Reliability optimization of friction-damped systems using nonlinear modes

Abstract

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.

Vibration Prediction of Bladed Disks Coupled by Friction Joints

“…This makes the approach interesting for comprehensive parameter studies, design optimizations and uncertainty analysis. For applications to forced response and flutter-induced limit cycle analyses of bladed disks coupled by shroud joints and underplatform dampers, see [83,85]. In the case of nonlinear modal interactions, it is generally possible to consider multiple nonlinear modes and to utilize a nonlinear projection method.…”

Reduced-order modelling using nonlinear modes and triple nonlinear modal synthesis

“…In this work, the definition of a nonlinear mode is that proposed by Laxalde and Thouverez in [15], and later used in several papers [24,25,[29][30][31]. This definition comes with a very flexible computation procedure inspired by the HBM, allowing to tackle a broad range of systems without any restriction as to the intensity, smoothness, and dissipation of the nonlinear effects.…”

A novel method for predicting the response variability of friction-damped gas turbine blades

“…There are two main strategies: develop computationally efficient modelling methods so that Monte Carlo studies become feasible (e.g. [3,4]); and / or develop methods for handling uncertainty that require a minimal number of nonlinear simulations (e.g. [5]).…”

“…Despite the intrinsic efficiency of single harmonic HBM, it remains computationally expensive to use it for Monte Carlo simulations for predicting the effect of uncertainty [4]. There is a need for modelling approaches that include the effects of uncertainty explicitly or which reduce the number of nonlinear simulations that need to be run.…”