臺灣博碩士論文加值系統

對於結構體-無限域流體互制作用的外部聲場，
一般文獻都是採用邊界元素法來分析。
但是由於場點的選擇位於結構體表面上，其積分式會有奇異性的現象。
為了迴避在奇異點上的數學計算，
本文耦合了有限元素法和邊界積分方程來分析無限域的流體，
結構體部份則以有限元素法計算。
其中邊界積分方程的場點是在結構體的外部，而不是在界面上，
所以積分式中的Green's Function也就沒有奇異點的數學運算。
整個聲場模型的元素網格共有兩部份︰
第一部份為有限域結構體的有限元素。
第二部份是在結構體外部的流體，
同樣是以有限元素分割一有限的區域，
此區域之邊界條件以邊界積分方程定義之。
其中源點位於結構體與流體之界面上，
場點則位於流體有限元素之外側虛擬邊界。
最後以厚球殼的放射為實例來測試本文的耦合方法，
並且和解析解及其他文獻的數值結果做比較。

This paper presents a numerical technique for the linear dynamic
analysis of a finite
axisymmetric elastic structure
immersed in an infinite homogeneous accoustic medium.
It is required to determine the vibrational motion of the
structure and
also the associated accoustic field in the fluid.
The fluid-structure coupling is effected through matching the
normal surface velocity
defined in the elastic equilibrium relationship to that defined
by the governing
equations of the fluid field.
However,
there is a computational difficulty in representing the exterior
pressure field with surface
Helmholtz integral equation.
The singularity needed to be evaluted additionally results from
the coincidence of field points and source points. To avoid
the numerical integration on singular points,
locations of field points are chosen on the infinite acoustic
medium exterior
to the surface.
A feature of the methodology implemented is the utilization of
adding the Helmholtz integral equation to the acoustic finite
element analysis. A finite
element formulation of the structural problem is coupled to
the variaton methodology of the acoustic problem.
The example is shown for radiation from a finite thick shell.
The results are compared with analytical and other accepted
approximate solutions.