Evaluation of the Lateral Vibration Response of Footbridges under Uncertainty Conditions

<p>The evaluation of the vibration performance of footbridges due to walking pedestrians is an issue of increasing importance in current footbridge design practice. The growing trend of slender footbridges with long spans and light materials has led to serviceability problems in lateral vibrations, which occur when the number of pedestrians reaches a “critical number”. Considering the mode of vibration in which the lateral instability is more likely to develop, the structural response depends on the modal characteristics of the footbridge; in particular, the natural frequency and the damping ratio. These modal parameters are stochastic variables, as it is not possible to determine them without a level of uncertainty. Thus, the purpose of this paper is to obtain the value of the lateral dynamic response of slender footbridges with a certain confidence level under uncertainty conditions. The uncertainties of those modal parameters are considered using a probabilistic approach. Both the natural frequency and the damping ratio are modelled as uncorrelated random variables that follow a predetermined probabilistic distribution function. Consequently, the structural response will also be described by a probabilistic distribution function, which can be estimated through Monte Carlo numerical simulations. As a result, the study allows the footbridge lateral response and the critical number of pedestrians to be calculated for different confidence levels and load scenarios, especially for crowd densities above the “critical number”.</p>

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.

Effect of altitude on the variation of pre-monsoon thunderstorm frequency during periods of higher sun spot number

The variation of pre-monsoon Thunder Storm Frequency (TSF) depending on the appearance of sun spot (S.S.) have been studied for the period 1955-80 for total 96 stations distributed allover India. For most of the stations we can identify a critical S.S. number in the neighbourhood of mean S.S. 140 above which a clear increasing or decreasing trend of mean TSF is observed with increase of S.S. number. It has also been seen that for almost all the stations having altitude greater than 280m, TSF increases with increase of S.S. number provided it is greater than the critical number.

$r$-Critical Numbers of Natural Intervals

The critical number $cr(r,n)$ of natural intervals $[r,n]$ was introduced by Herzog, Kaplan and Lev in 2014. The critical number $cr(r,n)$ is the smallest integer $t$ satisfying the following conditions: (i) every sequence of integers $S=\{r_1=r\leq r_2\leq \dotsb\leq r_k\}$ with $r_1+r_2 +\dotsb +r_k=n$ and $k\geq t$ has the following property: every integer between $r$ and $n-r$ can be written as a sum of distinct elements of $S$, and (ii) there exists $S$ with $k=t$, which satisfies that property. In this paper we study a variation of the critical number $cr(r,n)$ called the $r$-critical number $rcr(r,n)$. We determine the value of $rcr(r,n)$ for all $r,n$ satisfying $r\mid n$.

COVID 19 breakthrough infection risk: a simple physical model describing the dependence on antibody concentration

The empirically-observed dependence of SARS-CoV-2 vaccine efficacy on antibody concentration has a rational explanation in the statistics of binding of antibody to spike proteins on the virus surface: namely that the probability of protection is the probability of antibody binding to more than a critical number of the spike proteins protruding from the virus. The model is consistent with the observed antibody concentrations required to induce immunity.

Analysis of make-to-stock queues with general processing times and start-up and lost sales costs

We consider a make-to-stock environment with a single production unit that corresponds to a single machine or a line. Production and hence inventory are controlled by the two-critical-number policy. Production times are independent and identically distributed general random variables and demands are generated according to a stationary Poisson process. We model this production-inventory system as an M/G/1 make-to-stock queue. The main contribution of the study is to extend the control of make-to-stock literature by considering general production times, lost sales and fixed production costs at the same time. We characterize the long-run behaviour of the system and also propose a simple but very effective approximation to calculate the control parameters of the two-critical-number policy. An extensive numerical study exhibits the effects of the production time distribution and the system parameters on the policy control levels and average system cost.

Reported Changes in Adolescent Psychosocial Functioning during the COVID-19 Outbreak

What effect the outbreak of the COVID-19 pandemic has had on adolescents’ psychosocial functioning is currently unknown. Using the data of 1767 (50.2% female and 49.8 male) adolescents in Sweden, we discuss adolescents’ thoughts and behaviors around the COVID-19 outbreak, as well as reported changes in substance use, everyday life, relations, victimization, and mental health during the outbreak. Results showed that (a) the majority of adolescents have been complying with regulations from the government; (b) although most adolescents did not report changes in their psychosocial functioning, a critical number reported more substance use, conflict with parents, less time spent with peers, and poorer control over their everyday life; and (c) the majority of adolescents have experienced less victimization, yet poorer mental health, during the COVID-19 outbreak. Adolescent girls and adolescents in distance schooling were likely to report negative changes in their psychosocial functioning during the COVID-19 outbreak. Based on these findings, we suggest that society should pay close attention to changes in adolescents’ psychosocial functioning during times of crisis.

Repetitive mild traumatic brain injury causes synergistic effects on mortality

Repetitive mild TBI (rmTBI) events are common in the U.S. However, rmTBI is challenging to study and this contributes to a poor understanding of mechanistic bases for disease following these injuries. We used fruit flies (D. melanogaster) and a modified version of the high-impact trauma (HIT) method of TBI to assess the pattern of mortality observed after rmTBI. We found that the pattern of mortality was synergistic after a critical number of injuries, similar to that observed previously at more moderate levels of TBI severity. The identity of cellular and molecular factors which contribute to the synergistic effect on mortality remain unknown, but this model offers a platform for investigation into such factors.