This paper develops a variational formulation for two-dimensional (2-D) vibro-acoustic analysis of a circular ring in unbounded acoustic domain. The Reissner–Naghdi’s generalized shell theory is adopted to formulate the energy functional of the circular ring, while the Helmholtz equation is used to derive the stored energy in the acoustic domain. A modified variational principle combined with a domain partitioning technique is adopted to formulate the coupled vibro-acoustic model. The continuity constraints on the common interfaces of adjacent acoustic partitions are imposed by using a least square weighted residual method. To satisfy the Sommerfeld radiation condition, the local absorbing boundary condition is adopted at an artificial acoustic boundary. With the spectral polynomials or series employed as the admissible functions, the structural displacements and acoustic pressure are expanded by a spectral method. The convergence, accuracy and efficiency of the present method for predicting the vibro-acoustic responses are demonstrated by comparing the obtained results with the exact solutions or FEM results. The effects of the local absorbing boundary and the radius of the exterior acoustic boundary are also investigated in both the light and heavy acoustic mediums.

本文为无界声域中的圆环的二维（2-D）振动声波分析开发了一种变分公式。采用Reissner-Naghdi的广义壳理论来公式化圆环的能量函数，而使用Helmholtz方程来导出声域中的存储能量。采用改进的变分原理结合域划分技术，建立了振动声耦合模型。通过使用最小二乘加权残差法，可以对相邻的声分区的公共界面施加连续性约束。为了满足Sommerfeld辐射条件，在人工声边界处采用了局部吸收边界条件。将频谱多项式或级数用作允许函数，结构位移和声压通过频谱方法扩展。通过将获得的结果与精确解或FEM结果进行比较，证明了本方法预测振动响应的收敛性，准确性和效率。在轻声介质和重声介质中，还研究了局部吸收边界和外部声学边界半径的影响。