I think it's a classic damped spring mass system with a forcing function. Soggyc has identified the forcing function. There are a lot of variables involved, some are difficult to control, others are more practical. For instance, it's difficult to change the Reynolds number for your airplane which has an effect on the force generated by the vortex shedding. You could change the stiffness of the gear legs, but come on... do you need to burn that kind of money? If so, maybe I can help.

Easiest parameter to change is mass. How? Go back to 8.50's except for gravel bars and other cool stuff.
Metal fatigue is difficult to predict and that's an awful big piece of metal holding up your gear, but, remember the toe bone is connected to the ankle bone.... Your wings ultimately absorb that shaking because they are holding up the fuselage that's holding up the gear. How much force is being applied and at what frequency and how much is damped out before the wing root attachments deal with it and is it a load case that Cessna thought of and examined during design? The British Comet airliner was brought down by metal fatigue due in part to a too-tight radius on the corners of its square windows. Ya never know.
Use the 8.50's. Go fast. Save gas. Sleep well at night.
YB