An improved mathematical model for the aerodynamic forces on tandem cylinders in motion with aeroelastic applications

Abstract

The quasi-steady theory of wake-induced flutter has been vindicated in the literature for the case where the wake-generating body is rigidly fixed. While several studies have attempted to extend the simple theory to the more general case where both windward and leeward bodies are in motion, none has really succeeded in producing a viable mathematical wake model which takes account of the effects of time delays associated with the gap between the bodies. The present paper, it is believed, provides such a model and deals with effects not previously conceived in this area, notably “bunching” of the wake due to accelerated motions of the windward body and “virtual displacement” of the leeward body due to flow retardation in its stagnation region. The new theory introduces, for the first time, an aerodynamic inertia matrix into the study of wake-induced flutter while the aerodynamic damping and stiffness matrices are shown to contain important new terms. The improved aerodynamic force model is applied in what is thought to be an important extension of a recently published transfer matrix procedure for the calculation of flutter boundaries for multi-conductor overhead transmission line spans. Eigenvalues, rather than flutter boundaries, are calculated for any windspeed—thus providing an immediate stability assessment. A significant numerical bottleneck in the previously published method is also removed.