Gyrations rhymes with:
administration's, administrations, administrations', arbitrations, castrations, celebrations, concentrations, consecrations, demonstrations, desecrations, durations, emigrations, frustrations, illustrations, integrations, migrations, ministrations, orations, orchestrations, registrations, vibrations
Gyrations sounds like:
garden's, gardenias, gardening, gardens, gardini's, gerding, girding, gordon's, gradations, grading, graduating, graduations, grating, greatness, greeting, greetings, gretna's, gritting, grouting, guardian's, guardians, guarding, gyrating, gyrodynes