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Classical quasi-steady galloping analysis deals exclusively with cases of across-wind vibrations, leaving aside the more general situation where the wind and motion may not be normal. This can arise in many circumstances, such as the motion of a power transmission cable about its equilibrium configuration, which is swayed from the vertical plane due to the mean wind, or for a tall slender structure in a skewed wind. Furthermore the generalisation to such situations, when this had been made, has only considered special issues. In this paper the correct equations for the quasi-steady aerodynamic damping coefficients for the rotated system or wind are derived, and differences from other variants are highlighted. Motion in two orthogonal structural planes is considered, potentially giving coupled translational galloping, for which previous analysis has often been limited or has even arrived at erroneous conclusions. For the two-degree-of-freedom case, the behaviour is dependent on the structural as well as aerodynamic parameters, in particular the orientation of the principal structural axes and the relative natural frequencies in the two planes. For the first time, differences in the aerodynamic damping and zones of galloping instability are quantified, between solutions from the correct perfectly tuned, well detuned and classical Den Hartog equations (and also an incorrect generalisation of it), for a variety of typical cross-sectional shapes. It is found that although the Den Hartog summation often gives a reasonable estimate for the actual aerodynamic damping even for the rotated situation, in some circumstances the differences can be quite large.
|Journal||Journal of Engineering Mechanics|
|Publication status||E-pub ahead of print - 1 Aug 2013|
- Galloping, Den Hartog, quasi-steady theory, aerodynamic damping, translational coupling