Timedomain Aeroelastic Analysis of Bridge using a Truncated Fourier Series of the Aerodynamic Transfer Function Jin Wook Park
ABSTRACT This study presents the exact relation between the real and imaginary parts of aerodynamic transfer functions for deriving impulse response functions that satisfy the causality condition. A truncated Fourier series is utilized to express the aerodynamic transfer functions, and the causality condition is defined in terms of the coefficients of a Fourier cosine and sine series, which represent the real and imaginary parts of the aerodynamic transfer functions, respectively. The impulse response functions that satisfy the causality condition are obtained through the inverse Fourier transform of the aerodynamic transfer functions that conform to the exact relation. The coefficients of the Fourier series are determined by minimizing the error between the transfer functions formed by measured flutter derivatives and by the Fourier series. Since the impulse response functions become a series of Dirac delta functions in the truncated Fourier series approximation method, the aerodynamic forces are easily evaluated as the sum of current and past displacements with the same number of the terms in the Fourier series. This study proposes these the truncated Fourier series approximation method. The validity of the truncated Fourier series approximation method is demonstrated for two types of bluff sections and one real bridge: a rectangular section with a width to depth ratio of 5, an Htype section and 2nd Jindo cable stayed bridge. Timedomain aeroelastic analyses are performed for an elastically supported system with each section. The applicability of the truncated Fourier series approximation method is also verified for a largescale bridge, 2^{nd} Jindo cable stayed bridge. The truncated Fourier series approximation method yields stable and accurate solutions for the examples efficiently.
Key Word Impulse response function; Transfer function; Fourier Series; Causality condition; Convolution integral; Aeroelastic analysis; Flutter derivative
