Implementation
Due to the frame acceleration in the rotor, inertial contributions to the virtual work are obtained by considering:
The variation of the position using Equation 6-1is
Using this equation and the acceleration from Equation 6-2, the inertial contribution to the virtual work is
The integration over volume can be split into an integration over the cross-sectional area followed by integration over the length. By using the fact that
,
the contribution to the virtual work is simplified to
where
and
For a geometrically linear formulation, , and higher-order terms in θ can be dropped. Then, the inertial contribution to the virtual work can be further simplified to
Due to the rotation of the rotor, the principal directions of the rotor cross section change orientation in the spatial frame. Therefore, all the strain and stress components are defined in the current principal directions of the cross sections.
For details about stresses, strains, and strain energy contributions to the virtual work, see
•
Strain–Displacement/Rotation Relation
•
Stress–Strain Relation
•
Implementation
in the Theory for the Beam Interface section in the Structural Mechanics Theory chapter of the Structural Mechanics Module User’s Guide.