Somebody didn't do a good resonance analysis. The tower was probably driven by periodic intervals of wind near the fundamental frequency, if I had to guess. Almost all of the video footage is pretty much worthless except for starting about 1:10 here: Looks like it's probably ringing at a higher harmonic than the fundamental, maybe longitudinal/compressional waves instead of or in addition to a transverse component? Those antennae (or whatever they are) seem to be mostly out of phase, so it can't be purely transverse.
I was gonna post a gif of galloping gerdie but decided that was too flippant. Someone's resonance analysis was likely driven by the meteorological conditions at the time. SEG Plaza was designed in 1997 and you can either spend a lot of money and eliminate all resonance or you can spend a little money and design against the resonances you know you'll encounter. Which have likely shifted. Urban areas create their own weather and Shenzen is probably the most rapidly-growing urban area in the world. 1997 is a halfway point between rural rice paddies and "Totalitarian Blade Runner." For all we know one of its neighbors shifted prevailing winds from "with the chord" to "across the chord" and here we are.Somebody didn't do a good resonance analysis.
