It seems that the amplifiers don't like this. If I run an experiment for more than a half hour, they die. (The speakers are ok.)
Just so that we understand completely, you are saying that the amplifiers fail completely and never work again,
but,
the speakers do work OK after the amplifiers have failed.
I'm not an electronics whiz, but I remember something about impedance matching. Do I need to put something
In some circumstances, impedance matching is useful, sometimes essential.
However, just to drive an audio amplifier from a function generator the impedance matching does not really matter, you can ignore it.
What could be a problem, depending on the output voltage from the function generator you could be overdriving the input stage of the amplifier.
How high is the volume control det on the amplifier?
Also, how loud are your "vibrations"?
It could be that you are running the amplifiers beyond their ratings and overheating them, at which point they fail.
Be aware that many consumer grade audio amplifiers are grossly overrated, most cannot provide anything like their rated power for more than a few seconds, if that.
JimB