A pair of these with an (ancient) Harman Kardon HK6300 (you can buy something similar for peanuts on Ebay). These are paired with my Alesis Point Seven monitors.
I don't want to tread on OP's toes here (amazing simpit either way), bass induction is awesome but I think that Buttkickers are quite overpriced.
For my setup I have a hifi amp (Harman Kardon HK6300) running my Alesis point seven studio monitors. The amp had a second set of speaker outputs so I simply plugged in two of these and mounted them to the lumbar support of my chair. Hey presto, stereo bass induction for about £60, which has become absolutely indespensable for everything from movies, to games, to music.
Obviously if you don't have an existing amp you'll need one, but I actually upgraded my amp to two simple 100w digital monoblocks. Buying one of these amps and one of those bass drivers will perform the same as a Buttkicker, but for only around £90. I just bought two for stereo, which still comes out as cheaper than anything Buttkicker does.
Those ones? I used 2 first, then 4, on my previous flight chair; but this one weights > 40 Kg without me on it, and it needed more punch. Hence I resorted to use the Sinuslive Bass Shaker attached to an aluminum plate.
It shakes well enough, but not as well as the other one with 4 Dayton Pucks.
Feel free to ask for more pointers during your build!
Sinus Live 11412 Basse pumpiii 4 ohms https://www.amazon.fr/dp/B0000WR4F2/ref=cm_sw_r_cp_api_fabc_MBD2Fb4S83JBS?_encoding=UTF8&psc=1
Carte Son USB Externe, Techole Adaptateur Audio Stéréo en Aluminium USB vers Jack 3,5mm, pour Windows et Mac, Plug and Play, sans Pilote Requis [Argent] https://www.amazon.fr/dp/B0789GFT5F/ref=cm_sw_r_cp_api_fabc_ICD2FbHV3B454?_encoding=UTF8&psc=1
ZHITING 200W Bluetooth Amplifier Board TPA3116,100W + 100W Audio Amp Board avec LC Filter Technique, Dual Channel DC8-24V, Password Free Connect to Phone Quietly https://www.amazon.fr/dp/B088N6Z9TB/ref=cm_sw_r_cp_api_fabc_7CD2FbWV07VCY?_encoding=UTF8&psc=1
I use these for a year now and I am quite happy:
https://www.amazon.de/gp/product/B0000WR4F2
https://www.amazon.de/gp/product/B0081BFVJU
edit: repaired broken link to bass shaker
I found this short video on how to do it on a Racing chair: https://www.youtube.com/watch?v=nbQ5y-54eWI
Basically it is:
I rerouted all signals below 100 Hz to my subwoofer channel in my soundblaster settings and connected it to the amplifier but a stereo signal would work as well if nothing else is available. You will need to raise bass volume in the amplifier and minimize treble volume so only the bass signals will go through to the bass shakers.
I use this bass shaker and amp: