二維聲場聲模之邊界積分方程新解法

Abstract

本文僅取對偶邊界積分方程式之奇異積分方程(UT式)與超奇異積分方程(LM式)中和函數的實部，即可成功地求得任意二維內城含不完全隔間聲場的自然聲頻與聲模，並可解決傳統邊界元素法於退化邊界所造成聲頻與聲模無法決定的困難。本法具有多倒易法(MRM)只在實部求解的優點，又可免除多倒易法繁瑣的疊代過程，利用影響係數矩陣的行列式直接搜尋法來求解自然聲頻，進而決定對應之自然聲模。本文導得的核函數的實部、經級數展開後和多倒易法所的的核函數僅差一個負數常數，因此本文亦會產生假根的問題。本文中利用超奇異積分式提出三種過濾假根的方法。並以三個實例比較本法和解析解、多倒易法、有限元素法所得的數值結果與實驗資料均相當吻合。驗證了本文方法的可行性。In this paper, the real parts of the kernels in the singular integral equation(UT kernel function) and the hypersingular integral equation(LM kernel function) of the dual integral formulation are used to solve the acoustic natural modes and frequencies of a two-dimensional sound field with an incomplete partition. Also, the degenerate boundary problems are solved. The present method is similar to the multiple reciprocity method(MRM) in that the computation is conducted in the real domain. However, the lengthy derivation required by the MRM has been circumvented. After comparing with the analytic solutions, MRM solutions, finite element method solutions and measured data using three examples, the applicability of the present method has been confirmed.