Vibration is a subject in the text books and on any structural engineering course which is too often off putting to all but the most mathematically able. It is argued that engineers should have at least a rudimentary working knowledge of the principles; particularly with a modern tendency for clients and architects to demand long span lightweight structures – which are especially prone to dynamic excitation.
The first part recaps on the main elements of dynamics followed by simple rules for finding fundamental natural frequencies.
A review of simplistic methods to assess peak structural response, together with examples which demonstrate how to identify areas of concern, is followed by a short summary of some response criteria. In conclusion aspects of building sway (dynamic response to wind loading and earthquakes) are discussed.
Natural frequency (2.5) equals forcing frequency (2.5)…
The 1st harmonic response (assuming resonance) is: 1.3xαxwp/(2xρxW) a/g = 1.3×1.5×1 /(2×0.03×8) = 4.1g
(ie an acceleration of 410%g)
Resonance and the extreme motion causes a significant response (4xg) which may also have strength implications).