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正态组合有限元法

针对浅水三维结构源辐射声场的计算，提出了一种结合正态模式的有限元法（FEM-NM）。有限元法用于计算近程声场，然后在一定的耦合范围内进行垂直和方位方向的模式扩展。因此，NM理论可以快速获得任意范围的真实三维声场。数值例子表明了该方法的效率和准确性。耦合范围和垂直模式的截断几乎不影响远场结果。