Why do my bass drivers shake violently listening to vinyl

We have seen this problem hundreds of times over the decades. The problem is NOT in your speakers. We believe as many others here it is compliance problem. The simple solution is to use a rumble filter, if you really want to find out what the problem is here is what we suggest. Take just your turntable to a completely different system and play it with several different albums, if it still has a rumble problem then the problem is in your turntable, if not it could be your phono pre or interconnects. If the problem exists in your turntable, first check your tonearm for problems like loose bearing or places where it maybe hanging up along it's arch also check your setup parameters on your cartridge to make sure they are correct ( We always suggest using a test LP on any setup) If the problem persists change the cartridge to one that is more compliant to your tonearm (check your setup again) If the problem still exists then it would have to be in your tonearm. Many times we had to change the tonearm to eliminate the problem, as strange as it may seem there are times when we changed the tonearm with the exact same model tonearm and it solved the problem, we refer to those pieces of equipment as having "spooks" in them, we ship all those pieces to the X Files. Good turntable isolation cannot be understated and definitely improves the quality of vinyl playback but we have placed turntables on solid concrete platforms and they still had rumble problems, how can that be? Don't know but it happened. More X files stuff.

lewm:
I don't know by what mechanism a phono pre or IC's can cause rumble problems the electronic wizards can give you dozens of explanations sometimes they can even find the reason for the problems other times it is all a mystery to them. All I can tell you is this, we have seen some weird and unexplainable things in the years we have been in audio. Once a manufacturer claimed it was a cracked IC board that caused the rumble problem. We have seen phono preamps and IC's that could pickup CB, airline and police broadcasts, electronic noise from passing vehicles and just recently we had one that was able to pickup noise from a flying drone, so picking up noises that can cause rumble is not out of the question. My job is to find the problems and fix them not explain why they happened. I can tell you from experience there have been times when replacing a phono pre or IC's  solved a rumble problem. You are correct about considering a platter bearing as a source of a rumble problem many times it is, my bad for not mentioning it. I mentioned the Technics tonearm because we have had so many problems and compatibility issues with them in the past.