I have a 2001 Miata LS with some moderate track modifications, including Bilstein coil-overs, a Hard Dog roll bar, Hawk HP+ brake pads, OMP seats with Schroth harnesses, Nitto NT01 tires, and more. It has an aggressive alignment (set up by a track alignment specialist) but still has a full interior and is very streetable.
I don't drive the car as much as I'd like so I can't remember when this started, but the car shakes fairly badly between about 65-75mph. Below that, it's very smooth, and above that, it can be a little rough, but it calms back down for the most part. It seems like there's a resonant frequency at highway speeds.
Some other notes:
The shake doesn't seem to be specific to the steering wheel or pedals - the whole car seems to shimmy rapidly from side to side. It's not violent, but it's bad enough that I can look in the rear-view mirror and see a lot of horizontal blurring. I can also hear slight tremors in my voice when I talk, kind of like when someone taps on your back or chest while you say "ahhhhh."
I recently replaced the brake rotors (all 4) and front hubs with OEM parts, and that seemed to helped slightly, but not much.
I think I can make out a reduction in vibration when I accelerate and unload the front wheels, which suggests to me a front wheel problem (part of why I replaced the hubs, but they also just needed it based on the 65K mileage).
The most baffling thing is that this doesn't happen constantly. More often than not, in the 65-75mph range, the car is vibrating, but often it's not. When it starts vibrating, it doesn't seem to correspond to changing pavement texture/conditions, steering or throttle input - it can just happen on its own without any changes at all, then eventually stop just as randomly. It doesn't seem to happen suddenly either way; the vibration just gets gradually worse or better over several seconds.
I spun off-track sideways onto smooth grass at about 70mph last year. I really don't remember if the car already vibrated like this beforehand, but maybe that knocked the steering out of alignment or caused a similar problem?
What could be causing these symptoms? I realize this is best diagnosed by a mechanic in person, and I'll probably resort to that eventually, but I'm trying to learn more about the car by working on it myself.
