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Steady states and nonlinear buckling of cable-suspended beam systems

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Abstract

This paper deals with the equilibria of an elastically-coupled cable-suspended beam system, where the beam is assumed to be extensible and subject to a compressive axial load. When no vertical load is applied, necessary and sufficient conditions in order to have nontrivial solutions are established, and their explicit closed-form expressions are found. In particular, the stationary solutions are shown to exhibit at most two non-vanishing Fourier modes and the critical values of the axial-load parameter which produce their pitchfork bifurcation (buckling) are established. Depending on two dimensionless parameters, the complete set of resonant modes is devised. As expected, breakdown of the pitchfork bifurcations under perturbation is observed when a distributed transversal load is applied to the beam. In this case, both unimodal and bimodal stationary solutions are studied in detail. Finally, the more complex behavior occurring when trimodal solutions are involved is briefly sketched.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli studi di Salerno, Fisciano, Italy

    Ivana Bochicchio

  2. DICATAM, Università degli studi di Brescia, Brescia, Italy

    Claudio Giorgi & Elena Vuk

Authors
  1. Ivana Bochicchio
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  2. Claudio Giorgi
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  3. Elena Vuk
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Correspondence to Ivana Bochicchio.

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Bochicchio, I., Giorgi, C. & Vuk, E. Steady states and nonlinear buckling of cable-suspended beam systems. Meccanica 53, 3365–3381 (2018). https://doi.org/10.1007/s11012-018-0880-9

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  • DOI: https://doi.org/10.1007/s11012-018-0880-9

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