Lateral Parametric Vibration of Footbridge under Pedestrian Excitation considering the Time-Delay Effect

Pedestrian excitation may consequently cause large-scale lateral vibration of the long-span softness of footbridges. Considering the influence of structural geometric nonlinearity, a nonlinear lateral parametric vibration model is established based on the relationship between force and speed. Taking the London Millennium Footbridge as an example, the Galerkin method is applied to formulate parametric vibration equations. In addition, the multi-scale method is used to analyze the parametric vibration of footbridge system theoretically and numerically. The paper aims to find out the reasons for the large-scale vibration of the Millennium Footbridge by calculating the critical number of pedestrians, amplitude-frequency, and phase-frequency characteristics of the Millennium Footbridge during parametric vibration. On the other hand, the paper also studies the influence parameters of the vibration amplitude as well as simulates the dynamic response of the bridge during the whole process of pedestrians on the footbridge. Finally, the paper investigates influences of the time-delay effect on the system parameter vibration. Research shows that: the model established in the paper is reliable; the closer the walking frequency is to two times of the natural frequency, the fewer number of pedestrians are required to excite large vibrations; when the number of pedestrians exceeds the critical number in consideration of nonlinear vibration, the vibration amplitude tends to be stable constant-amplitude vibration, and the amplitude of vibration response is unstable constant-amplitude vibration when only linear vibration is considered; the following factors have an impact on the response amplitude, including the number of pedestrians on footbridge per unit time, damping, initial conditions, and the number of pedestrians in synchronized adjustment. At last, when considering the lag of the pedestrian’s force on the footbridge, the time-lag effect has no effect on the amplitude but has an effect on the time needed to reach a stable amplitude.

Remediation of Benzene and 1,2-Dichloroethylene in Groundwater by Funnel and Gate Permeable Reactive Barrier (FGPRB): A Case Study

Funnel and gate permeable reactive barrier (FGPRB) is an effective method to treat groundwater pollution. In order to clarify the impact of FGPRB on groundwater dynamic conditions, this study takes a site pilot test as the research object and establishes an FGPRB downstream of a petrochemical industry. The results show that the concentrations of 1,2-dichloroethylene and benzene in the downstream groundwater, after setting FGPRB, are lower than the detection limit. The numerical simulation results show that after setting FGPRB, both point source and area source pollution can achieve a good delay effect, extending from about 27 d to about 65 d of response time, but changing the thickness and permeability coefficient has no obvious effect on the delay effect. The tracer test shows the average permeability coefficient of the medium from the injection well to the monitoring well after the construction of FGPRB decreases from 77.0 m/d to 31.2 m/d after the construction of FGPRB. The average seepage velocity from the injection well to the monitoring well decreased from 0.19 m/d to 0.078 m/d after the construction of FGPRB. At the same time, when the FGPRB is not built, the maximum concentration time from the injection well to the monitoring well is about 10 d. After the FGPRB is constructed, the maximum concentration time of the tracer received by the monitoring well is about 27 days. These results confirm that the establishment of FGPRB will change the hydrodynamic conditions of groundwater and delay the response time of pollutants in the monitoring well.

Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

In this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Existence of Hopf bifurcation at co-axial equilibrium is investigated. The stability of bifurcating periodic solutions is discussed, and the time length for which the solutions preserve the stability is estimated. Furthermore, we have derived the conditions for the direction of bifurcating periodic solutions. Theoretically, it was observed that the system undergoes different states if we vary the system’s parameters. Some numerical simulations are presented to verify the obtained mathematical results.

Erosion Resistance Performance of Surface-Reinforced Levees Using Novel Biopolymers Investigated via Real-Scale Overtopping Experiments

This study evaluates a novel biopolymer-based material reinforcement method. A real-scale experiment minimizing flood disasters and economic losses incurred by the collapse of river levees due to overtopping was conducted. At the Andong River Experiment Center, lateral overflow was reproduced to induce levee collapse using sand, reinforced novel materials, and vegetation levees represented as cases 1, 2, and 3, respectively. The flow in the upstream and downstream areas was measured, and fluctuations in the lateral overflow discharge were calculated using an acoustic Doppler current profiler. To quantitatively verify the performance of this method, the collapse delay effect based on the surface loss rate of the levee slope was analyzed using image pixel analysis and three-dimensional point cloud modeling. Comparing the collapse delay effect of the new-material levee with that of the non-reinforced levees, we found a time delay of approximately 2.7–7 times from the occurrence of overtopping via the lateral flow to the end of the test. These results indicate that we can secure time for emergency repairs and operations by reinforcing the levee surface using the material proposed in this study. These research findings are expected to provide the basis for the proper design and construction of river levees.