Benefitting from economic development and technological progress, long-span suspension bridges, with their superior span capacity and good economy, have been built in large numbers in recent decades. However, the excessive cumulative longitudinal displacement at the girder ends in the process of bridge operation leads to the degradation of, and fatigue damage to, the connecting components. This study aims to solve the problem with an effective parallel damping scheme of friction dampers and viscous dampers. Firstly, the phenomenon that quasi-static longitudinal displacement accounts for the majority of cumulative displacement is confirmed by the decomposition of measured displacement data at the girder end, which is caused by the asymmetric geometric deformation of the main cable induced by the moving vertical loads of a long-span suspension bridge. An efficient control performance analysis method is proposed based on the formation mechanism of the quasi-static longitudinal displacement. Secondly, the friction damper with a continuous damping model is employed to achieve an effective control performance with respect to the quasi-static longitudinal displacement. Thirdly, in order to realize the target of operational and seismic dual control, a parallel scheme of friction dampers and viscous dampers is proposed, aiming to reduce the cumulative value in the operational state, and maximum value in the seismic state, for longitudinal displacement at the girder ends of a long-span suspension bridge.

Live load of moving vehicles has a very important effect on the fatigue life of suspension bridges, which causes not only vertical deformation but also longitudinal deformation. In this study, a general analytical formulation for analyzing the quasistatic longitudinal displacement of suspension bridges under vertical live loads is developed, and the underlying deformation mechanism is revealed. First, the analytical vertical and longitudinal deformation equations for the single main cable subjected to live loads are formulated considering the geometric nonlinearity. Then, the relation of longitudinal displacements between the stiffening girder and the main cable for a single-span suspension bridge is established through analyzing the geometric configuration of deformed deck-suspender segment and imposing the null longitudinal force condition. The relation is further modified to incorporate the effect of central buckles (CBs). Compared with the finite-element (FE) prediction, the proposed analytical solution is quite accurate for both concentrated and distributed loads. It is found that the coupling of vertical and longitudinal displacement of main cables and the longitudinal constraint between the cables and girder, are responsible for the longitudinal displacement of the girder. The effects of sag-to-span ratio, CB, and inclined suspenders are studied. The longitudinal displacement of the girder can be reduced by about 20% when the sag-to-span ratio is varied from 1/9 to 1/11, and the CB with proper stiffness is more effective in reducing the longitudinal displacements. The proposed formulation can be conveniently applied for parameter optimization in the preliminary design stage so as to avoid tedious repetitive FE analysis.

The nonlinear model and energy dissipation of a rotary axial eddy current damper (ECD) and the dynamic responses to harmonic and seismic base excitations of a linear elastic SDOF system with the nonlinear ECD (SDOF-ECD) are investigated. Firstly, the nonlinear force-velocity relationship of the ECD is studied using finite element simulation, experimental testing and mathematical model fitting. Secondly, the energy dissipated by the nonlinear ECD under a cycle of harmonic motion is derived analytically and its optimal critical velocity is determined such that the energy dissipation is maximized. Finally, the responses of the SDOF-ECDs subjected to harmonic and seismic base excitations are calculated using numerical algorithm, where the displacement and acceleration control performance and the energy dissipation capacity of the ECD are compared with those of the conventional fluid viscous dampers (FVDs). The results indicate that the seismic control performance of ECDs outperforms that of FVDs in most cases and it is anticipated that the ECDs can be used as good alternative devices to conventional FVDs for seismic control applications.

An enhanced approach of empirical mode decomposition based random decrement technique (EMD-RDT) is proposed for output-only modal parameter identification of structures using ambient vibration measurements. In the conventional EMD-RDT method, modal parameters are identified for each mode through Hilbert transform or least-square fitting from the free-decay modal responses, which are produced by EMD and RDT sequentially. The identification process is time consuming, and many uncertainties are involved. The novel enhancements of the proposed method lie in two aspects: computation efficiency and uncertainty treatment. On one hand, a novel decomposition method is proposed to separate the mode shape and the modal coordinates from the free-decay modal responses, thus making the identification process more efficient. On the other hand, a bootstrap approach is employed to quantify the uncertainties of modal parameters by providing surrogate estimates to generate useful statistics. Examples using both simulated data from a six degrees-of-freedom (six-DOF) system and experimental data from a three-story shear building structure are presented to demonstrate the proposed method, of which the effectiveness and the efficiency are confirmed by the identified results.

A novel probabilistic approach for model updating based on approximate Bayesian computation with subset simulation (ABC-SubSim) is proposed for damage assessment of structures using modal data. The ABC-SubSim is a likelihood-free Bayesian approach in which the explicit expression of likelihood function is avoided and the posterior samples of model parameters are obtained using the technique of subset simulation. The novel contributions of this paper are on three fronts: one is the introduction of some new stopping criteria to find an appropriate tolerance level for the metric used in the ABC-SubSim; the second one is the employment of a hybrid optimization scheme to find finer optimal values for the model parameters; and the last one is the adoption of an iterative approach to determine the optimal weighting factors related to the residuals of modal frequency and mode shape in the metric. The effectiveness of this approach is demonstrated using three illustrative examples.