Experimental Investigation on Relations between Flutter Derivatives and Aerodynamic Admittances

Abstract

Two kinds of relations between flutter derivatives and aerodynamic admittance functions (AAFs), which have been used in bridge aerodynamics, are discussed in this study by means of theoretical analysis and experiments. The first kind, called substitutive Kϋssner function method in this study, assumes equivalence between the Wagner function and the Kϋssner function. In doing so, the AAFs can be calculated based on flutter derivatives. The other one involves a concept of equivalent Theodorsen function, and the relation is built up by utilizing the classic relation between the Sears function and the Theodorsen function. Both methods are reasoned to be logically problematic in this study. Furthermore, these relations were examined with wind tunnel experiments. Flutter derivatives and AAFs of a flat plate and a rectangular cylinder with an aspect ratio of 4 were tested. The measured AAFs were compared with those calculated from flutter derivatives. The results show that, as frequency increases, the gap between the measured AAFs and those by the substitutive Kϋssner function method increases drastically. In comparison, the AAFs based on equivalent Theodorsen functions are closer to measured results in the low-frequency range; however, as frequency increases, they deviate from the measured AAFs in the form of violent oscillation, streamlined and bluff sections alike. It is shown that this kind of fluctuation originates from the illogicality inherent in the method.