The tuned-mass damper is used to dampen oscillations in tall building. A
large concrete block (400 tons) slides "floating" on a layer of oil.
According to Eugene Hecht's PHYSICS CALCULUS:
"One end of the block is attached to pneumatic springs fixed to one side
of the building while the other end is attached to a hydraulic piston that
acts like a large shock absorber, mounted to the other end (sic) of the
building. The device is called a tuned-mass damper because it's tuned to
oscillate at the natural frequency of the building. As the tower begins
to sway, the block goes into resonant oscillation out-of-phase with the
building."
Tipler describes the same motion in his third edition and says the
oscillation is 180 degrees out of phase with the motion of the building.
What I don't understand is the 180 degree phase angle. It seems to me
that at resonance the driving force and the displacement of the
oscillating mass are 90 degrees out of phase, and if the driving force is
provided by a helical steel spring (not a pneumatic spring--whatever that
is) the displacements of the opposite ends of the spring are 90 degrees
out of phase. Am I correct? If so, do pneumatic springs operate
differently so that at resonance the opposite ends are 180 degrees out of
phase?
Gene
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Eugene (Gene) P. Mosca Phone 410-293-6659 Office
Physics Department 410-267-0144 Home
572 Holloway Road 610-683-3597 Summer
U.S.Naval Academy Mailstop 9C, Michelson Rm 339
Annapolis MD 21402 email: mosca@nadn.navy.mil
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