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We report a micromagnetic investigation of the propagation of spin waves in bi-component magnonic crystal waveguides. The investigated nanostructured waveguides are in the form of regular square lattice arrays of circular Fe dots embedded in a yttrium iron garnet matrix. Magnonic bandgaps of the order of 10 GHz are observed in both calculated frequency power spectra and dispersion curves of spin wave. The effect of the variation of the period along the direction perpendicular to spin wave propagation on magnonic band structures of magnonic crystal waveguides has been investigated. Micromagnetic simulations show that the first bandgap is more sensitive to variations of period than the second bandgap.