The influence of human motion state on human-structure interaction

. Under pedestrian load, significant vibration and comfort problems are easy to arise for large-span low-frequency structures so that human-structure interaction should be considered in the design. However, different human motion states have different human modal parameters, which makes the design more difficult. The Spring-Mass-Damper (SMD) model is used to conduct numerical simulation experiments on 6 box beams with different fundamental frequencies in 4 different human motion states, based on which the dynamic characteristics of the structure under 30 working conditions are compared and analyzed. It is recommended to use the modal parameters of the standing human body in the vibration comfort design, and use the modal parameters of the human body at normal walking speed for the design of the low-frequency structure.


Introduction
Large-span, light and flexible structural systems are widely used in large public buildings such as theaters, stadiums, pedestrian bridges, and airports. Such structures have low fundamental frequency and damping ratio, and the interaction between people and structure is obvious, and significant vibration is prone to appear under pedestrian loads. The problems of structural failure, casualties and discomfort caused by human-induced vibration have become increasingly prominent, bringing economic losses and social impacts that cannot be underestimated. After the London Millennium Bridge incident [1] , the influence of human-structure interaction on structure has attracted much attention, and academia has launched a comprehensive research on this.
The research of human-structure interaction mainly revolves around two aspects (human-structure coupling system dynamic model and human dynamic parameters). Commonly used human-structure coupling system dynamic models include MD model, SMD model and MMSD model [2][3][4] . The MD model does not take into account the influence of human modal stiffness, so there are limitations in use. Both the SMD model and the MMSD model take into account the effects of human modal quality, modal stiffness and modal damping, and reflect the human-structure interaction reasonably, and are suitable to be dynamic models of the human-structure coupling system. Research shows that the calculation results of SMD model and MMSD model are basically the same, and the additional mass in the MMSD model has little effect on the dynamic response of the structure. Compared with MMSD, the application of SMD model is easier and more suitable for structural designers [4] . The determination of human body dynamics parameters is another important point in determining the humanstructure interaction. In recent years, researchers have tried to identify human dynamics parameters through the frequency response function expression of the humanstructure coupling system combined with the measured values. Y. Matsumotoa and M.J. Griffinb gave the dynamic parameters of a standing human body [2] , J. Alonso, A. Saez, et al. gave the dynamic parameters of pedestrians [5] .The pedestrian dynamic parameters given by F. Silva, H. Brito, et al. vary with pedestrian quality and stride frequency [6] . It can be seen that different human body motion states have different human body dynamic parameters so that the human-structure interaction is different, which causes difficulties for structural designers to use human body dynamic parameters.
In summary, when conducting human-structure mutual analysis, the SMD model is easy for structural designers to use and meets engineering accuracy requirements. However, the change of the human body motion state brings changes to the human body dynamic parameters, which makes the design more complicated, and the designer cannot determine how to use various parameters. In this regard, this article uses the dynamic parameters of the standing human body in literature [2] and the pedestrian dynamic parameters in literature [6], and employs the SMD model to analyze the impact of changes in the human body motion states on the humanstructure interaction in order to optimize the design.

Human-structure coupling system motion equations and pedestrian modal parameters
The human body is a mechanical system with mass, rigidity and damping, which will interact with the structure to form a human-structure coupling system. The SMD model simulates pedestrians as a spring-mass-damper system (as shown in Figure 1) and takes into account the influence of human modal stiffness, mass and damping on the structure, making it easy for structural designers to use by meeting engineering accuracy requirements. When the human body motion state changes, the pedestrian modal parameters change accordingly. To predict the influence of the human motion state on the human-structure interaction, the motion equation of the coupled system needs to be established first.

Pedestrian SMD model-structure coupling system motion equation
According to the principle of structural dynamics, the dynamic equation of the human-structure coupling system is: , are the modal mass, stiffness and damping of pedestrians respectively. Then the free vibration equation of the humanstructure coupling system is: Suppose the solution of equation (2) is Among them, is the eigenvalue, and is the eigenvector.
Substituting (3) into (2) to get: The eigenvalues obtained by the solution are complex numbers, and the corresponding eigenvectors are also complex numbers. The natural frequency and damping ratio of the system are:

Modal parameters of SMD model
The human body's motion state is different, so the modal parameters are different. When standing, the modal parameter has higher modal quality, stiffness and damping.

Human-structure interactions in different human motion states
This section uses ANSYS finite element software to establish a human-structure coupling system. Using the modal parameters of the pedestrian SMD model in the 4 human motion states in Table 1 and 6 large-span box beams with different fundamental frequencies, a total of 30 working conditions are compared. The crowd density takes 0.5 • [7] the maximum density at which pedestrians can walk freely. The calculated span of the box beam is 30m, and both ends are simply supported, using Q345 steel. The box beam section size is shown in Table 2, the finite element model of the human-structure coupling system in Figure 2, and the box beam section in Figure 3. The fundamental frequency of the structure is , and the frequency ratio is the natural frequency of the human body divided by the fundamental frequency of the structure. In order to explore the influence of changes in human motion state on the dynamic characteristics of the box beam. Firstly, modal analysis of H0.5-H1.5 box beams is implemented to obtain the dynamic characteristics of the empty bridge. Then, modal analysis of the box beam considering the human-structure interaction is carried out to compare changes in the dynamic characteristics of the structure. Pedestrian modal parameter is taken from Table   1 in 4 different motion states. Take the frequency change factor as the structural fundamental frequency of empty bridge divided by the structural fundamental frequency with pedestrian influence, and take the damping ratio change factor as the structural damping ratio of empty bridge divided by the structural damping ratio with pedestrian influence.  Figure 4 shows the comparison between the fundamental frequency of the structure with human-structure interaction and the fundamental frequency of the unloaded structure. The comparison shows that: (1) The standing human body has a great influence on the structural fundamental frequency, no matter whether it is highfrequency structure or low-frequency structure, and the human-structure interaction is obvious. Fundamental frequency of human-structure coupling system maintains around natural frequency of standing human body and will not lead to the reduction of low frequency. (2) The human body at the three walking speeds has roughly the same impact on the structural fundamental frequency, and has a greater impact on the low-frequency structure, which reduces the fundamental frequency of the low-frequency structure but has basically no effect on the structure with a higher frequency ( >3.6). Figure 5 shows the influence of the human body at different walking speeds on the structural fundamental frequency, and shows the influence of the walking human body on the structural fundamental frequency when the frequency ratio is different. The comparison shows: (1) When the frequency ratio >1.6, the frequency change factor is almost equal to 1. At this time, the influence of the walking human body on the structural fundamental frequency can be ignored. (2) The human body at normal walking speed ( ℎ =2.0 Hz) has the greatest impact on the structural fundamental frequency. When the frequency ratio ∈ 1,1.4 , the structural fundamental frequency is significantly reduced. Figure 6 shows the change rate of the structural damping ratio with human-structure interaction, and provides the influence of the human body in different motion states on the structural damping ratio. It can be seen from Figure 6 that: (1) The human body has roughly the same influence on the structural damping ratio in the four motion states. When the frequency ratio is smaller, the human body has a greater influence on the damping ratio. But with the increase of , the influence of the human body on the structural damping ratio is greatly reduced regardless of the state of motion. (2) When <1, regardless of the motion states, the structural damping ratio will always increase. (3) When >2, almost equals to 1. At this time, the influence of the human body on the structural damping ratio can be ignored.  The influence of the human body at different walking speeds on the fundamental frequency of the structure.

Conclusion
In this paper, theoretical analysis and numerical simulation are combined to conduct numerical simulation experiments on 6 box beams with different fundamental frequencies in 4 different human motion states. Based on this, the dynamic characteristics of the human-structure coupling system are studied in order to explore the influence of the human motion state on the human-