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A continuous approach to the aeroelastic stability of suspended cables in 1 : 2 internal resonance. (English) Zbl 1229.74067
Summary: This paper proposes a continuous perturbation treatment of the nonlinear equations of a cable, which is characterized by possible aeroelastic instability and internal resonance conditions. The objective is to evaluate the influence of stable modes (called passive) usually ignored when discretizing the model. The first step concerns the description of the structural equilibrium path under the action of the mean wind forces. Then, a multiple scale perturbation analysis of the integro-differential equations of motion is performed. Analyzing the stability of the reduced system, the existence of some limit cycles and of successive bifurcations is investigated. The comparison with previous papers, developed in the discrete field, allows clarification of the actual influence of the static equilibrium path and the contribution of passive modes.

MSC:
74H55 Stability of dynamical problems in solid mechanics
74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics
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