It's an interesting idea. We all dream of a self-cleaning apartment and I would definitely use it.
What would be the source of vibrations?
Does it require a floating vibrating floor or it can be done by having a large bass-like source of vibrations on a conventional solid floor?
Can it be applied on already existing floors somehow or do we need a complete redesign?
How strong should the vibrations be to remove the bigger pieces of dust or dried maple syrup?
Would the vibrations affect human health?
Do you maybe have an example of vibration cleaning systems?