[Early B.]

This metal frame inside my fireplace rattles during certain low bass passages. It only occurs on a handful of songs; nonetheless, I want to fix it. There's metal throughout the fireplace, including the rear section and I don't know what part of the frame is rattling. This fireplace hasn't been used for 20 years and we have no plans to use it again, but it needs to remain functional, so ripping out the metal won't happen. Any suggestions for restraining the vibrations?   

[FullRangeMan]

The chimney duct goes into resonance with the bass of some songs, the metal window has to be covered.

[S Clark]

If it's just the metal frame, bolt some wood trim to it to change the resonance frequency.  Trial and error reign supreme.   
Don't forget to remove it if you ever build a fire.   

[Early B.]

The chimney duct goes into resonance with the bass of some songs, the metal window has to be covered.

Good point about the chimney duct. The metal chimney cap 20 feet up might also be vibrating. I initially thought the culprit was the metal fireplace cover until I replaced it with a wooden one, but the problem persisted. I could be chasing my tail.

[WGH]

Sounds (pun intended) like the flue damper, try caulking everything that moves.

I would try high temperature caulk

Fireplace Mortar comes in a caulk gun tube and dries hard so rattles may come back
https://www.acehardware.com/departments/heating-and-cooling/chimney-and-flue/chimney-brushes-and-accessories/46621

Permatex makes a lot of high temperature automotive calks that stay flexible, the Ultra Red is good up to 650 degrees F.
https://www.acehardware.com/search?query=high%20temperature%20automotive

[Early B.]

Sounds like the flue damper,

Yeah, that's probably it. 

[Early B.]

I finally looked up the chimney today. Above the fireplace brick, the chimney is lined in sheet metal on all four sides (isosceles trapezoid) for about two feet. I originally assumed the metal flue damper was the source of the ringing, but now I'm guessing the sheet metal is resonating when low bass notes hit it. Any ideas on how to prevent this sheet metal from vibrating?

[Phil A]

I don't have a fireplace in the current house.  In an old house (where I lived until late 1996), I had my speakers in front and on the sides of a fireplace and the entire wall was brick with a small mantle/shelf in the middle which was a little bit above the height of the speakers.  I used to take a comforter and put heavy objects on it so that the space behind the speakers (both the brick and the glass doors of the fireplace with built in heatilator were covered (and several inches of space were between the comforter and the wall). 

In another old house (where I lived from mid 1997 to the end of 2013), I had a two sided (which went from the grand room to the morning room in the kitchen - pics below) gas fireplace on the opposite wall from the speakers and just left of my position.  The fireplace didn't see tons of use so I kept a canvas painting in from of the glass doors and the few times it saw use I just moved the painting. 

Besides covering the fireplace as recommended above, perhaps get something like a foam mattress topper (cut to size) or a foam upholstery cushion (cut to size - e.g.  https://www.amazon.com/GoTo-Foam-Height-Upholstery-Cushion/dp/B07W3JDYN3/ref=sr_1_2?crid=1C0GOL1VOV0IS&dib=eyJ2IjoiMSJ9.gfxlvr0LMbeQQWSvEWaEr5uNN_dixiymQSbEFXFrQi2K-zZ2548I0B7f5M0FmAox1ocfFHdHweiOPytZKtTpWyxdrDeuds4ZdCTzlOf0wjX_zWITnfZED5yTx3wcFv_xVAme1iKWufvHaVikG_ARJi3JT5C9YJpAxamkAy1T97JiBDJQaex6ivundu4TVb8U80G_7E8nOtW6zz3wnH1A5X-sgZJIPjq4tWm7NVO7wXK4HwYDy_U_P_EcUk4ScbuN897hNB7mR8ENtfAI-OHUc4UoQQUk8TBw0DVoKA38yt0.m4HlZaWTeDO3VlusteTZXzivaJ_0GwjCS3wlsH5Hj84&dib_tag=se&keywords=upholstery+foam+4+inch&qid=1708522990&s=arts-crafts&sprefix=foam+up%2Carts-crafts%2C188&sr=1-2-spons&sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&psc=1)   If it is rattling all the way up the chimney it probably will be hard to fix that.  You could also try closing the flue when listening to music and not using the fireplace.

[Early B.]

Hmmm... good idea -- stuffing some high-density foam inside the fireplace might work. Oh, I should mention that I have two 12" dual servo subwoofers with rear-facing woofers firing into the wall where the fireplace is located and a third sub three feet in front of the fireplace. It's a not major problem since the rattling only occurs on a few songs, but I want to fix it, if possible.