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- Thread starter JimLin
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AlephZero

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If the gyro effects are negligible but the stiffness changes with stress (e.g. the frequencies of flexible blades on a rigid rotor) a better formula would be to say that ##K = K_e + \omega^2 K_\sigma## where ##K_e## iis the elastic stiffness and ##K_\sigma## the stiffness from the internal stresses. Since ##f = \sqrt{ K/M }## (approximately, assuming the mode shapes don't change much) this leads to the relationship ## f = \sqrt{a + b\omega^2}##.

If the temperature changes you might want to scale ##K_e## for the temperature corresponding to different speeds as well - in other words ##a## is some function of ##\omega##, not a constant.

Gven the number of assumptions in all this, it may be simpler just to run the analysis at several speeds across the range.

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How do you come up with this equation f=sqrt (a+ b*ω^2) ? Is it listed in any document ?

To my understanding, it is actually one of the formulas used by many industries.

a = f0^2 b = (f_max^2 - f0^2) / ω_max^2

where f0 is the freq at bench and f_max is the freq at max speed, ω_max is the max speed

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AlephZero

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My earler post derives it from assumptions about the way the stiffness changes with rotation speed, and the assumption that the vibration mode shapes don't chage with speed.How do you come up with this equation f=sqrt (a+ b*ω^2) ? Is it listed in any document ?

It has been around for a very long time. I can't remember where I first came across it. Here's a reference from the 1960s (see eq 4). http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890068582_1989068582.pdf

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The correlation using another formula f = a + b*w^2 is pretty good too (for component dynamics). Nice to talk to you.

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