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@article{faucris.112550284,
abstract = {Non-linear normal modes (NNMs) can be considered as a non-linear analogon to the description of linear systems with linear normal modes (LNMs). The definition of NNMs can be found in [1]. Small systems with a low number of degrees of freedom and non-linear couplings (cubic springs) are investigated here. With increasing energy in the system the progressive non-linearity leads to a hardening effect. One typical dynamical property of non-linear systems is the frequency-energy dependency of the resulting oscillations. A good graphic illustration is to plot such a dependency in a so called *frequency-energy plot* (FEP). A NNM branch can be calculated by a numerical continuation method with starting at low energy level in a quasi linear regime and increasing the energy and reducing the period of the oscillation iteratively. Thereby a branch is a family of NNM oscillations with qualitatively equal motion properties [2]. In non-linear systems internal resonances and other phenomena can occur. Several tongues can bifurcate from a NNM branch. Therefore ordinary continuation methods may fail at such bifurcation points. Here a predictor-corrector-method is used and different corrector algorithms are discussed for the branch continuation.},
author = {Jerschl, Martin and Willner, Kai},
doi = {10.1002/pamm.201410131},
faupublication = {yes},
journal = {Proceedings in Applied Mathematics and Mechanics},
pages = {287--288},
peerreviewed = {Yes},
title = {{Arclength} {Continuation} {Methods} for the {Investigation} of {Non}-linear {Oscillating} {Systems} with the {Concept} of {Non}-linear {Normal} {Modes}},
volume = {14},
year = {2014}
}