The Impact of Different Equilibrium Hypothesis on the Non-Linear Response of Bladed Disks

Underplatform dampers (UPDs) are widely used in bladed disks to mitigate blades’ vibration amplitude. Such devices introduce localized nonlinearities, whose modelling requires nonlinear solution techniques. When the Harmonic Balance Method (HBM) is used to compute the nonlinear forced response of blades with UPDs, two different implementations are available: i) the uncoupled approach, where the static equilibrium is determined in advance and used as input to determine the dynamic equilibrium; ii) the coupled approach, where the static and dynamic equilibria are determined simultaneously. A common issue for both approaches is the variability in the static tangential contact forces, when the Coulomb friction model is used, that can result in multiple static equilibria and in multiple vibration levels. In this paper, the two approaches are used to determine the variability in the response levels of blades with UPDs and results are compared and discussed. Due to the large computation times associated with optimization algorithms implemented to compute the response limits, lumped parameter models are used, nevertheless the main findings of the paper can be considered general. In particular, results show that the coupled approach systematically overestimates the uncertainty with respect to the coupled approach and that UPDs geometry affects the range of variability of the response.