{
  "id": "1610.02252",
  "version": "v1",
  "published": "2016-10-07T12:36:47.000Z",
  "updated": "2016-10-07T12:36:47.000Z",
  "title": "Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations",
  "authors": [
    "Robert Szalai",
    "David Ehrhardt",
    "George Haller"
  ],
  "comment": "32 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-07T12:36:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-degree-of-freedom mechanical vibrations",
      "spectral submanifolds",
      "approach reproduces backbone curves",
      "smoothest invariant manifolds tangent",
      "experimental nonlinear model identification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}