A Study on understanding of Coupled Flutter of Long-span Bridges Hitoshi Yamada, Hiroshi Katsuchi and Pham Hoang Kien Yokohama National University, Yokohama 240-8501, Japan ABSTRACT: Flutter analysis has come to be used widely at the design stage of long-span bridges. This is attributed to the study and the understand of nature of unsteady aerodynamic forces, mechanism of mode-coupling and methodology of multi-mode flutter analysis. One of the great contributions will be the study on the Akashi Kaikyo Bridge. A large scale aeroelastic-model wind-tunnel test together with multi-mode coupled flutter was carried out and various new findings were brought out. In this paper, methodology of flutter analysis is first presented and then multi-mode coupling on flutter understood so far is reviewed based on the results of the wind-tunnel test of the Akashi Kaikyo Bridge. KEYWORDS: Flutter analysis, Mode coupling, Multi mode, Akashi Kaikyo Bridge 1 INTRODUCTION Flutter is one of the utmost concerns for wind-resistant design of a long-span bridge. Wind-tunnel test is typically employed for the purpose of investigation on wind-induced response and decision of the final cross section. For such a purpose, a 2D section model test reproducing the deck cross section is often employed. It has some advantages that a relatively large scaled model can be used, it does not need a large wind tunnel nor does it cost too much. However, in the case of a very long-span bridge such as the Akashi Kaikyo Bridge, 3D characteristics prevail so that a large size aeroelastic full model test is required. Since a full-model test required a large wind tunnel and cost much, an analytical prediction method of flutter, what is called “flutter analysis”, was developed [1 and 2]. Because flutter analysis applies sectional unsteady aerodynamic forces to a 3D FE model of a bridge, once sectional unsteady aerodynamic forces are measured, it very flexibly predicts 3D response of the bridge numerically. It is very advantageous that flutter analysis does not need a large scale full-model test but it yields much information quantitatively on flutter. When the Akashi Kaikyo Bridge was designed, a large scale aeroelastic model test and comparative flutter analysis was carried out. Owing to that, the wind-resistant safety of the Akashi Kaikyo Bridge was successfully secured. In addition, characteristics of coupled flutter of a long-span suspension bridge were quantitatively elucidated [3 -5]. This paper presents first methodology of flutter analysis and then characteristics of coupled flutter of a long-span bridge obtained from the large wind-tunnel test project of the Akashi Kaikyo Bridge. 2 METHODOLOGY OF FLUTTER ANALYSIS Since flutter is one of the vibration modes at the flutter onset wind speed, it can be obtained by eigenvalue analysis for the equation of motion to which unsteady aerodynamic forces are exerted. The unsteady aerodynamic force is expressed via non-dimensional flutter derivatives as in Eq. (1). Multiplying by 2π, these are converted to the well-known flutter derivative notation by Scanlan [2]. 141