Superposability of unsteady aerodynamic loads on bridge deck sections

Abstract

The 2-dimensional unsteady aerodynamic forces, in the context of both a thin airfoil where theory of potential flow is always applicable and a bluff bridge-deck section where separated flow is typically induced, are investigated from a point of view of whether or not they conform to the principle of linear superposition in situations of various structural motions and wind gusts. It is shown that some basic preconditions that lead to the linear superposability of the unsteady aerodynamic forces in cases of thin airfoil sections are no longer valid for a bluff section. Theoretical models of bridge aerodynamics such as the one related to flutter-buffeting analysis and those concerning aerodynamic admittance (AA) functions, however, necessitate implicitly this superposability. The contradiction revealed in this work may throw light on the perplexing problem of AA functions pertaining to the description of buffeting loads of bridge decks. Some existing theoretical AA models derived from flutter derivatives according to interrelations valid only for thin airfoil theories, which have been employed rather extensively in bridge aerodynamics, are demonstrated to be illogical. Finally, with full understanding of the preconditions of the applicability of linear superposability of the unsteady aerodynamic forces, suggestions in regard to experiment-based AA functions are presented.