Aeroelastic stability of a 3DOF system based on quasi-steady theory with reference to inertial coupling

This paper investigates the galloping stability of a two-dimensional three-degree-of-freedom (3DOF) system with an eccentric shape, such as an iced cable or power transmission line, incorporating inertial coupling along with the aerodynamic damping. The inertial coupling is a result of the offset of the centre of mass with respect to the elastic centre. A theoretical model is firstly constructed for the derivation of the aerodynamic damping matrix, based on quasi-steady theory, as well as the inertial coupling components in the mass matrix. The model is then employed to investigate the effects on the aeroelastic stability of the system of incorporating the inertial coupling and the results are compared with both dynamic test results and predictions from previous models. The comparisons indicate that even small eccentricity can lead to significant change of the stability of the system, for both detuned and perfectly tuned natural frequencies of the different degrees of freedom. For a system with perfectly tuned natural frequencies, and neglecting structural damping, analytical solutions of the eigenfrequencies and eigenvectors allowing for the inertial coupling, are derived for the case of no wind. Subsequently, an approximate solution is found for the prediction of the galloping stability of a system coupled by the aerodynamic damping as well as the inertial coupling. Finally, the approximate solution is verified against numerical results using examples with two cross-section shapes, showing excellent agreement.