Asymptotic description of flutter and forced response vibration saturation by friction forces

Abstract: The estimation of the final vibration amplitude of a bladed disk is of extreme practical importance: it constitutes an essential information for the prediction of the level of high cycle fatigue of the blades, and for the subsequent estimation of its operative life span. Both, in the case of aerodynamic instability (flutter) and forced response, the increase in the vibration level is saturated by the nonlinear damping introduced by the friction forces at the interfaces between blade and disk, or at the included dampers. The computation of the final amplitude of the saturated vibration requires to solve a quite complicated nonlinear problem, which can be reduced to a single sector with phase lag boundary conditions, and requires considering several time harmonics in order to capture the details of the nonlinear periodic oscillation that sets in. If the small unavoidable differences among blades (mistuning) are also taken into account, then the situation becomes even more complicated because the solution of the mistuned vibration problem requires to consider not only a single sector but the complete bladed disk. In this talk I will discuss the application of multiple scales techniques in order to drastically simplify this problem. The idea is to take into account the fact that all relevant effects present (forcing and/or flutter growth rate, nonlinear friction damping, and mistuning) are, in most practical situations, small effects that develop in a time scale that is much longer than that associated with the elastic vibration frequency of the tuned system. The resulting asymptotically simplified models will be used to analyze the characteristics of the final vibration states of both the tuned and mistuned bladed disk