Vibration while stopped

[johnwk]

Hi everyone. I've searched around a bit for information about this, but I have some pretty specific symptoms, so I'm hoping the answer will be obvious to someone.

My Yaris (automatic transmission) has 172k miles, and I changed the spark plugs around 167k. Around then, I started noticing that the car would vibrate a little bit while waiting at a light with my foot on the brake. It was pretty gentle, and it was easiest to notice when my turn signal was on, because the vibration would pulse at the same rate as the turn signals.

More recently (possibly related to the summer heat?), the car seems to be vibrating quite a lot while waiting at a light with my foot on the brake. (A passenger recently commented on how loud it was. It's almost as if a helicopter is flying a few hundred feet overhead.) As soon as I release the brake, or if I shift into neutral, the vibration stops.

I did some experimenting today. The vibration does not happen when the engine is still cold, but it starts after warming up. To my surprise, the primary source of noise turned out to be the hood vibrating. While the car is in drive, with the emergency brake on, I could silence nearly all of the noise by simply touching the hood with my finger. I stuck some rubber pads around the edge to dampen it.

Of course, something mechanical was causing the hood to vibrate, and dampening it didn't stop that. The vibrating is strongest when my foot is on the brake and the car is stopped. The final twist is that the vibrating completely stops when I turn on the air conditioner. (My AC system is all out of refrigerant, so I normally don't turn it on at all.) The fan isn't enough—the AC has to be on, too.

Summary: engine vibrates while stopped with my foot on the brake, and stops vibrating if I shift into N or turn on the AC.

If this is a problem an eager amateur with a few tools can fix, I would love to give it a shot. But if it's a major safety concern, or just a wild goose chase, that information would be useful as well. Thanks!