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A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system

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Abstract

The classical Lindstedt–Poincaré method is adapted to analyze the nonlinear normal modes of a piecewise linear system. A simple two degrees-of-freedom, representing a beam with a breathing crack is considered. The fundamental branches of the two modes and their stability are drawn by varying the severity of the crack, i.e., the level of nonlinearity. Results furnished by the asymptotic method give insight into the mechanical behavior of the system and agree well with numerical results; the existence of superabundant modes is proven. The unstable regions and the bifurcated branches are followed by a numerical procedure based on the Poincarè map.

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Authors and Affiliations

  1. DISG, University of Rome “La Sapienza”, via Eudossiana, 18, 00184, Rome, Italy

    Fabrizio Vestroni & Achille Paolone

  2. DISAT, University of L’Aquila, Monteluco di Roio, 67040, L’Aquila, Italy

    Angelo Luongo

Authors
  1. Fabrizio Vestroni
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  2. Angelo Luongo
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  3. Achille Paolone
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Correspondence to Achille Paolone.

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Vestroni, F., Luongo, A. & Paolone, A. A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system. Nonlinear Dyn 54, 379–393 (2008). https://doi.org/10.1007/s11071-008-9337-3

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  • DOI: https://doi.org/10.1007/s11071-008-9337-3

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