Stiffen the Floor
If there is vibration, stiffening the floor is your best bet. The way to do it is with 3/4-inch plywood. Surface flooring (tile, vinyl, etc.) needs to be removed, exposing the subfloor. Cut plywood to the size needed to go under both washer and dryer, plus about 3 inches all the way around. Radius the front corners to prevent bumped toes.
Now use Liquid Nails to glue the plywood to the subfloor, then use plenty of screws to screw the plywood through the subfloor to the joists underneath.
Finish with a layer of surface flooring on top of the plywood, and aluminum countertop edging to trim the front exposed edge of the plywood. Move the washer and dryer into place and enjoy the quiet.
This trick is particularly effective in mobile homes, though in those structures, the subfloor often has to be replaced with plywood as well, since particle board is the usual subfloor material from the factory. Particle board deteriorates and turns mushy when it's exposed to moisture. But a replacement plywood subfloor topped with an extra layer of plywood quiets everything down and makes the floor last.