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Nonlinear Dynamics

Nonlinear oscillations of mechanical and mechatronic systems exhibit several new phenomena compared to linear oscillations. Examples are the existence of multiple solutions with dependence on initial conditions, amplitude dependent frequencies of free vibrations, multi-frequent solutions in case of mono-frequent excitation or chaos. Typical academic nonlinear oscillators are the Duffing-oscillator or the van der Pol oscillator. Applications investigated at the chair of Mechatronics and Machine Dynamics are e.g. limit cycle oscillations in brakes or multi-stable energy harvesting systems.

Methods applied in these investigations are e.g. Harmonic Balance, Perturbation Analysis, Numerical Integration or system reduction methods.

Some publications:

Gräbner, H.; Tiedemann, M.; von Wagner, U.; Hoffmann, N.: Nonlinearities in Friction Brake NVH - Experimental and Numerical Studies. SAE paper 2014-01-2511, 2014.

von Wagner, U.; Lentz, L.: On some aspects of the dynamic behavior of the softening Duffing oscillator under harmonic excitation. Archive of Applied Mechanics 86 (8), 1383 – 1390, 2016.

Zhao, X.; Gräbner, N.; von Wagner, U.: Theoretical and experimental investigations of the bifurcation behavior of creep groan of automotive disk brakes. Accepted for publication in Journal of Theoretical and Applied Mechanics in 2018. 


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