With the Cruze, was a plastic heater hose hitting a brake line causing the vibration on acceleration, fixed solid to the firewall, other to the engine that tips back during acceleration. Cure, bend that brake hose up a little bit.
78 Fleetwood almost drove me nuts, sounded like a bad rod knock during acceleration and really loud. Blocked up all four wheels told my son to put slight pressure on the service brakes and hit the gas. Was the flywheel cover banging away like crazy. Was held on by four 1/4"-20 bolts where all four were only about a 1/4 turn loose. When I tightened those, noise went completely away. But to prevent it, opened the holes to 5/16"-18 bolts with internal tooth lock washers and added two more.
How about a couple of loose bolts on a rotor shield, or a rubber grommet missing on one of the corners of that appearance cover. Older vehicles have motor mount problems with oil dripping all over them. Not easy with a V-6 or 8, but on a little tiny four, and put both hands on the block and shake it back and forth, loose bolt in one of the motor mounts?
Also engine hesitation, spark plugs not torqued properly, electrode gaps all over the place. Found this on my brand new Elantra next morning, while some specs say 45 mils that's crazy, smallest was around 30 mils, gaped all four at 26 mils, what a difference. Kids Kia was even worse with some at 50 mils, did the same thing for hers. But still not enough improvement, where are you buying your gas?
At a cut rate gas station using E10, noted for bad mixes and water in the gas. Told her to fill it up with 91 octane ethanol free, now she is noting a huge difference in both vibration and performance. Since she is a nature lover, said tantamount to you trying to start a camp fire using green wood in the rain. They don't understand that while the engine my creep along with 87 or even worse with a poor mix, the combustion cycle is greatly reduced and the engine is struggling to make the thing go. All they do is to look at the pump price.
Is this a plastic or a metallic noise, for us guys that been around the block a couple of times, no such thing as a plastic noise, was all metal. Does give a hint where to look, won't find any loose screws, all this plastic snaps together, air cleaner has two spring clips, are both of those closed? Part of it is attached to the chassis other part to the engine that can move, if a guy wouldn't tighten that thumb nut on an older fashion all metal air cleaner, would really get a heck of a noise.