Abstract A theoretical model is presented for the prediction of sound radiated from a semi-infinite unbaffled long enclosure with the ground. This geometrical arrangement forms an idealized representation of traffic tunnels and railway stations where noise propagates inside the long enclosures and radiates to the outside through the openings. Despite the fact that the model described here applies only to idealized situations, it contains essential elements of realistic configurations which are conducive to understanding the physics of the sound radiation phenomenon and significant for the proposal of appropriate noise control strategies. First of all, by expressing the sound field in terms of the superposition of propagating modes inside the long enclosure and adopting the Fourier transform in other regions, the intractable boundary value problem in the natural domain is reduced to a scalar modified Wiener-Hopf (W-H) equation of the second kind in the spectral domain. Then, its solution is obtained using the standard factorization and decomposition procedures, and the radiated sound field is attained through the inverse Fourier transform which involves a contour integral that can be evaluated approximately via the saddle point method. After that, the finite element method (FEM) is adopted to validate the model. Far-field directivity patterns of the radiated sound fields are presented. Finally, the properties of the sound fields both inside and outside three enclosures with different boundary conditions are analyzed, based on which, potential noise reduction methods by using acoustic liners are discussed.

中文翻译：

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来自地面无挡板长外壳的声辐射预测

摘要 提出了一种用于预测半无限长无挡板长箱体与地面辐射声的理论模型。这种几何排列形成了交通隧道和火车站的理想化表现，其中噪音在长围墙内传播并通过开口辐射到外面。尽管这里描述的模型仅适用于理想化的情况，但它包含现实配置的基本要素，这些要素有助于理解声辐射现象的物理原理，并且对于提出适当的噪声控制策略具有重要意义。首先，通过长箱体内传播模式的叠加来表达声场，其他区域采用傅立叶变换，自然域中难以处理的边值问题被简化为谱域中的第二类标量修正 Wiener-Hopf (WH) 方程。然后，使用标准因式分解和分解程序获得其解，并通过傅里叶逆变换获得辐射声场，该变换涉及可通过鞍点法近似评估的轮廓积分。之后，采用有限元法（FEM）对模型进行验证。呈现了辐射声场的远场方向性模式。最后，分析了三种不同边界条件的箱体内外声场的特性，并在此基础上讨论了可能的声学衬垫降噪方法。