Two different shaft supporting conditions are discussed namely: fluid film bearings which have anisotropic elastic and damping properties and then rolling element (ball/roller) bearings with only elastic (isotropic) characteristics. Expressions are derived, after linearisation, for additional terms to be introduced in the corresponding element stiffness [K^e] and/or damping [C^e] matrices. The complementing terms for a beam element with fluid, film bearing at one end are determined by applying hydrodynamic considerations and since they depend on the angular velocity of the RSDS updating of the element matrices is necessary for each time step when transients are analysed by time stepping integration. Hertz-type contact is taken into account which only produces constant additional terms in the [ K^e] matrix of a beam element with rolling element bearing at one end.

All these specifications which, in fact, introduce some new elements (if we accept that the "signature" of a certain type of finite element can be thus defined) allow for a more accurate finite element modelling of a RSDS dynamic behaviour.

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