The bike shakes at agiven speed because the conditions are right to set up a harmonic vibration. It will happen with some bikes even when everything is adjusted appropriately.

You need to change those conditions. knee into top tube dampens the vibration, and stops the wobs. Also relaxing your grip on the bars, and flexing your elbows can help, sliding forward or back on the seat can change the harmonics, and slowing down, or speeding up can change them. ( a bike that shakes at 70km/hr may not shake at 60km/hr, or 80 km/hr)

The major takeaway is stay loose and press a knee into the the top tube. The wobs only become a serious problem if you freak.