The alternator was replaced and the issue with the battery not charging has been resolved. However, this did not correct the vibration sound I was hearing. After further research, it was the crankshaft pulley/harmonic balancer. I have attached the pictures so you can see what I saw. It looks like the rubber fill was separating and moving through the back of the pulley so it was difficult to see what was going on when it was still mounted. The rubber fill was rubbing on the engine making the vibrating sound I was hearing. Good thing I caught this when I did. Again, thanks to everyone helping me out.