HU Chuan-xin, WANG Xiang-long, ZHAO Lin, GE Yao-jun
Vortex shedding and drifting are common characteristics of the flow field around bridge girders during the occurrence of vortex-induced vibrations. Based on the spatial and temporal pressure field of the main beam surface, the spatial distribution characteristics of the statistical parameters of the vortex-induced dynamics (e.g., correlation coefficient, contribution value, dimensionless work) are systematically analyzed. The basic theory of simplified vortex-induced dynamics is established, and simplified vortex-induced mechanisms of typical bridge main beams are proposed. This method can deduce the characteristics of key flow fields and the spatiotemporal evolution model of the dominant synchronous aerodynamic force to reveal the vortex mechanism. Using a typical box girder as an example, the simplified vortex method is verified by combining the time-frequency characteristics of aerodynamic force, numerical flow field, and spectral proper orthogonal decomposition (SPOD). The results show that the correlation coefficient, contribution value, and dimensionless work are similar harmonic functions of the phase lag between the pulsating pressure and vortex-induced force (moment) when vertical (torsional) vortex-induced vibration occurs. When the phase lag changes monotonically, the aforementioned statistical parameters show wave-like distribution, and the corresponding dominant aerodynamic force shows traveling wave, space-time evolution characteristics along the flow direction, collectively referred to as aerodynamic traveling wave mode. This mode and the corresponding simplified vortex mode map each other and form the simplified vortex mode together. In vertical vortex-induced vibration, the drift distance from the vortex leading edge separation to the trailing edge is approximately k wavelengths, which requires k vibration cycles; that is, the kth order vertical simplified vortex mode induced by the separation point dominates. The drift distance from the vortex leading edge separation to the trailing edge is approximately (k+0.5) wavelengths, and it requires (k+0.5) vibration cycles, where k is a positive integer; that is, the kth order torsional simplified vortex mode induced by the separation point is dominant. The aerodynamic dominant SPOD mode on the upper surface of a typical box girder presents a traveling wave evolution along the flow direction, the correlation coefficient presents a wave-like distribution, and the wave-vortex modes map each other, which verifies the simplified vortex method well. In this paper, the basic theory of simplified vortex is systematically established, and a simplified vortex method system with multiscale aerodynamic spatiotemporal evolution characteristics associated with vibration effects is described as “one body.” A simplified vortex model with key flow field characteristics is deduced, and an aerodynamic traveling wave “two wing” model is constructed to perform accurate simulations of the aerodynamic spatiotemporal evolution characteristics. It provides a new theoretical basis for the analysis of the physical mechanism of eddy vibration in bridge girders, the construction of a mathematical model of eddy-induced force, and the comparison and selection of eddy vibration suppression measures.