Vibration has two components: frequency, and intensity.
The brain is “floating” in cerebrospinal fluid, so your question can be deconstructed into two parts: how much of that vibration would the fluid transmit, and how would brain cells react to the resultant internal vibration.
We know that high intensity vibration can cause the skull to directly hit the brain, and/or compress the fluid to a point where just the pressure can start causing brain damage. I think you can find the (mostly) safe limits in OSHA regulations.
With high enough frequency vibrations, you could induce cavitation in the fluid, making it behave like an ultrasonic cleaner. That could start popping brain cells like balloons. Don’t do that. You might search ultrasound imaging equipment frequency and intensity limits, to have an idea of what is safe.
If it’s low frequency and intensity, that “we would consider safe”… there is no reason for it to not be safe, for the brain. That doesn’t mean it would be equally safe for other structures not floating in cerebrospinal fluid, like eyes, ears, teeth, the whole skull, muscles, spine, neck blood vessels, and similar. Cells are elastic to some degree, much more than bone, so soft tissues are less likely to get damaged by “safe” vibrations.
If you strapped a tiny vibrator to a head, there shouldn’t be any damage to the brain. One kind of such “vibrator” that many people use, is headphones. You could probably check the energy output of most toy vibrators with a dB meter for a rough comparison.
Strapping a head to a road vehicle… would depend on the vehicle’s shock absorbers, but there is a reason why seats usually have some additional cushioning on them.
If you want to check on some more extreme vibration limits, look at NASA’s manned rocket launch parameters. They aren’t pleasant, yet are limited so to not cause damage. (Don’t look at fighter jet limits, those are a tradeoff between “getting shot down” vs “some brain damage”).