Nonlinear model identification and spectral submanifolds for   multi-degree-of-freedom mechanical vibrations
  In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy. 
Robert Szalai and David Ehrhardt and George Haller
math.DS nlin.CD