In this paper, an iterative method is proposed to reduce the order of the coupled eigenvalue problem related to fluidstructure 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 reexpressed 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 convergence criterion is defined to investigate the way to reach the convergence using the transformation matrices computed in each iteration. Moreover, three fluid-structure systems are analyzed, including a two-dimensional fullyfilled concrete tank, a two-dimensional gravity dam-reservoir, and a three-dimensional arch dam-reservoir, to assess the correctness and accuracy of the presented method. Findings prove the efficiency and accuracy of the proposed method.

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