Complex non-linear modal analysis for mechanical systems: Application to turbomachinery bladings with friction interfaces

Abstract

A method for modal analysis of non-linear and non-conservative mechanical systems is proposed. In particular, dry-friction nonlinearities are considered although the method is not restricted to these. Based on the concept of complex nonlinear 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 nonlinear 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 nonlinear 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.