what could cause car to have a hard & loud vibrating sound when driving

Agree with the previous person . If the vibrating started after a tire rotation, you would look at the tires first. Check the condition of the tires. If they look good, check to see if they are balanced. Checking the balance requires you to bring it to a shop. Make sure they do a test drive along with a good overall inspection. It MAY be the tires or another issue could have come up coincidentally at the same time. The general inspection should catch that.

Suspect 'scalloped' or 'unevenly' worn tire tread on one or more tires... Problem more pronounced since tire rotation.