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研究生:盛夢徽
研究生(外文):Sheng, Meng Huei
論文名稱:同心球體的音場脈衝響應理論與數值計算研究
論文名稱(外文):A Theoretical and Numerical Study of Point Source Responses of Spherically Layered Acoustic Media
指導教授:張弘文張弘文引用關係
指導教授(外文):Chang, Hung Wen
學位類別:碩士
校院名稱:國立中山大學
系所名稱:光電(科學)研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
畢業學年度:84
語文別:中文
論文頁數:63
中文關鍵詞:聲學球體脈衝響應數值計算
外文關鍵詞:AcousticSphericalImpulse responseNumerical caculation
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聲學的應用,目前廣泛地存在於醫學超音波診斷、地震波研究、還有聲納
掃描等方面。而隨著計算機科技的進步,對任意複雜介質中聲波交互作用
的複雜物理特性已能量化分析。像 "有限差分"、"有限元素" 等威力數值
方法,在求解聲波暫態問題上雖然十分有力,但卻受限於只能夠在工作站
級的電腦上求解二維問題,於是我們冀求尋找一種有效的半解析法以便處
理三維結構。最完整的空間三維結構而能以一維方法求解的,莫過是利用
頻域處理多層球體問題了。在本論文中,我們將探討同心球體的音場脈衝
響應。我們的方法是架構在眾所周知的 "汨氏解答" 上,此解是頻域上平
面電磁波打到任意大小的介電質球體的正解。透過矩陣數值方法,我們將
可推展求解多層球體結構,再利用傅氏反轉換即可得到時域的解。為了獲
得較佳的數值解,我們須要有高精確性的數值架構,以便計算各類的球體
貝索函數。文中,我們設計使用上升及下降式遞迴公式來解決貝索函數的
問題,這種數值方法已被公認是安全且穩定的。然而對於貝索函數的參數
及階數都很大時,所可能遭遇的電腦浮點數格式無法處理實際數值的情形
,我們另外也利用了擴充浮點運算區域的方法來改進以達到成目的。

Acoustic energy have found many applications in areas such as
the medical ultrasonic diagnostics, seismic exploration and so
on. With the advent in computer technology, it is possible to
conduct quantitative analysis of the complex physics of
acoustic waves interaction with arbitrary complicated media on
a computer. Pure brute-force numerical methods such as the
time-domain finite- different method and the finite-element
method thougt extremely powerful for solving general acoustic
transient problems, are restricted to a 2-D geometry running on
a workstation or a high- end PC. Therefore we seek for an
efficient semi-analytical method to handle a 3-D geometry. The
most complex 3-D structure that can still be solved by an 1-D
method in the frequency wavenumber domain is multiple
spherically layered medium. In this thesis we present
numerical study of point-source impulse responses of acoustic
waves scattered from a spherically layered medium. Our method
is based on the well known Mie solution which gives the exact
frequency domain solution of a plane electro-magnetic wave
impinging upon a spherical dielectric object of any size and
the time-domain solution can be obtained by taking the inverse
Fourier transform. Furthermore, by matrix numerical method Mie'
s technique can be extended to a spherically layered structure.
To obtain good numerical solutions one needs to have high-
quality numerical algorithms for computing spherical Bessel
functions. In this paper we propose to solve this problem by
using the upward/downward recurrence formula to compute
spherical Bessel functions. It is known to be accurate and
stable. However, one is likely to encounter floating point
number overflow and under- flow in the process when both
arguments and orders of Bessel functions are very large. In
that case, extended range floating point arithmetic must be
used.

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