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
Induction cooking works by generating an electric current in the metal cooking vessel and converting that current into heat, which requires a resistive material (i.e. a poor conductor).
It's a bit of a catch-22, because you need a good conductor to actually distribute that heat. This is why some of the best induction cookware is clad metal - two layers of (magnetic) steel around an inner layer of highly-conductive aluminum or sometimes copper, sometimes layered multiple times this way. The thick magnetic sheets generate heat, and the thin conductive sheets transfer it.
Thicker metal means that the surface is slightly farther away from the magnetic field source, but also has significantly more resistance (since resistance is proportional to length, and we are talking about doubling or even tripling that), so theoretically it should be much more effective at converting the electric current to heat, and heat up faster.
The disadvantage of a thicker metal - assuming that there is no additional heat transfer material - is hot spots. This doesn't matter at all for a skillet, but if you're trying to cook with, say, a cast-iron stock pot or dutch oven, you'll find that the hot spots are even worse on an induction cooktop than an electric or gas cooktop, since the surface heat is generated very rapidly but takes forever to spread.
Carbon steel is a pretty good compromise, which is why it's generally the material of choice for woks, and that's the material I'd choose for an induction cooktop for any vessel other than a skillet or frying pan (assuming I had to choose a single material; again, copper/aluminum-clad stainless steel works better). For pans/skillets, you want the heat to stay focused on the surface, which makes heavy/thick cast iron a better choice.
I can't honestly say that I've had much experience with forged iron, but all my instincts are telling me not to bother with it because it would be combining the worst of both worlds - lower resistance at the surface but still relatively high resistance up the sides. The only caveat to this would be a possibly significant difference between the magnetic susceptibility/permeability of forged vs. cast iron, but this is likely going to vary from vessel to vessel anyway (not all cast/forged iron is the same) so I think your best bet there is to try sticking a magnet to it. If it sticks much harder to the forged than cast iron (doubtful) then it might be good for surface cooking; I still wouldn't choose it for a larger pot.
Best Answer
You seem to be mixing up some things here.
The difference is not between "normal" and "inductive". The difference is between pans which happen to have a ferromagnetic body, and thus work on induction, and all others. All pans with ferromagnetic body also work on resistive or gas stoves, so they are sold as "normal" pans, just like the non-ferromagnetic ones. "Ceramic" has nothing to do with the pan body **, that's a coating which can be put over a body made of a variety of metals, some of them ferromagnetic and some not.
Most steel pans and all iron ones should work on an induction stove, regardless of how they are coated. You can test this with a magnet - if it sticks, it will work. If it doesn't, don't try it anyway - in the worst case it can be an aluminium pan, and
melt on the stovebad things can happen - my memory is patchy about what exactly happens, but the general advice is "don't".You are likely to already have enough pans to use on the induction. But if you want to keep using some existing pan which is not ferromagnetic, you can simply use metallic discs which are sold for this purpose. The downside is that the performance of the stove drops to levels comparable to old-style resistive stoves (non-glasstop). But you can continue with your existing pans, and ditto for pots.
** I assume here that you mean ceramic-coated nonstick pans. The word "pan" is ambiguous in English and can also mean e.g. a lasagna pan whose body is 100% ceramic. But these are not used on stovetop, so I think we can exclude them here. Another option is a series of solid ceramic pots and pans developed for the stove, like Arcoflam/pyroflam but they are quite rare. None of the full body ceramic will work on induction, no matter if intended for the oven or stovetop.