  A novel probabilistic approach for the design of mechanical structures with
friction interfaces is proposed. The objective function is defined as the
probability that a specified performance measure of the forced vibration
response is achieved subject to parameter uncertainties. The practicability of
the approach regarding the extensive amount of required design evaluations is
strictly related to the computational efficiency of the nonlinear dynamic
analysis. Therefore, it is proposed to employ a recently developed parametric
reduced order model (ROM) based on nonlinear modes of vibration, which can
facilitate a decrease of the computational burden by several orders of
magnitude. The approach was applied to a rotationally periodic assembly of a
bladed disk with underplatform friction dampers. The robustness of the optimum
damper design was significantly improved compared to the deterministic
approach, taking into account uncertainties in the friction coefficient, the
excitation level and the linear damping. Moreover, a scale invariance for
piecewise linear contact constraints is proven, which can be very useful for
the reduction of the numerical effort for the analysis of such systems.
