=+For sake of simplicity, the system is modelled using a single beam finite element. Its stiffness and mass matrices being directly available, only the geometric stiffness matrix resulting from the centrifugal force needs to be computed (remember that the geometric stiffness matrix

(5.142) is for a constant axial prestress and cannot be used for the present case).

In order to get insight in the vibration behaviour of the system, the dynamic equilibrium problem will be put in nondimensional form. Therefore a dimensionless displacement vector q̃ is defined for the finite element by the transformation:

q =

⎡

⎢

⎢

⎢

⎣

 000 0100 0 0  0 0001

⎤

⎥

⎥

⎥

⎦

q̃

The stiffness and mass matrices can then be expressed as:

K = EI

2 K̃ and M = m2M̃

with nondimensional matrices K̃ and M̃ .

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