Selfhosted

Honestly, I think your approach using the MEMS accelerometer in your smartphone is fine - just make sure to tape the back of your phone firmly to the board to get a rigid connection. This will be of particular importance if you want to do any kind of tuning, as you might measure spurious frequencies if the device is not properly attached.

Smartphone accelerometers are actually used in civil engineering / industrial applications to determine frequencies of e. g. bridges or check for bearing wear. If you are interested, here are some papers:

https://www.spiedigitallibrary.org/conference-proceedings-of-spie/9804/98040C/Identification-of-the-operational-frequencies-of-300-bridges-using-smartphones/10.1117/12.2222097.short#_=_

https://www.scielo.br/j/lajss/a/ZnWZ8T86HHBLFvdksCh7g9s/?lang=en

https://www.mdpi.com/1424-8220/19/14/3143

https://www.mdpi.com/1424-8220/15/2/2980

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9824767/

That being said, the accuracy of the frequency readings is not super important for your application, as what you are after is pretty much only a reduction in amplitude. I would assume spinning hard drives show different responses to different vibrational frequencies, but I did not have the time to research this myself. However, here are two papers that explore what you are trying to do, which I will link since they also mention a few related papers that show the impact of vibrations on hard drives:

https://link.springer.com/article/10.1007/s00542-012-1592-z

https://content.iospress.com/articles/shock-and-vibration/sav00458

This would in theory incentivise to optimize dampening certain frequencies, but I suspect you will quickly get into the realm of overengineering / premature optimization, as the dampening might be good enough to tune out all relevant frequencies without simulations or tuning etc. However, it's still certainly a worthwhile effort for educational purposes though.

As for a practical approach, I'd probably simply start out with some super cheap foam obtained at the nearest home improvement or crafts store and see how a sandwich using that affects signal amplitude. You could even introduce artifical vibrations using a DC motor with a weight mounted off-center on the shaft, which you can get ready-made for next to nothing on eBay ("vibration motor", ~ $2).

If you want to get into tuning / experiment / analysis territory, I would like to include additional motivation. Not only might proper decoupling increase the lifetime of your drives, but it could also improve performance. I will include the following video as humorous proof of that:

https://www.youtube.com/watch?v=tDacjrSCeq4

P.S.: I firmly believe that research should be freely accessible, so I feel obligated to mention that all papers linked above are, if not available for free on their respective webpages, obtainable via a certain scientific hub.