Theory of Flexible Bodies

The equations of motion in a fixed reference frame of a rotor operating at speed, Ω is[1]

where,

[M ] = Modal Mass matrix

{g} = Degrees of freedom in the fixed reference system

[BS ] = Modal damping in fixed frame

[BR ] = Modal damping in rotating frame

[G ] = Gyroscopic matrix

[K ] = Modal stiffness matrix

[KC ]R = Circulatory matrix due to damping in rotating frame

[KG ] = Differential Stiffness due to axial (radial) centrifugal load

[FS ] = External force vector in fixed reference frame

Rearranging Equation (79) above and combining terms we have:

where,

Here, {QS} contains the local rotor dynamics terms as a function of Ω in the fixed reference frame. It is applied in Adams as a distributed force acting on the flexible rotor with a dependency on Ω. To accomplish this, the MNF needs to include [G ], [KC ]R and [KG ], in addition to [M ], [K ] and [B ].

[1] MSC.Nastran Rotordynamics Guide