Efficient Method for Wet Modal Analysis of Cyclic Periodic Fluid/Structure Systems

In this paper, we propose an efficient method for the modal analysis of vertical cyclic periodic tanks partially filled with liquid. The fluid effect on the vibration of the structure is modeled by introducing an added mass matrix. Because the added mass matrix formed by the boundary element method is fully populated, it requires considerable computer memory when the wet modal analysis involves substantial wetted elements. Additionally, the dense added mass matrix will destroy the sparsity of the total mass matrix, resulting in a significant computational burden for solving the eigenvalue problem. Based on the cyclic periodic property of the fluid/structure system, it is proved that the added mass matrix of the vertical cyclic periodic tank also has a block-circulant property. Therefore, according to the group representation theory, the original eigenvalue problem of the wet modal analysis can be decoupled into a series of independent subproblems. Because the computational scale of the subproblems is much smaller than that of the original eigenvalue problem, the proposed method can significantly reduce the computational cost. Numerical examples show that the proposed method can solve the modal analysis of the cyclic periodic fluid/structure system with high accuracy and efficiency.