Direct Identification of Coefficients of Rational Function Approximation for Self-Excited Aerodynamic Forces

The identification of coefficients of a rational function is the precondition for flutter analysis of long-span bridges based on rational function approximation. The number of lag terms of rational functions has a large influence on the identification accuracy. The coefficient identification of rational function approximation in existing methods are generally based on one lag term, which easily causes distortion problems in both aerodynamic description and coefficients and thus further affects the accuracy of flutter predictions. This paper proposes a direct identification algorithm of rational function coefficients by considering multiple lag terms, according to the principle that the self-excited aerodynamic force of sinusoidal signals is equal to the rational function in time domain and using the least square fitting method.. Then, the forced vibration test of a thin flat plate with harmonic vibration is carried out to characterize the self-excited forces, and the proposed algorithm is used to identify the coefficients of the rational function with different number of lag terms. Influences of the number of lag terms on the accuracy of self-excited aerodynamic force reconstruction and critical flutter wind speed calculation are analyzed. The accuracy of the algorithm is validated by comparing the critical wind speeds obtained from free vibration wind tunnel tests with those from flutter analysis using the identified coefficients. Results show that the calculated values of critical flutter wind speeds are in good agreement with the tested values, which verifies the effectiveness and accuracy of the proposed algorithm. Compared with the existing identification methods of rational function coefficients, the proposed identification method takes both efficiency and accuracy into account, and can be widely used in coefficient identification of rational function approximation for self-excited forces of bridge girders.