Elimination of Frequency Dependence
of Aerodynamic Forces in the Time Domain
for the Aeroelastic Analysis of Bridge Decks
Kil Je Jung
This study proposes the methods for time-domain aeroelastic analysis of bridge decks by eliminating the frequency dependence of aerodynamic forces. Due to the frequency dependence of the aerodynamic forces, the aeroelstic analysis becomes nonlinear problem, and moreover, for the time-domain aeroelastic analysis, the modal information of the aeroelastic system should be defined. To overcome this complexity, this study proposes the elimination methods of aerodynamic forces in time domain, which are penalty method and MWLS method.
The penalty method is an evaluation method of impulse response functions for the convolution integrals of aerodynamic forces. 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 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 via two numerical examples. Time-domain aeroelastic analyses are performed with the proposed method for a thin rectangular section and a bluff H-type section.
The MWLS method, which is an efficient and unified approach for the aeroelastic analysis in the time and frequency domains, is also proposed. The aeroelastic transfer function is approximated by the second order polynomial matrix with respect to frequency, and the unknown coefficient matrices are determined by the minimization of the norm of the weighted errors. The transfer function of an aeroelastic system in the reduced solution space is chosen as a weighting function. Through the inverse Fourier transformation, the approximated transfer function of an aeroelastic system results in a simple second order differential equation in the time domain. The validity of the MWLS method is examined for a cable-supported structure with two extreme types of deck section in the viewpoint of aerodynamics.
aeroelastic analysis, frequency dependence, aerodynamic force, causality condition, branch method, RFA, penalty method, MWLS method