Evaluation of Impulse Response Functions for Convolution Integrals of Aerodynamic Forces by Optimization with a Penalty Function

Abstract

This paper presents a new algorithm for evaluating impulse response functions for the convolution integrals of the aerodynamic forces of bridge decks. The impulse response functions formed by measured flutter derivatives are modified to satisfy causality conditions through optimization. The error function in the object function is defined as the least square errors between the measured and the modified transfer function, and the causality condition is imposed as a penalty function. The modified transfer functions are interpolated with the cubic spline. The selection of the optimal penalty number is presented for obtaining a balanced solution between the effects of the error function and the penalty function. The proposed method is verified using two numerical examples. Time-domain aeroelastic analyses are performed with the proposed method for a thin rectangular section and a bluff H-type section, and the results are compared to values obtained by the rational function approximation (RFA) and the analytical particular solution of the equation of motion. The proposed method yields accurate and stable solutions for both types of sections, whereas the rational function approximation results in erroneous solutions for a bluff H-type section.