The lamp is a replica, so would allready be a Tungsten filament
Carbon filaments i think were quite flexible, as some decorative carbon lamps actually contained a magnet on the stem to make the filament vibrate, making a spot of light like a flame. With Tungsten i think it won't go as well, as it gets brittle especially as it ages
Now lets think what is actually going on there :
At full power (60 Hz sine) it does not vibrate, allthough in the "loop" formed by the filament is induced the maximum magentic field
At some medium power position it vibrates. That is the position where the dimmer cuts the sine near the center , so quarter of the sine is getting through and quarter is stopped. In this state, the filament vibrates. And possibly not with the mains voltage frequency, but some double of it or such, tat causes some mechanical resonance with the filament (as a string)
This might be solved, if you dim the lamp not by a Phase control dimmer, but by something that still lets through an "undamaged" sine wave :
- Step down transformer
- Choke in series with the lamp (Fluorescent or PL choke would do, just make sure the current drawn does not exceed the current of the original lamp the choke was intended for, to not overheat the choke)
- Capacitor in series with the lamp (something on the order of up to few uF, Polyester, rated for the grid voltage, and installed in a safe way as capacitors sometimes fail spectacularly, even correctly rated ones)
- Another lamp in series with the lamp
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