The Impact of Nonunique Residual Tractions on the Nonlinear Dynamics of Jointed Structures: Probabilistic Perspectives

The nonuniqueness of residual tractions is an epistemic uncertainty that can lead to significant variability in the dynamic behavior of friction-damped structures. While numerous studies have addressed this phenomenon with deterministic perspectives, probabilistic approaches have never been considered in its consideration. In this study, we treat the nonuniqueness of residual tractions as a source of stochastic uncertainty and use a probabilistic approach, namely polynomial chaos expansion, to investigate its influence on the variability of dynamics of friction-damped structures. A planar three-mass oscillator representing a simplified model of two adjacent blades with an underplatform damper is employed as a numerical benchmark for the study. The uncertainty is first quantified on the amplitude-dependent modal parameters, and it is then propagated to forced response for a given harmonic excitation level with the closed-form expression governing the amplitude-frequency curves. The outputs are also parameterized by uncertain contact parameters, i.e., coefficient of friction and contact stiffness, to compare which parameter exerts a greater impact on the observed variability in the system’s behavior. The results indicate that in fully stuck and gross slip regimes, the response variability is dominated by variances in contact stiffnesses, but in the partial slip regime, the influence of nonunique residual tractions exhibits a pronounced dominance.