Well I'm grateful for all the quick responses this morning. I hope it's something simple I can do at home. I'll try he suggestion of reseating the tire and reinflating your welcome tube. I'll also try using my valve locks (those little screws that come with the valve to secure it to the rim) and hope that resolves the issue.
It's good to know that it wil always shake a littler in the stand, I'll take it for a spin in the next few days and see if that works!