Jerschl M, Willner K (2014)
Publication Language: English
Publication Type: Journal article
Publication year: 2014
Publisher: Gesellschaft für Angewandte Mathematik und Mechanik (GAMM)
Book Volume: 14
Pages Range: 287--288
Journal Issue: 1
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.
APA:
Jerschl, M., & Willner, K. (2014). Arclength Continuation Methods for the Investigation of Non-linear Oscillating Systems with the Concept of Non-linear Normal Modes. Proceedings in Applied Mathematics and Mechanics, 14(1), 287--288. https://dx.doi.org/10.1002/pamm.201410131
MLA:
Jerschl, Martin, and Kai Willner. "Arclength Continuation Methods for the Investigation of Non-linear Oscillating Systems with the Concept of Non-linear Normal Modes." Proceedings in Applied Mathematics and Mechanics 14.1 (2014): 287--288.
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