It would help if you explained your purpose. The knowledgeable people here (not me) might come up with alternative/better suggestions, as well as being better able to evaluate your suggested approach.
Yes, more info on application needed. But firstly the system you suggest should work ok except why do you want to use Phonos to connect the speakers? They have standard spade terminals* and the amp has binding posts (presumable with banana plug sockets) both of which are easy enough to connect/disconnect.
* If the other speakers you want to try have different connectors it may be worth making up adapter leads.
The Exciter is rated at 40W, the proposed amp at up to 100W. If you are sticking the exciter on something that doesn't want to vibrate, the temptation will be to turn up the volume control until you get a sound at a decent level, which will make it easy to burn out the Exciter without realising.
But whether you'll get 100W per channel from that amplifier from the USB power supply and voltage adapter is another matter. The Ugreen battery power unit spec is PD3.0, which on USB C gives a maximum of 100W. So that's already limiting you to 50W per channel (plus internal losses), so maybe 45W per channel if you use more than one Exciter. The USB-C 5v to 18-20v converter is also going to take some power to operate. A PD3.1 USB-C supply should provide up to 240W.
There are probably limitations on the maximum instantaneous current draw with the voltage converter, so you may get a lot of signal distortion as the amp can't get enough power. The similar-looking voltage converters to the one in your diagram that I've found on Amazon seem to be for 65W to 100W supplies, so these may well burn/overheat if you try taking more power from them.
An external 24v PSU with a good current rating (I'd suggest at least 3A) will be fine with the amp, but there are normally some limitations when using batteries.
Also, make sure the power converter has the right voltage polarity on it's barrel jack for the amplifier. Centre positive.
My first concern for an exciter "not permanently fixed to an object in the house, but free to be placed on random objects that I find during field recording trips, outdoors" is the:
Pre-applied 3M VHB™ adhesive for quick, durable installation
I hope this isn't quite as durable as claimed, as otherwise you'll only get to attach it to the first random object you find during field recording trips, and then not be able to prise it off again
That 3M tape is very strong, we use if for fixing a flushing gasket to the bottom of boats and it will last for several years in a pretty hostile environment.
@BillB It would help if you explained your purpose...
I want to do field recording (or/and outdoors sound recordings) for sound design purpose. What are the exciters for? To transduce the vibration of a given sound to any compatible object outdoors (glass, metal, surfaces, etc....) and then capture how the sound is transformed by the vibrating object (and eventually by the environment) with my recorder (Tascam Portacapture).
@Wonks Link to more data on the proposed Exciter...
Yes indeed I want to use these exciters but I may want to experiment with other models. Therefore I picked a 40W model because many are 40W.
Some of them are much less than 40W though. But let's focus on 40W for now to keep it simpler.
@Martin Walker and @Sam Spoons The adhesive...
Yes you guys got it right, I can use adhesive or other means to temporarily support the exciter on an object. It just needs to last minutes. Most times I could simply hold it with my hand.
I really appreciate this experimentation sharing ...
Tiny bit of history -
There was a wonderful composer named David Tudor who created a piece called Rainforest. Numerous suspended objects in a room or gallery had transducers attached to them and then audio was played through them. The audience walked between the objects. Back at university we recreated Rainforest under David’s guidance. I remember I had a 5’ x 6’ sheet of glass suspended from the ceiling. I don’t remember what audio was played through it.
I also remember the composer Bill Fontana who liked to put microphones inside various vessels and amplify the results. In essence you would hear what the object ex: giant bottle, hears. I don’t recall if Bill did any exploring of transducers.
Ok, after reading the very useful message from @Wonks (thank you), I understand much more.
Looks like I'll need to be careful or I will end up with a fireworks show.
What about a: Krisdonia Power Bank per Laptop 32000mAh Caricabatterie Portatile 100W PD Batteria Esterna - 2X DC (Fino a 24V) - 2X USB QC3.0-1X PD TYPE-C 100W ?
I've got no idea just how much power you'll need to make the Exciter vibrate something enough so that it's loud enough to record. 1 Watt or so is enough for a guitar speaker to produce a good volume, but that's designed to make a noise. I assume that you'll need more than that for a lot of objects, so just be careful how much power you give the Exciter.