Something I hear a lot from students who’re new to vibrato is “when I apply vibrato to a string, the string knocks against the surrounding strings causing them to ring out.”
The best way to stop this from happening is to understand how to effectively mute surrounding strings for vibrato.
If you’re applying vibrato to the B string, like I am in this video – mute the G string by resting your pick on top of it.
Then mute the high E string by holding onto it with the middle finger of your picking hand.
This should allow you to apply vibrato to the B string for as long as you want without the sound of surrounding strings ringing out.