Indicial Functions for Bridge Aeroelastic Forces and Time-Domain Flutter Analysis

This paper presents a detailed numerical algorithm for time-domain flutter analysis of elongated bridges, emphasizing in particular some problematic issues with regard to the application of the indicial functions involved wherein. Some typical characteristics of the indicial functions adopted early in airfoil aeronautics and those in bridge aerodynamics are first reviewed. The paper then presents the indicial-function-expressed aerodynamic forces and the recursive functions involved in the integral of the memorial terms in them. The theoretical description and numerical results indicate that the aeroelastic forces expressed with indicial functions are, if the model parameters are well identified, equivalent to those with flutter derivatives. However, this is merely an equivalence of frequency spectrum, and the transient characteristics of the indicial functions so identified, therefore, may not be physically true. This may result in excessively distorted aeroelastic forces and extraordinary time-consuming attenuation of the incorrect transient responses. To avoid such problems, a methodology of linear searching of the indicial-function parameters in predefined ranges is developed, on the basis of which the influence of some important factors, such as the time step size and numerical ranges of model parameters, are investigated. Numerical results show that large time step size may induce nonnegligible additional phase differences between the simulated aeroelastic forces and the structural motions and thus affect the total work accumulation and, consequently, the flutter threshold. Therefore, care should be taken in selecting an appropriate time integral step size.