Keywords: cable-stayed bridge, buffeting, time-domain analysis, wind field simulation, self-excited force, multi-mode coupled buffeting.

Since exactly measuring aerodynamic admittance of a deck is difficult, there usually are some errors between analytical results and test results. The frequency-domain analysis method is widely adopted in buffeting analysis of long span bridges. Comparison between frequency-domain analysis and time-domain analysis is the main way to indicate the feasibility and reliability of time-domain analysis for buffeting of long span bridges.

A railway three-pylon cable-stayed bridge across the Yangze River in China (in the preliminary design) is selected as an example in this paper. Using the same parameters, buffeting response of the cable-stayed bridge is analyzed respectively by the time-domain method and the frequency-domain method. The vibration shape, RMS (Root-Mean-Square), PSD (Power Spectrum Density) of the buffeting response by two methods are compared in order to check the reliability of time domain analysis method for bridge buffeting. In a frequency-domain buffeting analysis, the multi-mode coupled buffeting analysis method [1] was adopted, in which the first 18 modes of the bridges were taken into account. A time-domain analysis method for the buffeting of the bridge is presented in this paper.

The simulation of wind velocity fields is the precondition of the time-domain analysis. Natural wind is spatially and temporally correlated. It is usually assumed as a multidimensional multivariate stationary Gaussian stochastic process for engineering applications. For engineering applications, these correlations are generally omitted. The spatial and temporal correlations of each component are considered. Thus, a three-dimensional correlated multivariate stochastic process is translated into three one-dimensional multivariate stochastic processes which are independent to each other. The spectral representation method can be utilized to simulate the stochastic processes. The application of FFT (Fast Fourier Transform) technique can improve the computational efficiency. When the deck of a long cable-stayed bridge is almost at the same height and the terrain features around the bridge site generally vary just slightly, it can be assumed that the mean velocity and wind spectrum are homogeneous along the bridge deck. Using explicitly expressing Cholesky's decomposition of the cross-spectral density matrix in such a case, the wind velocity fields along the deck can be simulated relatively fast.

In time-domain buffeting analysis, the buffeting force adopted is in quasi-steady form, and self-excited force adopted is in the form presented by Y.K. Lin [2]. An iterative process is presented for the determination of self-excited force. A model of the bridge can be established by the FEM. The motion equations of overall bridge are solved by the Newmark- method.

Using the same parameters, the buffeting of the bridge is analyzed in both the frequency domain and the time domain by a self-developed bridge analysis software BANSYS (Bridge ANalysis SYStem). Vibration shapes, RMS and PSD of analysis results by frequency-domain and time-domain methods are compared with each other. Furthermore, some conclusions can be obtained as follows.

1. The time-domain analysis is feasible and reliable for buffeting response of long span bridges. The results by time-domain method agree well with those by frequency-domain method.
2. Variances exist in the time-domain analysis to some extent for the buffeting of long span bridges.
3. The time-domain method can represent the contribution of higher order modes on buffeting responses.
4. The first modes in the vertical, lateral and tosional direction play an important role in buffeting response of long span bridge.

1

Jain A., Jones N.P., Scanlan R.H., "Coupled flutter and buffeting analysis of long-span bridges", J. of Structural Engineering, 122, 716-725, 1996. doi:10.1061/(ASCE)0733-9445(1996)122:7(716)

2

Bucher C.G., Lin Y.K., "Stochastic stability of bridges considering coupled modes", J. Eng. Mech., 12, 2055-2071, 1987. doi:10.1061/(ASCE)0733-9399(1988)114:12(2055)

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