Studies of a geometrical nonlinear friction damped system using NNMs - Jerschl, Martin; Süß, Dominik; Willner, Kai; Jerschl, Martin (34th IMAC, A Conference and Exposition on Structural Dynamics, 2016, 2016)
In the 1960s Rosenberg extended the definition of linear normal modes (LNM) for conservative systems to nonlinear systems: On a Nonlinear Normal Mode (NNM) every degree-of-freedom (DOF) vibrates in unison. Later Shaw and Pierre provided a definition for nonconservative systems and defined NNMs as invariant manifolds in phase space. If the system vibrates on such a manifold all other modes shall remain quiescent for all time. Nowadays there are many publications using the concept of NNMs to investigate systems with polynomial nonlinearities. But until now the upper mentioned definition is mostly used to investigate viscously damped systems. In this paper an oscillator containing a geometrically nonlinear (cubic) spring and a dry friction damper is considered. The system is driven into resonance and decay processes are evaluated. Wavelet analysis is used to identify which frequencies and harmonics remain during the decay process.
Keywords: Friction; Nonlinear coupling; Nonlinear dynamics; Nonlinear normal modes (NNMs); Optimal system design