A method for modal analysis of non-linear and non-conservative mechanical systems is proposed. In particular, dry-friction non-linearities are considered although the method is not restricted to these. Based on the concept of complex non-linear modes, eigensolutions are written as generalized Fourier series and the eigenproblem is then formulated in the frequency-domain. An alternating frequency-time domain method is used for the calculation of implicit non-linear forces. A two degrees-of-freedom example featuring dry-friction illustrates the method and highlights the effects of dissipation on modal parameters. The stabilizing effects of friction in presence of negative damping in the system are also addressed. Then an application on a large-scale non-linear system consisting of a turbomachinery blade, with dry-friction interfaces is proposed. In the latter, an original framework for the description of two-dimensional frictional motions by complex variables is proposed and applied, in particular, to a Dahl model. Effects of friction parameters and models on the blade's modal characteristics are investigated.

The present review article addresses the vibration behavior of bladed disks encountered e. g. in aircraft engines as well as industrial gas and steam turbines. The utilization of the dissipative effects of dry friction in mechanical joints is a common means of the passive mitigation of structural vibrations caused by aeroelastic excitation mechanisms. The prediction of the vibration behavior is a scientific challenge due to (a) the strongly nonlinear and non-uniform contact interactions involving local sticking, sliding and liftoff, (b) topological complexity of the coupled structure, and (c) the multidisciplinary character of the problem associated with the need to account for structural mechanical as well as fluid dynamical effects. The purpose of this article is the overview and discussion the current state of the art of vibration prediction approaches. The modeling approaches in this work embrace the description of the rotating bladed disk, the contact modeling, the consideration of aeroelastic effects, appropriate model reduction techniques and the exploitation of the rotationally periodic nature of the problem. The simulation approaches cover the direct computation of periodic, steady-state externally forced and self-excited vibra

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