A hybrid computational method is proposed for three-dimensional structural-acoustic radiation in shallow water, which combines the wave superposition method (WSM) with the adjustable Green function and the multi-physical-coupled finite element method (FEM). A low-frequency acoustic model in the near field is established by the FEM to discretize the continuous and arbitrary-shaped radiator, and the normal vibration velocity on the wetted surface is used as the input in the WSM to calculate the strengths of simple sources enclosed within the radiator. Finally, the sound propagation in the far field of the elastic structure is efficiently computed by superimposing the sound field of each simple source. The numerical examples of the pulsating sphere and elastic spherical shell in the shallow water are developed to verify the high accuracy and efficiency of the presented method, respectively. Moreover, the regularization algorithms are employed as the complementary approaches to improve the stability of this method in engineering practices, it is found that the algorithms can significantly hold the calculation accuracy in case the velocity data contain noise, and the least-squares QR is an efficient and accurate method with a few iteration numbers and better stability effect as compared with other algorithms.

中文翻译：

---

浅水区 3D 弹性结构声辐射的半解析方法

提出了一种将波叠加法（WSM）与可调格林函数和多物理耦合有限元法（FEM）相结合的浅水三维结构声辐射混合计算方法。采用有限元法建立近场低频声学模型，对连续任意形状的辐射体进行离散化，以湿面法向振动速度为输入，计算封闭简单源的强度散热器内。最后，通过叠加每个简单源的声场，可以有效地计算出弹性结构远场中的声音传播。建立了浅水中脉动球和弹性球壳的数值例子，分别验证了所提方法的高精度和高效性。此外，在工程实践中采用正则化算法作为补充方法来提高该方法的稳定性，发现该算法在速度数据包含噪声的情况下可以显着保持计算精度，并且最小二乘QR是一种与其他算法相比，迭代次数少，稳定性效果好，是一种高效准确的方法。