In this paper, an iterative method is proposed to reduce the order of the coupled eigen- value problem related to fluid-structure interaction systems. In fact, it is required to solve a smaller eigenvalue problem rather than the larger one (original) to compute the natural frequencies and mode shapes of the system. To this end, all degrees of freedom (DOFs) of the system are divided into master (retained) and slave (eliminated) ones. Then, the problem is re-expressed based on the master DOFs and a transformation matrix is introduced. The results show a remarkable decline in computational costs, whereas the accuracy of the modal outputs does not significantly decrease. A stopping criterion is defined to check whether the iterative process converges. Moreover, three fluid-structure systems are analyzed, including a two-dimensional fully-filled concrete tank, a two-dimensional gravity dam-reservoir, and a three-dimensional arch dam-reservoir, to assess the correctness and performance of the presented method. Findings prove that the proposed method is able to reduce the order of the eigenvalue problem of fluid-structure systems.

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