That is a great question, and worth debating.
In one respect this is an immovable object meeting an irresistible force question. People use resonance frequency analysis to measure the stability of an object. The higher the frequency, the more stable the object.
True Adamantium itself which holds incredible molecular stability once it has hardened and cooled does not chip, flake, or break. The question of it being manipulated by resonance frequency would depend upon whether vibranium was one of the alloys mixed in with the metal. As stated in the article, the ingredients to adamantium is a closely guarded secret.
That said, I would feel relatively confident that an object like Captain America's shield - a product of Proto-Adamantium or an adamantium-vibranium mix - would be immune to that process as the vibranium in that make-up would absorb the sound and disperse the energy harmlessly.
What we do know is that while working vibranium is immune to such a process, we also know that nothing - outside of the vibranium cancer episode - has been able to break Cap's shield.
There are very few (if any) true examples of adamantium breaking for any reason. The one time I remember seeing a chip of adamantium in an object from stress came after a version of the Hulk, freed from Bruce Banner's persona, struck a statue of himself and the picture showed visible cracking. Whether this was true adamantium or secondary adamantium is unknown.
In any event, my final answer is that it is unlikely that simple resonance frequency techniques could manipulate adamantium. I think it would only confirm its indestructibility.