Characterization of bifurcating non-linear normal modes in piecewise linear mechanical systems |
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Authors: | Paolo Casini |
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Institution: | Dipartimento di Ingegneria Strutturale e Geotecnica (DISG), Università degli Studi di Roma “La Sapienza”, Via Eudossiana 18-00184 Roma, Italy |
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Abstract: | The non-linear modal properties of a vibrating 2-DOF system with non-smooth (piecewise linear) characteristics are investigated; this oscillator can suitably model beams with a breathing crack or systems colliding with an elastic obstacle. The system having two discontinuity boundaries is non-linearizable and exhibits the peculiar feature of a number of non-linear normal modes (NNMs) that are greater than the degrees of freedom. Since the non-linearities are concentrated at the origin, its non-linear frequencies are independent of the energy level and uniquely depend on the damage parameter. An analysis of the NNMs has been performed for a wide range of damage parameter by employing numerical procedures and Poincaré maps. The influence of damage on the non-linear frequencies has been investigated and bifurcations characterized by the onset of superabundant modes in internal resonance, with a significantly different shape than that of modes on fundamental branch, have been revealed. |
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Keywords: | Non-linear normal modes Piecewise linear systems Internal resonance Damaged systems |
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