Dynamic instability of inclined cables under combined wind flow and support motion |
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Authors: | Angelo Luongo Daniele Zulli |
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Institution: | 1.DISAT,University of L’Aquila,L’Aquila (AQ),Italy |
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Abstract: | In this paper an inclined nearly taut stay, belonging to a cable-stayed bridge, is considered. It is subject to a prescribed
motion at one end, caused by traveling vehicles, and embedded in a wind flow blowing simultaneously with rain. The cable is
modeled as a non-planar, nonlinear, one-dimensional continuum, possessing torsional and flexural stiffness. The lower end
of the cable is assumed to undergo a vertical sinusoidal motion of given amplitude and frequency. The wind flow is assumed
uniform in space and constant in time, acting on the cable along which flows a rain rivulet. The imposed motion is responsible
for both external and parametric excitations, while the wind flow produces aeroelastic instability. The relevant equations
of motion are discretized via the Galerkin method, by taking one in-plane and one out-of-plane symmetric modes as trial functions.
The two resulting second-order, non-homogeneous, time-periodic, ordinary differential equations are coupled and contain quadratic
and cubic nonlinearities, both in the displacements and velocities. They are tackled by the Multiple Scale perturbation method,
which leads to first-order amplitude-phase modulation equations, governing the slow dynamics of the cable. The wind speed,
the amplitude of the support motion and the internal and external frequency detunings are set as control parameters. Numerical
path-following techniques provide bifurcation diagrams as functions of the control parameters, able to highlight the interactions
between in-plane and out-of-plane motions, as well as the effects of the simultaneous presence of the three sources of excitation. |
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