Flexural-Torsional Galloping of Prismatic Structures with Double-Symmetric Cross-Section

Abstract

The linear galloping of prismatic structures having double-symmetric cross-section, subjected to steady wind flow acting along a symmetry axis, is investigated. The continuous system is reduced to a three degree-of-freedom system via a Galerkin approach. The quasi-steady assumption for the aerodynamic forces is applied, under the hypothesis that the galloping instability is well-separated from the vortex induced vibration phenomenon. Due to the structural symmetry conditions and accounting for the aerodynamic coupling, galloping is of flexural-torsional type, occurring in the direction orthogonal to the incident wind. Moreover, coupling is stronger close to the resonance between the flexural and torsional degrees of freedom. A linear stability diagram is built up in a two-parameter space, highlighting the role of coupling in modifying the critical wind velocity, and in producing a veering phenomenon between the two modes. The existence of points at which a double-Hopf bifurcation manifests itself is detected. Both exact and perturbation solutions are provided, these latter in the non-resonant and resonant cases, useful to throw light on the interactive mechanisms. The resonant perturbation solution permits to analytically investigate under which conditions coupling has a detrimental effect on galloping, which manifests at a wind velocity lower than the flexural and torsional critical velocities. Situations where coupling between modes leads to beneficial effect with respect to the Den Hartog's critical wind velocity are also highlighted. As an application, galloping of a family of multi-story tower buildings having a square cross-section is studied.