"Why you need anti-vibration pads?
Everyone would hate having a machine screeching and groaning while it’s doing its thing. However, having a loud machine would be a great bother for most other people as well. In particular, the people who have their machines in their apartments might find it difficult to sleep if their machine is making loud noises – that is, if they’re making use of the cheaper nighttime electricity fees to do their laundry.

Most washing machines produce at least some level of vibration, especially during their spin cycles. However, some of them are bound to make more noise than others – older machines vibrate more than new ones, of course.

Additionally, front-loading ones are louder than top-loading machines, because they spin faster. Inside of front-loading machines, the clothes are plastered to the top, only to fall back down again and again, while the clothes in top-loading ones just get thrown around the sides of the barrel.

Ultimately, I suppose there is tow than one way to fix this.
1.Change to a brand new washing machine or dryer.
2.Buy a set of anti-vibration pad.

Hosom's anti-vibration pad
Made of high-grade rubber to reduce noise
Bottom grain can increase grip and keep washing machine from moving
Universal size design for more than 90% of washing machines
If there are any quality problems within 5 years, you can request a replacement or a full refund.

If you bought Hosom's anti-vibration pad
Your machine won’t be able to damage your floor by vibrating against it
The machine won’t be able to “walk” across the room
You won’t have to push it back into place, and hurt yourself (or your floor) while you’re doing it
Anti-vibration products will save your machine and your floor. And they’ll even save your back, since you won’t need to push the machine around. Not to mention you’ll be able to sleep soundly when you run it at night."