For dynamic modal analysis of the gravity dams, it is required to solve the non-symmetric eigenvalue problem which is a time-consuming process. This paper aims to propose a new procedure for this purpose. In this novel method, there is no need to solve the non-symmetric coupled eigenproblem. Instead, two novel eigenvalue problems are formulated and solved. They are simultaneously applied for dynamic modal analysis of concrete gravity dams. These are the cubic-symmetric forms of the corresponding non-symmetric eigenvalue problem, and they are entitled “cubic ideal-coupled eigenproblems”. Moreover, it is proved that the decoupled and ideal-coupled schemes presented in the previous works can be considered as special cases of the current more general procedure. For solving the aforesaid cubic eigenproblems, the classical subspace algorithm is generalized. To assess the accuracy of the suggested technique, it is employed for the dynamic analysis of two well-known benchmark gravity dams in the frequency domain. The responses of the dam crests are computed as a result of upstream and vertical excitations for two values of wave reflection coefficients. Then, the obtained results are compared with those of the decoupled and ideal-coupled approaches.

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