True and Spurious Eigensolutions of Two-dimensional Acoustic Cavities with the Mixed-type Boundary Conditions using BEMs

Abstract

In this paper, four differeny methods, the complex-valued BEM, the real-part BEM, the imaginary-part BEM and the multiple reciprocity methd (MRM), are employed to solve the eigenproblem with the mixed-type boundary conditions and the FEM is implemented for comparisons. No spurious eiganvalues are found by using the complex-valued BEM, while there are spurious eiganvalues by using the real-part BEM, the imaginary-part BEM and the MRM. It is shown that the occurance of spurious eiganvalues depend on the adopted method (direct method: singular or hypersingular; indirect method: single layer or double layer) no matter what the given types of boundary conditions for the problem are.本文採用複數型邊界元素法、實數部邊界元素法、需數部邊界元素法及多導易法有限元素法求解混合型邊界條件聲場之自然聲頻與自然聲模並與FEM的結果來比較。以複數行邊界元素法解內域問題不會有假特徵值。採用實數部邊界元素法、虛數部邊界元素法或多導易法解內域問題則會產生假特徵值。此結果與Dirichlet邊界條件或Neumann邊界條件之聲場問題所產生的假特徵值相同，再次說明了假特徵值的出現只與使用的方法(奇異方程或超強奇異方程、單層勢能或雙層勢能)有關，而與問題的邊界條件形式無關。文中算例均成功地予以數值驗證。