This is a fascinating idea... don't think of it as a tone generator for a heatsink (well, not initially -- though that may be one use case)... think of this as a research project... heat dissipation vs. temperature vs. vibrations vs. material vs. shape...

In other words, the more materials you could test at different temperatures, with different types of vibration going through them, the more you'd gain an understanding of the phenomena... perhaps there's a new theory or discovery in there... I can see the research paper or theory: "Heat dissipation via pulsation in different materials at different frequencies".

Of course, you might fail... but you'd (have to!) learn a lot of things from diverse areas of physics (and probably math too) in the process!

That would be a win, no matter what.

I'll be interested to read your upcoming initial blog post/research

This is really interesting