What kind of 2D behavior did you specify? Is it plane stress, plane strain, or axisymmetry?
Also, which release of Ansys Mechanical are you using?
It should work for 2D plane stress and plane strain, for example. Be warned, however, that if you specify linear periodic, it's as if the portion is repeated indefinitely, so you would miss modes that would appear for a structure of finite length (or, in the case of plane stress, finite thickness, too, like out-of-plane bending modes).
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