. (1977) ``The Coupling of the Finite Element Method and Boundary Solution Procedures,International Journal for Numerical Methods in Engineering, Vol. 11, pp. 355--375. 11.Brebbia, C. A. and Dominguez, J. (1992) Boundary Element an Introductory Course, Second Edition, Computational Mechanics Publications, Southampton Boston. 12.Shaw, E. A. G. (1974) 'Transformation of Sound Pressure Level from the Free Field to the Eardrumin the Horizontal Plane," The Journal of Acoustical Society of America, Vol. 56, pp. 1848--1861. 13. Peake, W. T. and Rosowski, J. J. (1992) 'Middle-Ear Transmission: Acoustic versus Ossicular Coupling in Cat and Human," Hear. Res.,Vol. 57, pp. 245--268. 14.Ciskowski, R. D. and Royster, L. H. (1988) 'Boundary Element Solution to Predict Steady-State Response of a 3-D Coupled Fluid-Cavity System," Noise Control Foundation,Vol. 88, pp. 579--584. 15.Morse, P. M. and Ingard, K. U. (1968) Theoretical Acoustics, McGraw-Hill Book Company, Inc., New York. 16.Burton, A. J. (1973) ``The Solution of Helmholtz Equation in Exterior Domains Using Integral Equations, NPL Report NAC30, National Physical Laboratory, Teddington, Middlesex. 17.Yang, S. A. (1999) 'A Boundary Integral Equation Method for Two-Dimensional Acoustic Scattering Problems," Acoustical Society of America,Vol. 105, No. 1, pp. 93--105. 18.Meyer, W. L., Bell, W. A., Zinn, B. T., and Stallybrass, M. P. (1978) ``Boundary Integral Solutions of Three Dimensional Acoustic Radiation Problems, Journal of Sound and Vibration, Vol. 59, pp. 245--262. 19.Terai, T. (1980) ``On Calculation of Sound Fields Around Three Dimensional Objects by Integral Equation, Journal of Sound and Vibration, Vol. 69, No. 1, pp. 71--100. 20.Amini, S. and Wilton, D. T. (1986) ``An Investigation of Boundary Element Methods for the Exterior Acoustic Problem,Computer Methods in Applied Methanics and Engineering, Vol. 54, pp. 49--65. 21.Amini, S. and Harris, P. J. (1988) ``Boundary Element and Finite Element Methods for the Coupled Fluid-Structure Interaction Problem, in: C. A. Brebbia, ed., {sl Boundary Elements X, Vol 1: Mathematical and Computational Aspects, Springer-Verlag, London, pp. 509--520. 22.Agur, A. M. R. (1988) Atlas of Anatomy, 9th Edition, Williams & Wilkins Publications, Baltimore. 23.Chenshaw, C. W. (1962) Natinal Physical Laboratory Mathematical Tables, Vol. 5, Her Majesty's Stationery office, London, England.
指導教授	鄔蜀威(Shu-Wei Wu)	審核日期	2001-6-21
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