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.

Entanglement dynamics for Unruh-DeWitt detectors interacting with massive scalar fields: the Unruh and anti-Unruh effects

We study, in the framework of open quantum systems, the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-Dewitt detectors interacting with a bath of massive scalar fields in the Minkowski vacuum. We find that the entanglement evolution for the quantum system coupled with massive fields is always slower compared with that of the one coupled with massless fields, and this time-delay effect brought about by the field being massive can however be counteracted by a large enough acceleration, in contrast to the case of a static quantum system in a thermal bath, where this time delay is not affected by the temperature. Remarkably, the maximal concurrence of the quantum system generated during evolution may increase with acceleration for any inter-detector separation while that for static ones in a thermal bath decreases monotonically with temperature, and this can be considered as an anti-Unruh effect in terms of the entanglement generated.

Stability and Time-Delay Effect of Rainfall-induced Landslide Considering Air Entrapment

Rainfall-induced landslide is a typical geological disaster in the Three Gorges reservoir area. The air entrapment in the pores of soils has a hindrance to the infiltration of the slope. It is mainly reflected in the hydraulic hysteresis after rainfall and the decrease of the slope anti-sliding force. A method considered the air entrapment of the closed gas in soil particles’ pores is developed to study the time-delay effect and slope stability under the rainfall process. The Green-Ampt infiltration model is used to obtain the explicit analytical solution of the slope infiltration considering air entrapment. Moreover, the relationship between the safety factor, the rainfall duration, and the depth of the wetting front under the three rainfall conditions (qrain=12, 26, 51 mm/h) is discussed. The results show that the air entrapment causes a significant time-delay effect of the landslide, and the hydraulic hysteresis is the strongest under the condition of heavy rainfall (qrain= 51mm/h). The time-delay effect lasts longer than low rainfall and heavy rainfall when the rainfall intensity (qrain= 26 mm/h) is slightly greater than saturated hydraulic conductivity Ks. Parameter analysis shows that when air entrapment is considered, the smaller the slope angle and the effective internal friction angle, the more significant the air entrapment has on the slope stability; the smaller the effective cohesion, the longer the air resistance lasts. Finally, the application of the Bay Area landslide is consistent with the actual state of the landslide.

Null geodesics in five-dimensional Reissner–Nordström anti-de Sitter black holes

The study of the motion of photons around massive bodies is one of the most useful tools to find the geodesic structure associated with said gravitational source. In the present work, different possible paths projected in an invariant hyperplane are investigated, considering a five-dimensional Reissner–Nordström anti-de Sitter black hole. Also, we study some observational tests, such as the bending of light and the Shapiro time delay effect. Mainly, we found that the motion of photons follows the hippopede of a Proclus geodesic, which is a new type of trajectory of the second kind, the Limaçon of Pascal being their analog geodesic in four-dimensional Reissner–Nordström anti-de Sitter black hole.