Resonant Frequency of a System with Two Inertia Discs and a Connecting

[parkerdude]

There are a lot of formulae "out there" to use for determining resonant torsional frequencies. I need the simplified formula that determines the resonant frequency for a system that can be simply modelled as two inertia discs (I1 and I2) connected by a shaft. Also... won't there be higher order modes? And how are these modes calculated short of using an FEA program???

 

[cbrn]

Hi,
you can very easily find out the formula you need, simply starting from equations of dynamics applied to the two bodies. By doing so you won't be limited to "two inertias connected by one shaft" but you will be able to derive formulas for n inertias connected by n-1 shafts.
These systems are "semi-definite", and the "trick" is to express the displacements in relative (not absolute) terms.
For systems having n degrees of freedom, and also for the vibrations of continuum, there are plenty of different formulas in order to calculate at least the lower modes, each has advantages and inconvenients. Dunkerly is very diffuse and explained in a lot of textbooks.
Regards

 

[GregLocock]

Holzer's method is the clasic for flywheel shaft ssytems

In the one you describe the shaft magically splits itself up so that the node occurs a distance along the shaft such that the stiffness in each part of the shaft is proportional to the inertia of its flywheel, or in other words the frequency of each of the two parts is equal.

The equation is then obvious. Incidentally the 'missing' mode in this 2dof system is the 0 Hz rotation.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.