2008 Mitsubishi Galant Car Rattling

Yesterday I noticed a certain rattling sound coming from the front of the car. It sounds like a tin can full of rocks vibrating at a high frequency. It only occurs when I push the gas pedal and decreases in volume at higher engine rpm. It is especially prominent when taking off after a red light. It also does not start immediately on a cold engine, but rather when the engine heats up to its normal working temperature. The noise does not occur in neutral or idle at any rpm. There are no other problems with the car and I have not hit any bumps recently. However I do drive to work every day on a road that is partially under repair, i.E. The asphalt on top is burned off, exposing the uneven concrete subsurface. After crawling under the car yesterday I did not find any loose covers or shields, although the noise is distinctly something thin and metal vibrating. However, by lightly tapping the suspect engine parts I think I found the possible culprit: the metal cover protecting the hot exhaust pipes coming directly off the cylinders. My theory is that although the cover itself is not loose, my car could have kicked up a rock inside of it, where it resides at the moments. During acceleration when the engine is shaking the most under the load, the cover, connected directly to the engine vibrates, agitating the rock inside. I do not want to screw the engine apart more than I have to. So, my question is how probable is this scenario, and if it is not probable, what is wrong?