Extraction of Flutter Derivatives
Based on the Force Controlled
Forced Vibration Test
Seung Heon Cha
This study presents a new excitation technique for the identification of flutter derivatives. When motion of a bridge perturbs the flow field, perturbed flow field induces a dynamic forces on a bridge. And the dynamic forces changes the motion of a bridge which perturbs the flow field again. This recursive nonlinear-interaction between movement of the section model and the flow field can be fully considered when prescribed excitation force is applied to the bridge section model without restraining the motion. Force controlled forced vibration test is conducted to check the effect of nonlinear interaction by comparing its flutter derivatives to those of displacement controlled forced vibration test. Sinusoidal force is enforced with four fan-shaped mass rotating on each corner of the model which is freely suspended on elastic springs. An Equation Error Estimation method (EEE) is employed to evaluate flutter derivatives, which is the minimization problem of the equation error of the equation of motion. However, when L2-Norm EEE is adopted, squared error lasts through minimization and leads to biased result. To examine the adequacy of L2-Norm EEE to this problem, L1-Norm EEE is composed utilizing a simplex algorithm. Since the amount of bias is not noticeable, L2-Norm EEE is used throughout this paper for its fast computing speed.
The validity of the force controlled forced vibration test is demonstrated for two examples, one is B/D=5 rectangular section and the other is Jido bridge section model. It can be said that the effect of nonlinear interaction can be ignored for bridge section for its small amount of influence on the flutter derivatives and time-domain aeroelastic analysis result.
Flutter derivative; Equation error estimation; FDM-FIR filter; Forced vibration test; Aeroelastic analysis; Simplex algorithm