When you are dealing with a mechanical resonant vibration, it's like applying 5lbs of force to a swing with some-one on it. Each time they return, the altitude is a little higher, and the energy of interia is summed up. The action of the pendulum, only looses energy as a product of wind resistance. A bell, however, is quite different. It's the combination of the elasticity of the metal, and the elasticity of air. That's why when you fill a glass with a uncompressable fluid like water, the crystal will ring at a higher frequency. If you filled with lanoline, the resonant frequency would drop because the speed of sound is so much slower in lanoline. It is concievable to move that all down an octive.
Now, if your material were piezoelectric, which of most is not really solid, nor hard, but if you had something that wasn't full of holes like a sponge, you could make a bell, and your first AC connection would be 90 degrees from the the piezoelectric transducer. The second would be + 45 degrees. A standing wave in a circular bell, produces a oval that is oscillating at 90 degrees from zero. But, with a piezoelectric material, you need a compression zone, and a decompression zone to produce power.
I have just done this experiment today, and it was too easy. I took the coin speaker from an old alarm clock, and used my signal generator, which has a peak to peak output of 2 volts, and the impedance of the output is 50 ohms. I couldn't turn up the power high enough to but barely hear that thing at it's own resonant frequency. But, finding the resonant frequency of a glass that was half full, made a very loud ear piercing resonant sound. You can talk, but you can't f*ck with the real world results.
I don't have the materials to research a machined bell made of peizoelectric ceramic, nor do I have access to that material. I have little tiny bits of the substance that is lodged in my cigarette lighter about the size of a flint. That tiny little object is probably resonant to frequency in the megahertz, if not nearly gigahertz. It is too small to evaluate such a set of conditions. The bell would have to be made of that piezoelectric material. Some materials make crappy tuning forks, and crappy bells. That could be true, but there are a range materials that fall into same catagory, that are not used in making these lighters. Without access, I can't say, and didn't say it was producing more power than it was using, I only held it in question, because the sound energy out is very obviously more than the sound energy in.