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3.3  Gyroscopic effects

• Fixed frame models
• Rotating frame models

SDT supports gyroscopic matrices in both rotating (body-fixed) and fixed frames (Eulerian representation of an axisymmetric structure). When performing assembly, the matrices in the local rotating frame are obtained with MatType 7 gyroscopic and MatType 8 centrifugal softening. MatType 70 corresponds to the gyroscopic matrix in the global fixed frame. There is no centrifugal softening in this frame.

3.3.1  Fixed frame models

The mass1 and beam1 elements gyroscopic matrices are only available in the global fixed frame (MatType 70). The rotation axis is assumed to be the axis of the beam for beam1 elements. Moments of inertia must be equal (axisymmetry). For mass1 elements the rotation axis is assumed to be the one whose rotation inertia is different from the 2 others that must be equal.
mass1 .Elt format: [n mxx myy mzz ixx iyy izz EltId]
One can build simple models of 1d rotor using mass1 elements to represent rigid disk and beam1 to represent the shaft. One can find an example of such a rotor in d_rotor('TestShaftDiskMdl'). See section ?? for more details on how to mesh such a rotor.
For volume and shell elements, the formulation of gyroscopic matrices in global fixed frame is unclear and thus not currently implemented.

3.3.2  Rotating frame models

For all volume elements, one can compute gyroscopic (MatType 7) and centrifugal softening (MatType 8) matrices in the local rotating frame.

Elements under development are

• mass1 : Only point masses with same mass along the 3 translation DOF and no rotation inertia are considered. Other are ignored.
• beam1 : Not supported.
• shell : Not supported.

In that case rotation axis must be given as a vector in info,Omega stack entry in the model. For example model=stack_set(model,'info','Omega',[0 1 0]) will define a rotation axis along Y. Note that the norm of this vector is assumed to be the rotation speed in rad/s. The norm of the rotation vector should be 1 so that matrices are assembled for a rotation speed of 1 rad/s. Indeed it is assumed that gyroscopic and centrifugal softening matrices have been assembled for a rotation speed of 1 rad/s in many functions (such as fe_rotor etc. ...).

Finer definition of the rotation speed is possible using a struct input with fields

• data the rotation axis defined as described above.
• unit optional, defintion of the rotation speed unit as a string, either rad/s or RPM.
• group optional, to apply gyroscopic coupling only to specified element groups.

The definition of the group field can be handled by fe_cyclic( 'OmegaGroup', model,findElt,[0 1 0]). The findElt argument can be either a FindElt string or a vector of EltId values. In both cases, gyroscopic coupling will be applied to the groups containing the element founds, with the rotation axis [0 1 0] in this example. Warning: the whole group will be impacted even if the findElt input only selects parts of it.