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Hi Ethan,
You're correct that General Axisymmetric is currently for static structural analyses only (this is noted in the Ansys documentation, under the "General Axisymmetric Overview" section of the Mechanical help).
For modal and other analyses, it may run with beta features turned on, but please exercise caution and check your results, as beta features are not fully supported or tested.
An alternative is to model the parts with a combination of beam, lumped mass, shell, or solid elements. This can increase the DOF count depending on the model, but it's worth noting that for the general axisymmetric elements, you often need several nodal planes to accurately capture the bending response, anyway, so that results in higher DOF count for general axisymmetric models. (The beam and lumped mass approach of modeling is the most computationally efficient.)
Regards,
Sheldon
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