Study On Human-induced Vertical Structure Vibration With An Upgraded Bipedal Walking Model

With the rapid increase of the need for civil engineering structures and the wide application of low-weight-high-strength materials,the structural span is increasing,while the structural natural frequency is decreasing.When the structural natural frequency approaches the walking step frequency of pedestrians,the human-induced structure vibration problem happens because of human walking loads.It is harmful to the safety of pedestrians and influences the transit of people,which can lead to problems of structural safety and serviceability.Among the tri-axial walking loads,the vertical component has the greatest magnitude,which may result in severe vertical structural vibrations.The vertical walking loads are widely considered in the current design guidelines.The phenomenon of the pedestrian altering the walking gait according to the structural vibration is referred to as the human-structure interaction,which changes the walking loads.It is the key question for human-induced vibration analysis.The current design guidelines generally use walking loads measured on the ground,neglecting the effect of structural vibrations on walking loads.This will lead to an inaccurate estimate of the human-induced vibration response.To improve the current design methods that have not yet accounted for the effect of human-structure interaction,this thesis uses the bipedal walking model to interact with the structure.With the joined method of theoretical and experimental analysis,this thesis investigates human-induced vertical structural vibrations.The works are summarised as follows:1.Comparison and upgrade of the bipedal human walking models for walking on the ground.Although several bipedal walking models have been trialed for human-structure interaction analysis,they have not yet been systematically assessed,making it difficult to choose a proper simple model for different research questions.In this thesis,the range of key walking load parameters is solved for the step frequency,dynamic load factor of the first harmonic of walking loads（DLF₁）,and walking speed of different models’stable periodic gaits.The simulated range is compared with the measured range to assess the performance of the available models.The spring-loaded inverted pendulum（SLIP）is found to walk with a high step frequency and DLF₁,covering little space of the measured parameters.The roller foot increases the average walking speed of the SLIP model.However,the step frequency and DLF₁ remain overestimated.The leg damping enables the SLIP to achieve some of the measured step frequency and DLF₁,but the model available in the literature cannot walk at low step frequencies.Hence,a bipedal walking model is developed with the time-variant leg damper and spring,which covers the parameter space of the measured step frequency and DLF₁.2.Calibrate bipedal walking model parameters for a pedestrian walking on the ground.Measurements of human walking are done on the ground for 14 test subjects,whose kinematic and kinetic data are recorded.Characteristic leg force–length curves are constructed from the measured data.Linear fitting of the leg force–length curve yields the spring length and stiffness of the bipedal walking model.The measured parameters are fed into the bipedal walking model.Accurate modelling of the step frequency and DLF₁ is achieved by tuning the energy input,attack angle,and damping.Simultaneously,the vertical displacement of the centre of mass（Co M）and ground reaction force（GRF）of the bipedal walking model coincide with the measured data.Based on the experimentally calibrated bipedal walking model,regression functions are proposed for estimating model parameters.A method is established for tuning model parameters for accurate modelling of a pedestrian.When the body height and weight of a pedestrian,together with the target gait parameters,are given,this method achieves accurate modelling of the target step frequency and DLF₁.3.Analysis of the bipedal walking model for walking on the vertically vibrating surface.Treadmill walking tests are done on a vibrating platform to study the effect of vertical harmonic vibrations on the test subject’s walking gait.When the frequency of vertical vibration is adjacent to the test subject’s step frequency,“beating”effects of the vertical displacement of the Co M and GRF are observed from the collected data for each test subject.Multiple peaks appear in the spectra of vertical GRFs at frequencies that are not equal to the integral multiples of the step frequency.These phenomena indicate that vertical harmonic vibrations influence the walking gait and walking loads of pedestrians.The bipedal walking model is utilised to simulate walking on vibrating surfaces with the stable periodic gait solved on the ground.As a result,the bipedal walking model well simulates characteristic observations of the“beating”effect and peaks in the force spectrum.The vertical displacement of Co M and GRFs of the bipedal walking model are in line with the measured data,verifying the bipedal walking model for simulating human walking on the vibrating surface.4.Analysis of the upgraded bipedal walking model for walking on the vibrating structure.Human-induced vibration tests are done on a full-scale footbridge to collect the vibration responses,in combination with the walking loads on both the ground and bridge by using pressure insole sensors.Consequently,the time history of vertical GRFs measured on the bridge is found different from overground walking,when the structural vibration is severe.The trough between the two peak forces is increased,while the second peak force is decreased.Part of the DLF₁ measured on the bridge is higher than those obtained on the ground due to the effect of structural vibrations.This is harmful to structural safety.To simulate human walking on vibrating structures,a finite element（FE）implementation method of the bipedal walking model is proposed.The accuracy of the FE implementation method is verified by comparing its outcome with the analytical solution of the bipedal walking model.A practical method of analysing human-induced vibration has been established by introducing the bipedal walking model to the FE model of civil engineering structures.The simulated acceleration of the bridge is in line with the measured data with a similar peak acceleration response.In addition,the measured and simulated spectra of acceleration coincide with each other.