Rayleigh Damping: Corotating Frame
Rayleigh damping is described by two coefficients: the mass damping coefficient αdM and the stiffness damping coefficient βdK. Rayleigh damping gives the following contribution to the virtual work:
Since a rigid body rotation will not cause any structural damping, contributions due to a rigid motion can be ignored in the corotating frame formulation. The resulting expression is
where the equality δu = Rδur is used.
For the stationary case, there is no damping contribution.
In a frequency-domain analysis, the contribution to the virtual work is
Since Rayleigh damping is added directly to the virtual work equation, it does not affect the constitutive relation. As a consequence, the stresses and strains for a linear elastic material will still be in phase. This stands in contrast to other damping models.