Media type: E-Article Title: Arclength Continuation Methods for the Investigation of Non‐linear Oscillating Systems with the Concept of Non‐linear Normal Modes Contributor: Jerschl, Martin; Willner, Kai imprint: Wiley, 2014 Published in: PAMM Language: English DOI: 10.1002/pamm.201410131 ISSN: 1617-7061 Keywords: General Medicine Origination: Footnote: Description: <jats:title>Abstract</jats:title><jats:p>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 <jats:italic>frequency‐energy plot</jats:italic> (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. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)</jats:p> Access State: Open Access