Jerschl M, Süß D, Willner K, Jerschl M (2014)

**Publication Type:** Conference contribution

**Publication year:** 2014

**Publisher:** Springer New York LLC

**Book Volume:** 4

**Pages Range:** 19-26

**Conference Proceedings Title:** Dynamics of Civil Structures

**Event location:** Orlando, USA

**ISBN:** 9783319007762

**DOI:** 10.1007/978-3-319-04546-7_3

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 Vakakis (Normal modes and localization in nonlinear systems, Wiley, New York, 1996). 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 (Peeters et al., Mech Syst Signal Process 23:195–216, 2009). In non-linear systems internal resonances and other phenomena can occur. Several tongues can bifurcate from a NNM branch. Therefore ordinary continuation methods fail at such bifurcation points. Here a predictor-corrector-method is used and different corrector algorithms are discussed for the branch continuation.

Martin Jerschl
Professur für Strukturmechanik
Dominik Süß
Lehrstuhl für Technische Mechanik (LTM)
Kai Willner
Professur für Strukturmechanik

**APA:**

Jerschl, M., Süß, D., Willner, K., & Jerschl, M. (2014). Numerical Continuation Methods for the Concept of Non-linear Normal Modes. In *Dynamics of Civil Structures* (pp. 19-26). Orlando, USA: Springer New York LLC.

**MLA:**

Jerschl, Martin, et al. "Numerical Continuation Methods for the Concept of Non-linear Normal Modes." *Proceedings of the 32nd IMAC Conference and Exposition on Structural Dynamics, 2014, Orlando, USA* Springer New York LLC, 2014. 19-26.

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