You can reduce the noise level of a washer and dryer by making sure the machines are level, by setting them on vibration pads and, on the dryer, by making sure that the drum support rollers are in good shape. Worn belts on either machine should also be checked regularly.
Washers and dryers sitting on an uneven floor can rock back and forth when in use. This vibration creates thumping or rattling noises, depending on the severity. Nuts on the feet of each appliance should be tightened with a wrench. Make sure all feet touch the ground. If one appears to be a bit elevated, a wooden shim, or wedge, can be placed between the foot and the floor for leveling.
Thick rubber vibration pads are available that fit under the feet of either appliance. This requires two people, one to lift the corners of the machine, another to slide in the pads. The rubber absorbs the vibration and the thumping that goes along with it.
Worn drum support rollers cause a dryer to shake and thump. Over time, the rollers develop flat spots, which cause the thumps. Worn belts on either appliance, or a belt idler pulley on a dryer, can cause squeaking. In these cases, the items need replaced.