Nonlinear normal modes, Part 2: Toward a pratical computation using numerical continuation techniques

in Mechanical Systems & Signal Processing (2009), 23

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartI.OnereasonofthestilllimiteduseofNNMsinstructuraldynamicsis that theircomputationisoftenregardedasimpractical ... [more ▼]

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartI.OnereasonofthestilllimiteduseofNNMsinstructuraldynamicsis that theircomputationisoftenregardedasimpractical.However,whenresortingto numericalalgorithms,weshowthattheNNMcomputationispossiblewithlimited implementationeffort,whichpavesthewaytoapracticalmethodfordeterminingthe NNMsofnonlinearmechanicalsystems.Theproposedalgorithmreliesontwomain techniques,namelyashootingprocedureandamethodforthecontinuationofNNM motions. Thealgorithmisdemonstratedusingfourdifferentmechanicalsystems,a weakly andastronglynonlineartwo-degree-of-freedomsystem,asimplifieddiscrete modelofanonlinearbladeddiskandanonlinearcantileverbeamdiscretizedbythefinite elementmethod. [less ▲]