may have misread what I wanted to read. Where framing changes length
within a bay, it is correct that the variation in frequency tends to
reduce or eliminate footfall vibrations because of the large number of
different vibration modes at play - there is no large area in which the
vibrations may be sustained.
The example in 7.2 is also a very regular structure, with the diagonal
areas both on the perimeter and around the atrium apparently not
affected by the vibration problems - the primary areas of stiffening
were in back-to-back regular orthogonal bays. (I only skimmed the
article to see what you were referring to, let me know if I missed some
of it) You can still have issues in non-orthogonal bays if the primary
frequency is related to the girder, but the joists/beams should tend not
to promote resonance unless they are all of similar stiffness, or all
fall in the lousy range.
Vibrations of plates and shells is greatly complicated by non-regular
geometry, and can effectively only be performed numerically. If you
have an issue with an unusual structure, the first thing to do (barring
obvious deduction) is to determine your mode shapes, frequencies, and
modal mass participation - then you can start to isolate where the
issues are. Your comparison of extending the vibration theory from wide
flange to tube is not analogous- extending from a wide flange to a
non-linear non-prismatic curved member would be more appropriate. And,
of course, the theory doesn't extend to such members.
(now where did I put that set of nomex khakis...)
Jordan
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