Experimental investigation on post-flutter characteristics of a typical steel-truss suspension bridge deck

Highlights

• A novel testing device specially developed for large torsional amplitude vibration was adopted in wind tunnel test.

• Coupling vertical deformation was found strongly related to the torsional amplitude and wind attack angle.

• A stable LCO and an unstable LCO under a given wind speed were observed and analyzed in detail.

• The effects of mechanical nonlinearities and aerodynamic nonlinearities on post flutter were quantitatively studied.

• The effects of mechanical damping on the post-flutter performance were investigated.

Abstract

A testing device that was specially developed for large torsional amplitude vibrations was adopted to investigate the nonlinear post-flutter behaviors of a typical steel-truss girder bridge deck. Firstly, a series of free decay vibration tests of a narrow rigid rod model and a section model of the bridge were conducted in still-air to obtain mechanical properties and still-air induced aerodynamic properties. Then, post-flutter experiments of the bridge section model under initial attack angles of −3°, −0°, +3°, +5°, +7°and with different mechanical damping ratios were carried out. Finally, nonlinear and coupling behaviors of the bridge section model during post-flutter were described and analyzed in detail from several different aspects such as aeroelastic center, vibration mode, and wind-induced aerodynamic damping. The results showed that the truss girder section exhibited significant vertical-torsional coupled soft flutter behavior at various attack angles and there was a stable limit cycle oscillation (LCO) and an unstable LCO under a given wind speed near the critical speed. Moreover, the added aerodynamic damping, the coupling vertical deformation, the aerodynamic torsional center, the wind-induced aerodynamic damping, and the soft flutter mode in the post-critical state all exhibited the characteristic of amplitude dependence. Meanwhile, it was found that the coupling vertical deformation was strongly related to the torsional amplitude and wind attack angle. Finally, the effects of mechanical damping on the post-flutter performance were discussed and the results showed that some nonlinear dampers whose damping increased with the increasing amplitude can be adopted to improve the critical flutter speed without deteriorating or even enhancing the post-flutter performance.

Introduction

Aeroelastic flutter is the most dangerous vibration behavior for long-span flexible bridges. In the classical linear flutter theory established by Scanlan (1993), the structural vibration is assumed going unbounded beyond a critical wind velocity, which is known as a hard-type of flutter. As such, the occurrence of flutter instability is strictly prohibited in modern bridge designs. However, it is worth noting that increasing the critical flutter velocity by optimizing the shape of bridge decks and/or increasing the stiffness of structures may greatly increase the construction cost of the bridge. For instance, a 14 m-high stiffening steel truss along with a central stabilizer was adopted in the Akashi-Kaikyo Bridge to satisfy a flutter check velocity of 78 m/s. A streamlined box-girder with a 6 m-wide central slot was adopted in the Xihoumen Bridge to improve its critical flutter velocity (Ge and Xiang, 2008). Thus it can be seen that the cost of design and construction of super long-span bridges is increasing rapidly to satisfy the design requirements of flutter velocity.

In reality, the old Tacoma Narrows bridge had experienced about 70 min of torsional oscillation with amplitudes of approximately ±30°–35° before its final collapse (Larsen, 2000). This observation indicated that the real aeroelastic flutter response did not behave as predicted by the linear flutter theory. Moreover, evidences from experiment and numerical simulations in recent years suggest that some bridge decks may perform limit cycle oscillations (LCOs) due to aerodynamic and/or structural nonlinearities (Casalotti et al., 2014; Katsuchi et al., 2016; Ying et al., 2017; Pigolotti et al., 2017; Gao et al., 2018; Tang et al., 2019; Wu et al., 2020). Through a series of wind tunnel tests, Matsumoto et al. (1992) found that the torsional flutter behaviors of H-shaped sections with a width-to-depth ratio <3.4 exhibited LCOs. Kubo et al. (2001) tested the flutter performance of π sections and the non-divergent type of instability was discovered. Náprstek et al. (2007) tested several bluff bridge sections in the post-critical state and LCOs in the torsional mode were observed. Zhang et al. (2017) and Gao et al. (2018) tested the flutter performance of a box-girder and a twin-side-girder bridge deck, respectively; they both found that the bridge decks exhibited significant LCOs with very slight vertical-torsional coupling effects. Due to their bluff aerodynamic configurations, the post-flutter behaviors of the above-mentioned sections mainly exhibited torsional LCOs with a relatively slight coupling of the vertical DOF. However, the coupling of vertical-torsional DOFs was found significant for a streamlined section. Through testing a thin plate in wind tunnel, Amandolese et al. (2013) found that the thin plate exhibited significant vertical-torsional coupled LCOs at the post-critical regime. Ying et al. (2017) and Gao et al. (2020a) both found that closed-box sections exhibited a vertical-torsional soft flutter beyond the linear flutter boundary. At the same time, some scholars modeled nonlinear aerodynamic forces to predict nonlinear flutter response of bridges, such as using a nonlinear polynomial-type model (Gao et al., 2018; Zhang et al., 2017), an amplitude-dependent flutter derivatives model (Zhang et al., 2020), a generalized nonlinear aerodynamic force model based on the nonlinear differential equations (Zhou et al. 2018, 2019), and some integration-type of nonlinear models in pure time domain (Wu and Kareem, 2015). However, most of the existing nonlinear models have their own limitations and were developed based on specific bridge deck thus needing more wind tunnel tests to validate their feasibility.

The development of nonlinear flutter theory is still an open issue and most of the current research is focused on closed-box girder and π – type of girder sections. The experimental and numerical studies for nonlinear flutter are still very rare for common bridge decks, particularly a typical steel-truss bridge deck, which is a common deck shape for many long-span suspension bridges, such as Akashi Kaikyo Bridge, Golden Gate Bridge, Aizhai Bridge, etc. In fact, the flutter problem of steel-truss section is very prominent and its internal flutter mechanism has not been fully understood due to its complex bluff body shape (Fujino, 2002; Al-Assaf, 2006; Hu, 2021). For instance, two long-span steel-truss suspension bridges with a similar cross-section, Aizhai bridge (without central slot) and Baling River Bridge (with central slot), even adopted completely opposite aerodynamic control measures to prevent the flutter (Li et al., 2008). Meanwhile, long-span steel-truss suspension bridges have been widely used in mountain gorge areas in China where the wind field is often very complex with strong turbulence, such bridges with more complex three-dimensional flow around may exhibit more prominent nonlinear behavior under large attack angles of wind, which deserves more research. On the other hand, the swing problem of the helical springs caused by large torsional amplitude vibrations of conventional testing device makes it difficult to test the bridge deck to large vibrations. Besides, the swing problem of the helical springs makes it difficult to quantify the aerodynamic nonlinearity accurately. Thus it is difficult to establish a precise nonlinear aerodynamic model to predict the post-flutter response. A detailed discussion of the limitations of the current commonly used wind tunnel testing devices can be found in Xu et al. (2021). Therefore, there is a pressing need to adopt a testing device which can produce large torsional amplitude vibrations to investigate the post-flutter behavior of bridge decks.

In view of the above discussion, a testing device that can keep the helical springs from tilting and swinging was adopted to investigate the nonlinear post-flutter behaviors of a typical steel-truss girder bridge deck in the present work. Firstly, a series of free decay vibration tests of a narrow rigid rod model and a section model of the bridge were conducted in still-air to obtain mechanical properties and still-air induced aerodynamic properties. Then, post-flutter experiments of the bridge section model under initial attack angles of −3°, −0°, +3°, +5°, +7°and with different mechanical damping ratios were carried out. Subsequently, due special attentions were paid to the aerodynamic behaviors especially the coupling vertical deformation, the steady state amplitude, the evolution of aerodynamic torsional center, the wind-induced aerodynamic damping, and the soft flutter mode at the post-critical regime. Finally, the effects of mechanical damping on the post-flutter performance were discussed.