Revisiting Convolution Scheme in Bridge Aerodynamics: Comparison of Step and Impulse Response Functions

Two elementary response features of bridge aerodynamics, namely unit-step (indicial) and unit-impulse response functions, as the fundamental building blocks for the convolution integral, are reviewed systematically. The comparison of these elementary response functions was carried out from theoretical, experimental, and numerical perspectives. Theoretically, their new interpretation is given in the context of bridge aerodynamics. Experimentally, the underlying mechanism concerning these elementary response functions as applied to bridge aerodynamics was investigated, e.g., the overshooting feature and the applications to the simulation of gust- and motion-induced forces. Numerically, a comparison of the indicial and rational function approximations, often utilized in the indirect identification of the effective unit-step and unit-impulse response functions, respectively, is highlighted by underscoring the underlying physics in the associated mathematical derivation. A numerical example of a long-span bridge is presented to demonstrate the fidelity of simulation based on these numerical approximations.