Reliability optimization of friction-damped systems using nonlinear modes

TL;DR

This paper introduces a probabilistic design method for friction-damped mechanical systems, utilizing nonlinear modes and reduced order models to efficiently optimize robustness under uncertainties.

Contribution

It presents a novel probabilistic optimization approach employing nonlinear modes and reduced order models for efficient design of friction-damped systems.

Findings

Robust damper design improves significantly over deterministic methods.

The reduced order model decreases computational effort by several orders of magnitude.

Scale invariance in contact constraints aids in reducing analysis complexity.

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.