Search:

трястись means to shake repeatedly
дотрястись means to get somewhere while shaking :)

You can see this до + main verb construction quite often.

добежать
доплыть
дойти
доехать

трястись - to shake.

That'd imlpy that the lift was juddering all its way up to the six floor, not that it juddered when it stopped there.

Шум is either a meaningless sound as was noted above or a sound you can't...