Evaluation of non-linear normal modes for finite-element models

In this paper, an alternative technique for the evaluation of non-linear normal modes is presented and applied to finite-element models. It is based upon the method of multiple scales, so that non-linear normal modes are evaluated as asymptotic expansions starting with the linear damped vibration modes. Non-linear normal modes are characterized both by the time response of all generalised coordinates and by explicit non-linear relationships between them and the modal variables. For the sake of an example, a non-conservative model of a cantilever beam, discretised with Bernoulli–Euler finite elements, is analysed.