I’ll start by saying that I have no interest in going down this rabbit hole, it’s too close to my career and I just want to ski. Someone else can have this “fun.”
The hypothesis, as I understand it, is that ski use results in changes to the natural frequency of the ski. There are a couple of potential ways that I can think of to test this hypothesis. 1) Hold the ski in a support that is firm and consistent. It cannot change between tests. The frequency of the test setup must be designed so that it is well outside of the primary modes of the ski in the clamped configuration. Mount an accelerator to the ski. It must be hard mounted or the mount should provide consistent transfer of motion (I’d probably start with screwing into a binding insert). Hit the ski at a consistent location away from the support and acquire the acceleration for modal analysis of the frequency spectrum. Do this though out the ski’s life and see if the prominent powers change frequencies.
2) Clamp the ski to a vibration table with an accelerometer, following all the stipulations above for clamping and gauge mounting. Perform a vibration sweep, recording input and output accelerations. The transmissibility is calculated and the results compared though out ski use.
There may be other ways to test as well, these are just my first thoughts without really spending time on it. I can see some potential challenges. Consistent setup and measurements are critical. The data acquisition needs to be done correctly, with proper sampling rates and anti-aliasing filter applied. The clamp may not be strong enough to keep from creating its own frequency mode and not damage the ski. Also, the sensitivity of changes in frequency with wear may be too small for capture in these methods. Maybe both are no big deal. I like the idea of seeing if something like this provides useful info. I have used modal changes during “large input” dynamic shock tests in order to determine the time that plastic strain begins to accumulate (waterfall frequency spectra are great for that). Again, this is too much like work for me and I just want to ski. More power to whomever does something with this.