Effective Vibration Length from Effective Buckling Length
The buckling strength of columns is readily brought home to designers through the Euler length factors, \elf\, but vibration analysis still remains less design-oriented. This study develops an effective-vibrating-length, \evl\ from \elf\ and more easily computes the frequencies of any frame assemblage; in essence the \evl\ is a pin-ended bar in uniform mass replacing the given frame. The use of the \evl\ by-passes assumed shape-functions in the Rayleigh quotient method. The introduction of length allows spectral responses to be found easily. The \evl\ by-passes in-determinate structural analysis to find sway and deflection accurately in an elementary way. The effective-vibrating-length does for vibration what the Euler-length-factor does for buckling.
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