Why there are no flexible speakers?

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Maybe, it is a stupid question, but why not use something like this?

I think you're not understanding. He means a rubber enclosure I believe. And as to why not to use it.... one would be worried about resonance at lower frequencies, and it'd need some sort of frame to keep the thing from falling over. Certainly it's worth trying if you feel the inclination, nothing like a real-world experience to let you know how things work.
I too would worry about resonance, but I wonder what would happen if you used really dense/thick rubber.

In computer cases I've encountered the trick of sticking vinyl tiles to the sides, simply mass loading the enclosure so much that it wouldn't resonate....
What tpsorin suggests here would not flop over if he used 1/2 inch thick conveyer belt or agricultural mat in it`s slightly thicker common size. These rubber products are very heavy (much heavier mass than wood) and generally very stiff. For a bookshelf sized speaker enclosure with say up to a 8 inch driver I`ll bet this idea would work at least as well as using all wood. In fact if internal wood bracing was employed and the rubber wall firmly attached to the bracing at regularly distributed points around the box, I see no reason why larger cabinets and drivers could not be employed expecially if `cow mat` which is darned stiff and heacy stuff was the vertical wall section as shown in the drawing.

If the idea was to make a speaker that could be pressed into a suitcase just too small for it to fit, forget it. Rubber products suitable for the sidewalls would be too stiff to deform, and the top and bottom end caps would prevent the ends fom collapsing.
That is an interesting concept. Back wave absorbition and generally good damping as well as a control over the pressure. Sorta of an aperiodic/sealed enclosure. I once put a RS-1354 in a Bball, low end was distorted as the ball expanded and contracted like a humming bird heart on 4 expressos. The stiffer medium might work well.

On general principle, any movement in the cabinet is considered a loss of movement to the speakers. So flexible speaker cabinets are not generally a good idea unless by some mysterious magic you can make that flexibility work for you.

If you have your speaker on a thick carpet and every time the woofer surges forward, the cabinet pushes back as an 'equal and opposite' reaction, that means less energy went into the speaker. You should be able to see that, in this case, cabinet movement softens speaker movement. It absorbs energy in a non-productive way.

Now say, we have a similar bass pulse, and the walls of the cabinet flex, again the 'flex' is absorbing energy that should have gone to the speaker, so, not a good thing.

That's why people look for the most solid possible material to build speakers out of. Some even going so far as to build their cabinets out of concrete.

If you use rubber that is of sufficient stiffness and thickness so as to not amplify this cabinet loss, then you really don't have flexible cabinets. You have hard dense cabinets that just happen to be made out of rubber. And, like all cabinets, are going to have to be sufficiently brace to discourage any vibration.

Still, assuming sufficiently stiff rubber, there could be some advantages. It would seem to be very dense and heavy, as well as, to some degree, able to absorb but not transmit vibration, so it might have some potential.

I wonder about building an inner layer of rubber as a sort of sound proofing. You built the cabinets out of regular MDF, then line the insides with a dense but relatively thin layer of rubber. The rubber absorbs sound but doesn't let it travel through the cabinet. On top of the rubber, you add your normal sound dampening material (poly, fiber glass, rockwool, etc...).

Just a few thoughts.

You could experiment with the baffles they use in car audio. Crutchfield and others have them to close off the rear of driver in a door or dash. They are light foam that you can form somewhat if you have equipment behind the driver, and are very cheap. Bass is where you will have issues, then again if you were to use them with a separate sub or other bass driver I suspect that type of enclosure could work just fine. In a car they will increase mid/midbass response but they do make a pretty small enclosure behind the driver. I just cut a hole in the bottom until it loosens up enough to sound the way I want. Maybe that would be aperiodic IB sort of.
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