A novel multi-modal analytical method focusing on dynamic mechanism of bridge flutter

Abstract

A novel three-dimensional (3D) multi-modal analytical method is proposed in the present study for investigating the dynamic mechanism of long-span bridge flutter. The multi-modal coupled flutter differential equations are derived in a practical manner utilizing the principle of virtual work in this method, and the explicit expressions of system damping and stiffness are established through the excitation-feedback mechanism. Consequently, this method can not only conveniently identify the critical point of 3D bridge flutter, but also provide a comprehensive understanding of the underlying mechanism involved in 3D bridge flutter. The well-known coupled aerodynamic damping related to flutter derivatives A1∗ and H3∗, which is principally responsible for the coupled flutter, is further subdivided in this study to reveal the intrinsic coupled mechanism of flutter participating modes: The aerodynamic coupled degree between a certain vertical bending mode and the fundamental torsional mode can be ascertained by evaluating the similarity factor between their mode shapes; the phase angle between a certain vertical bending mode and the fundamental torsional mode, which is largely dominated by the numerical relationship between natural and flutter frequency, determines whether the aerodynamic coupled effect associated with the two modes drives or restrains flutter.