Study On Calculation And Optimal Control Of Human Walking Induced Structural Vibration

Structural vibration induced by human walking has increasingly become a highlighted problem which is companied by continuous springing up of long-span footbridges and floors. When such kind of structures are excited by pedestrian walking forces, they possibly vibrate too heavily to meet the requirements of serviceability limited state, and even seem at the risk of dynamic instability. Nowadays, researches carried out to tackle above problem mainly rest on aspects including pedestrian step forces, calculation of structural dynamic responses, evaluation methods and measurements of serviceability, vibration control, etc. Parts of research results have been adopted in serviceability design of long-span structures. However, a series of systematic design methods with remarkable efficiency and convenience will not exist until the stochastic characteristic of pedestrian step forces and complexity of structural multiple-modes vibration have been exhaustively studied.This paper concentrates on simple design methods for long-span footbridges and floors, including calculation of structural dynamic responses and optimal design of vibration-control system. Studies are carried out in following aspects:1. Monte Carlo simulation of pedestrian induced vibration. This paper has set up mathematical models of structural vertical and lateral vibration respectively. The lateral vibration model has taken into account the crowd-bridge dynamic interaction by introducing a theoretical negative damping model, which is derived from the social force model combining with a mechanical analysis of human gravity center locomotion on a swaying bridge. Based on a stochastic step force model represented by Fourier series, in which random parameters have been well studied, a series of simulation processes have been proposed to calculate structural dynamic responses under the condition of low-density crowd walking. Through simulation method, precise structural responses can be acquired as standards to testify the calculating efficiency of simple methods below.2. The response spectrum method. This part of paper begins with an introduction of a standard vibration system, which is derived from the structural motion equation through modal decomposition.30 series of typical vertical and lateral step force time history, which reflect the variability among pedestrians, are respectively constructed through uniform design. When each record of these step forces is exerted on standard vibration system, a structural response spectrum was acquired accordingly. And the envelope of 30 series of spectrum is defined as standard response spectrum. Based on the sensitivity analysis as for structual features, the correction factors are given so that the standard spectrum would be adaptable to structures with varying design requirements. The response spectrum method can fulfill structural response calculation with acceptable accuracy and relatively high efficiency.3. Dynamic amplifying factor method accounting for crowd-bridge lateral interaction. This part starts with the negative damping model derived in part 1. When correlations among structural modal vibrations have been specifically discussed, the expression of dynamic amplifying factor is deduced from structural motion equation. The corresponding response calculating method is proposed. This method shows similar precision and costs less computational efforts when compared with time history analysis.4. Optimal control of long-span floor vibration. This part focus on multiple tuned mass dampers (MTMD). Since floor vibration of multiple modes is simultaneously controlled by MTMD system, an optimization model with multiple objectives is set up. Based on this model, an advanced response surface method which consists of uniform design and ACE regression is proposed to construct the explicit relationship between control parameters of MTMD system and structural responses. This optimization method has considered the random characteristic of step force and the variability of control parameters among single TMDs in the MTMD system. Optimal results of proposed method are compared with those obtained through genetic-algorithm based method, showing that it is more reliable and efficient in computation.