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In this paper, a novel full-wave method for the modal characterization of closed metallic periodic structures based on arbitrarily shaped waveguides is presented. This method relies on an integral equation formulation solved via the method of moments, which finally leads to the solution of a standard eigenvalue problem. The required modal spectrum of waveguides with arbitrary cross section is determined through the boundary integral-resonant mode expansion technique. For validation purposes, the proposed analysis method is first successfully applied to standard waveguide periodic geometries already considered in the technical literature. Our new algorithm is then used to identify the higher order Floquet modes, as well as to compute the related Brillouin diagrams, of complex closed metallic periodic structures loaded with arbitrarily shaped waveguides.