My dryer is shaking violently and making loud motor noises. How to fix?

Does the drum slide around if you try to wiggle it?

It sounds like the dryer belt. I had to have mine replaced by sears

Could be the gasket clips have worn away!? Is there a smell of burning plastic? If the gasket has become unclipped, it will interfere with the rotation of the drum, causing a winding noise, like rubbing surfaces….. Possibly your problem!? this is still a tricky job to undertake……
More so if you’re not sure what you are doing…

Sounds like you need a new one or even get someone professional to go and have a look at it.

Violent shaking means it’s off-balance.

As for the sound, electric motors sound completely different from car engines (which many erroneously call “motors”) so I would like a description of the noise. However, if it’s off balance enough, that will cause the motor to work harder, so you might hear it hum loudly. Any sort of thinking, clunking, or clicking means anther problem elsewhere in the drivetrain.