A function for calculating the natural frequencies and mode shapes for an elastic beam undergoing rotation is given in:
Matlab script: Vibrationdata Signal Analysis Package
The function can be accessed via:
>> vibrationdata > Miscellaneous > Structural Dynamics > Beam Bending > Rotating Beam, FEA
An option is included for calculating the response to a uniform force/length.
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See also: Beam_FEM_rotating.pdf
– Tom Irvine