The accuracy and efficiency of the finite element method-finite element method (FEM-FEM) for 3D vibro-acoustic problems degrade gradually with the increase of the excitation frequency due to the “dispersion error”. In this study, a novel efficient 3D vibro-acoustic analysis method, the partition of unity finite element method-finite element method (PUFEM-FEM), is proposed based on the PUFEM applicable to acoustics and the FEM for thin plates, where the coupling of non-matching meshes is realized by dividing virtual elements, implementing coordinate transformation and introducing continuity conditions at the interface. The proposed method not only fully exploits the advantages of the PUFEM in suppressing “dispersion error” and reducing computational size, but also takes full use of its ability to analyze multiple frequencies without the need for repeated meshing, while retaining the FEM's ability to model the complex structures in great detail. Numerical examples demonstrate that the PUFEM-FEM has better accuracy, efficiency and convergence than the FEM-FEM for 3D vibro-acoustic problems.

由于“色散误差”，随着激励频率的增加，有限元法-有限元法（FEM-FEM）对3D振动声学问题的精度和效率逐渐降低。在这项研究中，基于适用于声学的 PUFEM 和适用于薄板的 FEM，提出了一种新的高效 3D 振动声学分析方法，单位有限元法-有限元法（PUFEM-FEM），其中耦合通过划分虚拟元素，进行坐标变换，在界面引入连续性条件，实现网格不匹配。该方法不仅充分利用了 PUFEM 在抑制“色散误差”和减小计算量方面的优势，同时也充分利用了其分析多个频率的能力，无需重复网格划分，同时保留了 FEM 对复杂结构进行详细建模的能力。数值例子表明，对于 3D 振动声学问题，PUFEM-FEM 比 FEM-FEM 具有更好的精度、效率和收敛性。