本論文主要目的： 1.探討不同頻率在長空間中傳播並不是以往預測中的呈線性衰減，而是受到頻率的影響，而 呈現非線性的衰減。 2.在波動方程式的理論上運用虛源法為基礎，分別從理論模型、數值模擬和實驗進行長空間 具有旁支及複雜的阻抗情況進行研究。 3.使用聲波理論導出長空間和垂直旁支管音場的理論解，並利用虛源法的相干模型對長空間 音場及噪音衰減進行預測。 對基於波動理論中的虛源法（或稱鏡像源法Mirror Image Source Method，簡稱MISM）做了 一定程度的研究與貢獻，對干涉模型（Coherent Model）的邊界參數進行了改進，研究了不同邊 界條件下某些平面或直線沿長方向的衰減，充分考慮聲波的頻率因素和波動性能，可以瞭解不同 阻抗邊界的長空間音場現象，亦對不同的音源位置進行了多種阻抗邊界條件下的數值分析。另 外，進行了原模型、有限長旁支模型、有限長旁支加寬模型、有限長旁支加長模、無限長旁支模 型及無限長旁支加寬模型的實驗，加上理論與數值模擬計算和比較。 文章安排如下： 第一章文獻回顧。 第二章介紹了長空間中聲傳播的特性以及長空間消音方法，概括了理論求解長空間音場的常 用方法。 第三章首先推導點音源激勵下長空間音場的理論解，再介紹了長空間中基於幾何聲學的虛源 法的運用，然後詳細研究了基於波動理論的虛源模型。不同空間情況對波動方程式的解法基礎 上，將單一表面球面聲波的反射及其在多面空間的擴展引入，綜合得到長空間中基於波動聲學的 複雜虛源法，即「干涉模型」，將其運用於不同阻抗邊界（貼上吸音材料）的長空間音場研究。 在第三章建立模型的基礎上，第四章進行Odeon 數值模擬及對於不同的音源位置進行了多種 阻抗邊界（貼上吸音材料）條件下的數值分析。所討論的音源位置分為三種：音源在長空間正中， 音源靠近側面邊界和音源靠近角落。每種音源位置對於不同的阻抗邊界（貼上吸音材料）進行了 音場衰減的預測和具體的分析。 第五章是具體的實驗。首先進行了，原模型、有限長旁支模型、有限長旁支加寬模型、有限 長旁支加長模、無限長旁支模型及無限長旁支加寬模型的實驗，透過理論與數值模擬計算和比 較，可以發現些規律。數值模擬解隨距離的衰減過於平滑，預測衰減量比實驗值大；而理論解隨 距離的衰減波動較大，預測衰減量比實驗值小。 第六章對於全文提出結論與建議。 The propagation of sound in long enclosures with branches has been studied theoretically and experimentally, and an efficient combined method is proposed to predict the sound field in long enclosures with branches. Based on the wave-acoustics theory, the theoretical analysis of the sound field of the long enclosures with branches is performed. This paper also investigated the sound field prediction of long enclosures with branches, by using the acoustic modeling program, ODEON. The results obtained by the theoretical analysis and the numerical simulation ODEON are compared with the experimental measurements, and the characteristics of the two methods for predicting the sound field of long enclosures with branches are analyzed. Compared with the experimental results, it is found that: 1) the results predicted by the theoretical analysis fluctuate relatively large with respect to the source-receiver distance, and the sound pressure level (SPL) attenuation obtained is smaller than that measured; and 2) the results predicted by the numerical simulation is smoother, and the calculated SPL attenuation is larger than that measured. To effectively predict the sound field of long enclosures with branches, a combined numerical method is thus proposed. The effectiveness of the proposed combined method is demonstrated by the scale-model experiments. A theoretical model has been developed for the prediction of sound propagation in a rectangular long enclosure. The model is based on the image-source method, and the effect of interference among the infinite number of image sources generated by multiple reflections is incorporated by coherently summing the contributions from the image sources. The various impedances of the boundaries are added in the model. Experiments are carried out to validate the proposed theoretical model, where the enclosure walls are lined with different kinds of sound absorption material to simulate different impedance boundaries. It is shown in the paper that the developed model agrees reasonably better with the experimental data than that of the ODEON software.
