Here is the link to the company that manages that library and all of them in Sumter County.

Let's all send a message about the loud banging doors and see what happens.

Contact | Lsslibraries

I see Tal had already shared this information. Sorry, haven't had coffee yet.

There is no charge for Sumter County Library Services.

There is no charge for use of libraries in Sumter County.
I was surprised too when I heard this. Here is more information;

Our Libraries | Lsslibraries

Whoops. Tal already posted the link. Anyway, this section shows how many library system this subcontractor runs in the U.S.

More and more people are reading E books. I like the ones with pages that really turn, but I can't even GIVE my books to friends anymore. I am behind the times. Times, they are a changin'.

Suggestion
 

With this and other similar issues, you must realize that the person you have written to and e-mailed to likely never sees what you have sent. Typically this stuff is filtered by a secretary.

I've not done it in many years so the cost may well have gone up.
At a cost of 5-6.00 you can send a registered, restricted delivery letter. The person who you have directed the letter is supposed to personally sign for it. If, nothing else, your letter will be noticed in the pile of letters these people get everyday.

The doors are tall and made of plastic and when they meet on closing they bang and the vibration causes them to rattle. I would think cost was a major factor. Cheap being the operative word.
Maybe felt or rubber strips could absorb some of the noise.

Silicone caulk would solve the problem. The library can get a tube for $6 at Home Depot. You could even use the bath and kitchen version, which is clear, however it isn't made for doors. The one made for doors is white, which might be unattractive when using it as a noise-proofing barrier between the door and the frame.

One doesn't need to be a construction engineer or architect or handyman to figure this stuff out. One only needs to have once been a housewife at some point in the last 4 decades.

Caulk would be useless in this situation. Caulk seals cracks, gaps, etc. No good between moving parts.

Spoken like someone who hasn't been a housewife even once within the past 40 years.

Silicone caulk is the perfect weatherproof buffer when a door is clanging against the door frame. You don't put it on the joints/hinges. Those aren't what is making noise. What's making noise is the edge of the door (where the doorknob/handle is) clanging against the frame. So you create a rubbery buffer by adding a thin line of caulk from top to bottom of the door near the outer edge.

Then, when the door automatically slams shut, it will make a "FOOF" sound instead of a "KERBLAM" sound.

Two Bills is right. Caulking would not work in this situation.

Must confess I have never been a house wife, but I know how to do housework and can boil water, also, I know where caulk goes, and it is not between moving surfaces.

The owner of the building (my somewhat educated guess - Sumter County) and tell the most important Official you can talk with the ridiculousness and for them to fix the annoying problem. I’m sure they will be “on it”.

We may be getting some action. I got an email from Joseph Duennes and a service ticket No. 223107, and a number for the help desk, 352-568-6699.
Also, the doors were set in the open position at the library, and not operating this morning. Much quieter with the doors open.

“Patience is a virtue”

Go team.

Was at that library today. Doors were locked in the open position. "Problem" solved.

Yes the doors are adjustable every were you go ..but no one knows how too