2000 C70 shuddering / vibrating while accelerating

[SoDoWarts]

Out of the blue my car started shuddering, but only when while accelerating up to about 40mph. The car has 140,000 miles on it and the tires have about 10k on them. There's no vibrating when going down hill or my foot off the accelerator. When it's still I feel a slight shudder but it's not there when I put it in neutral. About 3 weeks later it seems to be doing it a bit as I go up toward 60mph. I can't ignore it any more -- it's not going to go away. Any info would be appreciated! Thank you!