Complex Non-Linear Modal Analysis for Mechanical Systems: Application to Turbomachinery Bladings With Friction Interfaces

Denis Laxalde (1) , Fabrice Thouverez (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

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 calcula- tion 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.

Mots clés: Non-linear modes; Fourier methods; two-dimensional friction; Dahl model; bladed disks

Domaines: Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

Denis Laxalde, Fabrice Thouverez. Complex Non-Linear Modal Analysis for Mechanical Systems: Application to Turbomachinery Bladings With Friction Interfaces. Journal of Sound and Vibration, 2009, 322 (4-5), pp.1009-1025. ⟨10.1016/j.jsv.2008.11.044⟩. ⟨hal-00343494v3⟩