A combined Finite Element Method with Normal Mode (FEM-NM) is proposed for calculation of the acoustic field radiated by a three-dimensional structural source in shallow water. The FEM is used to calculate the near range acoustic field, then the modes expansion at the vertical and azimuthal direction is performed at a certain coupling range. Hence, the true three-dimensional acoustic field at any range is obtained rapidly by the NM theory. The numerical examples show the efficiency and accuracy of this method. The coupling range and the truncation of the vertical modes hardly affect the far field results.

中文翻译：

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浅水弹性结构声辐射的模态有限元组合法。

提出了一种结合普通模式的有限元方法（FEM-NM），用于计算三维结构源在浅水中辐射的声场。有限元法用于计算近距离声场，然后在一定的耦合范围内在垂直方向和方位角方向上进行模式扩展。因此，通过NM理论可以快速获得任何范围内的真实三维声场。数值算例表明了该方法的有效性和准确性。耦合范围和垂直模式的截断几乎不会影响远场结果。