Power generation through building damping systems

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Hello, first time posting. If this is in the wrong forum, please move it to the correct one. (its a cross mechanical/structural/civil/electrical engineering idea)

I was thinking on the way home Power generation.
In order to generate power, wave motion can be used (such as tidal/wave power sources). Could damping of skyscrapers and other large buildings, be used to generate power.
Since there is a fair amount of energy in building movement, especially during storms.
Could varying amounts of electricity be produced as well as reduce the vibration effects on buildings.

Since the motion is similar on each side of the building, could one be reversed and the other kept as normal, and through a system of gears, create the rotational movement necessary to generate electricity.
Alternatively Hydraulic systems may be used for damping, which can either be used for turbines, or even interconnected to each side of the building and push pistons (or something similar), which could then be in turned used for mechanical motion and hopefully adapted for electrical generation.

If this problem could be solved, and assuming the amounts of energy aren't insignificant, could this be a viable supplementary source of electrical generation, or even non electrical energy usage ?
 
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I'd be surprised if there was a lot of energy in it, but certainly you could generate energy by damping the oscillation of a skyscraper. You should look into the properties of the counterweight systems they use.
 
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There is a basic problem with this idea.

Assume the wind force on the building does not depend on the amplitude of the movement of the building. That is not exactly true, but unless the building is unstable (like the Tacoma Bridge for example) it is a good approximation.

The work done on by the wind on the building = force times distance, integrated over time.

Therefore, if you design an effective damper, it doesn't work by taking energy out of the building. It really works by stopping the energy getting into the building in the first place, by reducing the building's displacement.

So, extracting a large amount of energy (to make the device cost effective), and designing an effective damper (to reduce the building sway) are contradictory requirements.

Putting a wind turbine on top of the building would probably be a simpler and much more efficient way to generate energy.