Abstract
Dunkerley's equation is derived from Raleigh's principle and is shown to hold well under certain conditions for the fundamental mode of vibration, but not at all for the higher modes. This is checked by exact solutions for the cantilever with end load and for a shaft bearing a central load and held in pin-type end bearings. For the loaded cantilever, equations are given for the motion produced by a shock applied either to the base of the cantilever or to the end load.
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