As you probably know, induction burners produce an alternating magnetic field that induces a current in the cookware. This process can produce attractive and repulsive forces as well that cause vibrations.
The problem can be caused not only by poor sandwiched construction but by an uneven bottom surface, or loose parts or lids.
I have read that some people have successfully used silicon baking pads to dampen the sound.
This page has some useful information on the subject:
http://theinductionsite.com/proandcon.shtml
My name is Tom Wirt, with Clay Coyote Pottery. I'll try to shed some light on the intricacies of clay cooking pots, especially tagines.
You can use any flameware tagine directly on the glass stovetop. This includes, Emile Henry, Le Crueset, and Clay Coyote flameware. These are pots with either a metal base (Le Crueset) , or a type of ceramic called flameware (Emile Henry, Clay Coyote which is formulated and made to take direct heat.
Normal stoneware clay pots and earthenware pots will not do this. Stoneware should never go on a direct heating source, gas, electric or glasstop. It will crack with or without a diffuser.
Earthenware ceramic pots, typically identified by a reddish clay color and some absorbency by the bare clay (typically the bottom), do need a diffuser and should be started over a low heat. They can crack if used over sudden or too high a heat. Remember that these pots were originally used over charcoal fires.
Metal, obviously is fine.
The flameware ceramic pots, are designed for direct heat and are actually especially good on glasstops as the top spreads the heat better than electric or gas.
Clay is a insulator, not a conductor. Thus the heat doesn't spread much, but, with a highly liquid food like a tagine, the liquid spreads the heat. Basically a tagine is cooked at a simmer, even though the pot would take the heat.
Induction stoves require a metal plate with ceramic cookware to turn the electromagnetic force into heat.
You can find more info on my blog.
Best Answer
I'm somewhat confused by your question, as GE appears to recommend copper-bottom cookware. At least if I've grabbed the right manual, lacking a model number.
Note the word recommended right below "copper bottom". Though they do warn you that you have to be diligent cleaning any residues left and not allowing cookware to overheat. (Though, depending on the thickness of that copper bottom, you may find that stainless with an aluminum disc is actually better cookware, and fairly cheap.)