Tire vibration

You are describing a tire with a broken belt. That is a common failure on tires nearing the end of their tread life, and at the mileage you listed, that would be about right for the original tires.

The people at any tire and alignment shop can inspect the tires. Some broken belts are real easy to spot. Some are hard to describe, but easy to explain when you are right there where the mechanic can point to it.

Tires should be replaced as a matched pair on each axle, and if the vehicle has anti-lock brakes, it is critical for proper operation that all four wheels rotate at the same speed. That means all four tires must have the same outer circumference. When one tire has a broken belt, and the others have the same mileage on them, it is best to buy a matched set of four tires.

Shaking or vibration in the floorboard indicates something wrong with the rear tires/wheels and shaking or vibration in the steering wheel indicates something wrong with the front tires/wheels.